Subgroups — C₃×#11717479 #72231621

Order 2400.

772 conjugacy classes of subgroups.

The subgroup lattice has 494 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×D₄×C₅⋊D₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#711	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×D₄×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#87886	C₂	1	2	yes	maximal, complemented
5	C₃×D₅×C₂²⋊D₅	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#6038	C₂	1	2	yes	maximal, complemented
7	C₃×#87879	C₂	1	2	yes	maximal, complemented
8	C₃×D₅×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#87874	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#87873	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#87871	C₂	1	1	yes	maximal, characteristic, complemented
12	#11717479	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅⋊D₅	C₂²	1	2	yes	complemented
14	C₂²×C₃×C₅×D₅	C₂²	1	2	yes	complemented
15	C₂×C₃×D₅²	C₂²	1	2	yes	complemented
16	C₃×C₅²×D₄	C₂²	1	1	yes	characteristic, complemented
17	C₃×C₂²⋊(C₅⋊D₅)	C₂²	1	2	yes	complemented
18	C₃×C₄⋊(C₅⋊D₅)	C₂²	1	1	yes	characteristic, complemented
19	C₃×C₄×C₅⋊D₅	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
21	C₃×C₅×C₂²⋊D₅	C₂²	1	2	yes	complemented
22	C₂×C₃×C₅×Dic₅	C₂²	1	2	yes	complemented
23	C₃×C₅×D₂₀	C₂²	1	1	yes	characteristic, complemented
24	C₃×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₄×C₅×D₅	C₂²	1	1	yes	characteristic, complemented
26	C₃×C₅×Dic₁₀	C₂²	1	1	yes	characteristic, complemented
27	C₃×#6039	C₂²	1	1	yes	characteristic, complemented
28	C₃×#6038	C₂²	1	2	yes	complemented
29	C₃×#6038	C₂²	1	1	yes	characteristic, complemented
30	C₃×#6038	C₂²	1	1	yes	characteristic, complemented
31	C₃×#6038	C₂²	1	2	yes	complemented
32	C₃×#6038	C₂²	1	2	yes	complemented
33	C₃×#6037	C₂²	1	1	yes	characteristic, complemented
34	C₃×#6036	C₂²	1	2	yes	complemented
35	C₃×D₅×Dic₅	C₂²	1	2	yes	complemented
36	C₃×#4149	—	5	1	no	maximal
37	C₃×#4144	—	5	1	no	maximal
38	D₄×C₅⋊D₅	C₂×C₃	1	1	yes	characteristic, complemented
39	C₅×#711	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×D₄×D₅	C₂×C₃	1	1	yes	characteristic, complemented
41	#87886	C₂×C₃	1	2	yes	complemented
42	D₅×C₂²⋊D₅	C₂×C₃	1	2	yes	complemented
43	C₂×#6038	C₂×C₃	1	2	yes	complemented
44	#87879	C₂×C₃	1	2	yes	complemented
45	D₅×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
46	#87874	C₂×C₃	1	1	yes	characteristic, complemented
47	#87873	C₂×C₃	1	1	yes	characteristic, complemented
48	#87871	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂²×C₃×C₅²	C₂³	1	2	yes	—
50	C₂×C₃×C₅⋊D₅	—	4	2	no	—
51	C₂×C₃×C₅⋊D₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅⋊D₅	C₂³	1	2	yes	—
53	C₂×C₃×C₅×D₅	—	4	2	no	—
54	C₂×C₃×C₅×D₅	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₅	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₅	C₂³	1	2	yes	—
57	C₃×D₅²	—	4	2	no	—
58	C₃×C₄×C₅²	C₂³	1	1	yes	characteristic
59	C₃×#1039	C₂³	1	1	yes	characteristic
60	C₃×C₅×Dic₅	C₂³	1	2	yes	—
61	C₃×C₅×Dic₅	C₂³	1	1	yes	characteristic
62	C₃×C₅×Dic₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×#41	—	5	1	no	—
64	C₂×C₃×C₅×D₄	—	5	1	no	—
65	C₂×C₃×C₂²⋊D₅	—	5	2	no	—
66	C₂×C₃×C₂²⋊D₅	—	5	2	no	—
67	C₃×#713	—	5	1	no	—
68	C₃×#713	—	5	1	no	—
69	C₃×#711	—	5	2	no	—
70	C₃×#711	—	5	1	no	—
71	C₃×#711	D₅	1	1	yes	characteristic, complemented
72	C₃×D₄×D₅	—	5	2	no	—
73	C₃×D₄×D₅	—	5	1	no	—
74	C₃×D₄×D₅	—	5	1	no	—
75	C₃×D₄×D₅	—	5	2	no	—
76	C₃×D₄×D₅	—	5	2	no	—
77	C₃×D₄×D₅	—	5	1	no	—
78	C₃×D₄×D₅	—	10	2	no	—
79	C₃×D₄×D₅	D₅	1	1	yes	characteristic, complemented
80	C₃×#709	—	5	2	no	—
81	C₃×#709	—	5	1	no	—
82	C₃×#709	—	5	1	no	—
83	C₃×#709	—	5	1	no	—
84	C₂×C₃×D₂₀	—	5	2	no	—
85	C₂×C₃×D₂₀	—	5	1	no	—
86	C₂²×C₅⋊D₅	C₂²×C₃	1	2	yes	complemented
87	C₂²×C₅×D₅	C₂²×C₃	1	2	yes	complemented
88	C₂×D₅²	C₂²×C₃	1	2	yes	complemented
89	C₅²×D₄	C₂²×C₃	1	1	yes	characteristic, complemented
90	C₂²⋊(C₅⋊D₅)	C₂²×C₃	1	2	yes	complemented
91	C₄⋊(C₅⋊D₅)	C₂²×C₃	1	1	yes	characteristic, complemented
92	C₄×C₅⋊D₅	C₂²×C₃	1	1	yes	characteristic, complemented
93	C₅×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
94	C₅×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
95	C₂×C₅×Dic₅	C₂²×C₃	1	2	yes	complemented
96	C₅×D₂₀	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₄×C₅×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
98	C₄×C₅×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
99	C₅×Dic₁₀	C₂²×C₃	1	1	yes	characteristic, complemented
100	#6039	C₂²×C₃	1	1	yes	characteristic, complemented
101	#6038	C₂²×C₃	1	2	yes	complemented
102	#6038	C₂²×C₃	1	1	yes	characteristic, complemented
103	#6038	C₂²×C₃	1	1	yes	characteristic, complemented
104	#6038	C₂²×C₃	1	2	yes	complemented
105	#6038	C₂²×C₃	1	2	yes	complemented
106	#6037	C₂²×C₃	1	1	yes	characteristic, complemented
107	#6036	C₂²×C₃	1	2	yes	complemented
108	D₅×Dic₅	C₂²×C₃	1	2	yes	complemented
109	#4149	—	5	1	no	—
110	#4144	—	5	1	no	—
111	C₂×C₃×C₅²	—	2	2	no	—
112	C₂×C₃×C₅²	C₂⁴	1	1	yes	characteristic
113	C₃×C₅⋊D₅	—	2	1	no	—
114	C₃×C₅⋊D₅	—	2	2	no	—
115	C₃×C₅×D₅	—	2	1	no	—
116	C₃×C₅×D₅	—	2	2	no	—
117	C₃×C₅×D₅	—	2	1	no	—
118	C₂³×C₃×C₅	—	5	2	no	—
119	C₂²×C₃×D₅	—	5	2	no	—
120	C₂²×C₃×D₅	—	5	2	no	—
121	C₂²×C₃×D₅	—	5	2	no	—
122	C₂²×C₃×D₅	—	5	2	no	—
123	C₂²×C₃×D₅	—	10	4	no	—
124	C₂²×C₃×D₅	C₂×D₅	1	2	yes	complemented
125	C₃×C₅×Q₈	—	5	1	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	5	2	no	—
128	C₃×C₅×D₄	—	5	2	no	—
129	C₃×C₅×D₄	—	5	1	no	—
130	C₃×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
131	C₃×C₅×D₄	C₂×D₅	1	1	yes	characteristic, complemented
132	C₂×C₃×C₄×C₅	—	5	2	no	—
133	C₂×C₃×C₄×C₅	—	5	1	no	—
134	C₂×C₃×C₄×C₅	—	5	1	no	—
135	C₃×C₂²⋊D₅	—	5	2	no	—
136	C₃×C₂²⋊D₅	—	5	2	no	—
137	C₃×C₂²⋊D₅	—	5	1	no	—
138	C₃×C₂²⋊D₅	—	5	1	no	—
139	C₃×C₂²⋊D₅	—	5	1	no	—
140	C₃×C₂²⋊D₅	—	5	1	no	—
141	C₃×C₂²⋊D₅	—	5	2	no	—
142	C₃×C₂²⋊D₅	—	5	2	no	—
143	C₃×C₂²⋊D₅	—	5	2	no	—
144	C₃×C₂²⋊D₅	—	10	4	no	—
145	C₃×C₂²⋊D₅	C₂×D₅	1	2	yes	complemented
146	C₃×C₂²⋊D₅	C₂×D₅	1	2	yes	complemented
147	C₂×C₃×Dic₅	—	5	2	no	—
148	C₂×C₃×Dic₅	C₂×D₅	1	2	yes	complemented
149	C₃×D₂₀	—	5	2	no	—
150	C₃×D₂₀	—	5	1	no	—
151	C₃×D₂₀	—	5	2	no	—
152	C₃×D₂₀	—	5	2	no	—
153	C₃×D₂₀	—	5	1	no	—
154	C₃×D₂₀	—	5	1	no	—
155	C₃×D₂₀	—	5	1	no	—
156	C₃×D₂₀	—	10	2	no	—
157	C₃×D₂₀	C₂×D₅	1	1	yes	characteristic, complemented
158	C₃×C₄×D₅	—	5	2	no	—
159	C₃×C₄×D₅	—	5	1	no	—
160	C₃×C₄×D₅	—	5	1	no	—
161	C₃×C₄×D₅	—	5	2	no	—
162	C₃×C₄×D₅	—	5	2	no	—
163	C₃×C₄×D₅	—	10	2	no	—
164	C₃×C₄×D₅	C₂×D₅	1	1	yes	characteristic, complemented
165	C₃×C₄×D₅	C₂×D₅	1	1	yes	characteristic, complemented
166	C₃×Dic₁₀	—	5	1	no	—
167	C₃×Dic₁₀	—	5	1	no	—
168	C₃×Dic₁₀	C₂×D₅	1	1	yes	characteristic, complemented
169	C₂²×C₅²	C₂³×C₃	1	2	yes	—
170	C₂×C₅⋊D₅	—	4	2	no	—
171	C₂×C₅⋊D₅	C₂³×C₃	1	2	yes	—
172	C₂×C₅⋊D₅	C₂³×C₃	1	1	yes	characteristic
173	C₂×C₅×D₅	—	4	2	no	—
174	C₂×C₅×D₅	C₂³×C₃	1	2	yes	—
175	C₂×C₅×D₅	C₂³×C₃	1	1	yes	characteristic
176	C₂×C₅×D₅	C₂³×C₃	1	1	yes	characteristic
177	D₅²	—	4	2	no	—
178	C₄×C₅²	C₂³×C₃	1	1	yes	characteristic
179	#1039	C₂³×C₃	1	1	yes	characteristic
180	C₅×Dic₅	C₂³×C₃	1	2	yes	—
181	C₅×Dic₅	C₂³×C₃	1	1	yes	characteristic
182	C₅×Dic₅	C₂³×C₃	1	1	yes	characteristic
183	C₃×H(5,𝔽₂)	—	25	1	no	Hall
184	C₅×#41	—	5	1	no	—
185	C₂×C₅×D₄	—	5	1	no	—
186	C₂×C₂²⋊D₅	—	5	2	no	—
187	C₂×C₂²⋊D₅	—	5	2	no	—
188	#713	—	5	1	no	—
189	#713	—	5	1	no	—
190	#711	—	5	2	no	—
191	#711	—	5	1	no	—
192	#711	C₃×D₅	1	1	yes	characteristic, complemented
193	D₄×D₅	—	5	2	no	—
194	D₄×D₅	—	5	1	no	—
195	D₄×D₅	—	5	1	no	—
196	D₄×D₅	—	5	2	no	—
197	D₄×D₅	—	5	2	no	—
198	D₄×D₅	—	5	1	no	—
199	D₄×D₅	—	10	2	no	—
200	D₄×D₅	C₃×D₅	1	1	yes	characteristic, complemented
201	#709	—	5	2	no	—
202	#709	—	5	1	no	—
203	#709	—	5	1	no	—
204	#709	—	5	1	no	—
205	C₂×D₂₀	—	5	2	no	—
206	C₂×D₂₀	—	5	1	no	—
207	C₃×C₅²	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
208	C₂²×C₃×C₅	—	2	4	no	—
209	C₂²×C₃×C₅	—	5	2	no	—
210	C₂²×C₃×C₅	—	5	1	no	—
211	C₂²×C₃×C₅	—	5	1	no	—
212	C₂²×C₃×C₅	—	20	2	no	—
213	C₂²×C₃×C₅	C₂²×D₅	1	2	yes	—
214	C₂²×C₃×C₅	C₂²×D₅	1	2	yes	—
215	C₂×C₃×D₅	—	4	2	no	—
216	C₂×C₃×D₅	—	5	1	no	—
217	C₂×C₃×D₅	—	5	2	no	—
218	C₂×C₃×D₅	—	5	1	no	—
219	C₂×C₃×D₅	—	5	2	no	—
220	C₂×C₃×D₅	—	10	2	no	—
221	C₂×C₃×D₅	—	10	4	no	—
222	C₂×C₃×D₅	—	20	2	no	—
223	C₂×C₃×D₅	—	20	2	no	—
224	C₂×C₃×D₅	—	20	2	no	—
225	C₂×C₃×D₅	—	20	2	no	—
226	C₂×C₃×D₅	—	20	4	no	—
227	C₂×C₃×D₅	—	20	4	no	—
228	C₂×C₃×D₅	C₂²×D₅	1	2	yes	—
229	C₂×C₃×D₅	C₂²×D₅	1	1	yes	characteristic
230	C₂×C₃×D₅	C₂²×D₅	1	1	yes	characteristic
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	5	1	no	—
233	C₃×C₄×C₅	—	5	1	no	—
234	C₃×C₄×C₅	—	5	2	no	—
235	C₃×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
236	C₃×C₄×C₅	C₂²×D₅	1	1	yes	characteristic
237	C₃×Dic₅	—	5	1	no	—
238	C₃×Dic₅	—	5	1	no	—
239	C₃×Dic₅	—	10	2	no	—
240	C₃×Dic₅	C₂²×D₅	1	1	yes	characteristic
241	C₃×Dic₅	C₂²×D₅	1	1	yes	characteristic
242	C₃×Dic₅	C₂²×D₅	1	2	yes	—
243	C₂×C₅²	—	2	2	no	—
244	C₂×C₅²	C₂⁴×C₃	1	1	yes	characteristic
245	C₅⋊D₅	—	2	1	no	—
246	C₅⋊D₅	—	2	2	no	—
247	C₅×D₅	—	2	1	no	—
248	C₅×D₅	—	2	2	no	—
249	C₅×D₅	—	2	1	no	—
250	C₃×#41	—	5	1	no	—
251	C₃×#41	—	25	1	no	—
252	C₃×#41	—	25	2	no	—
253	C₃×#41	—	25	1	no	—
254	C₃×#41	—	25	1	no	—
255	C₂×C₃×D₄	—	5	1	no	—
256	C₂×C₃×D₄	—	25	1	no	—
257	C₂×C₃×D₄	—	25	2	no	—
258	C₂×C₃×D₄	—	25	2	no	—
259	C₂×C₃×D₄	—	25	2	no	—
260	C₂×C₃×D₄	—	25	1	no	—
261	C₂³×C₅	—	5	2	no	—
262	C₂²×D₅	—	5	2	no	—
263	C₂²×D₅	—	5	2	no	—
264	C₂²×D₅	—	5	2	no	—
265	C₂²×D₅	—	5	2	no	—
266	C₂²×D₅	—	10	4	no	—
267	C₂²×D₅	C₂×C₃×D₅	1	2	yes	complemented
268	C₅×Q₈	—	5	1	no	—
269	C₅×D₄	—	2	2	no	—
270	C₅×D₄	—	5	2	no	—
271	C₅×D₄	—	5	2	no	—
272	C₅×D₄	—	5	1	no	—
273	C₅×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
274	C₅×D₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
275	C₂×C₄×C₅	—	5	2	no	—
276	C₂×C₄×C₅	—	5	1	no	—
277	C₂×C₄×C₅	—	5	1	no	—
278	C₂²⋊D₅	—	5	2	no	—
279	C₂²⋊D₅	—	5	2	no	—
280	C₂²⋊D₅	—	5	1	no	—
281	C₂²⋊D₅	—	5	1	no	—
282	C₂²⋊D₅	—	5	1	no	—
283	C₂²⋊D₅	—	5	1	no	—
284	C₂²⋊D₅	—	5	2	no	—
285	C₂²⋊D₅	—	5	2	no	—
286	C₂²⋊D₅	—	5	2	no	—
287	C₂²⋊D₅	—	10	4	no	—
288	C₂²⋊D₅	C₂×C₃×D₅	1	2	yes	complemented
289	C₂²⋊D₅	C₂×C₃×D₅	1	2	yes	complemented
290	C₂×Dic₅	—	5	2	no	—
291	C₂×Dic₅	C₂×C₃×D₅	1	2	yes	complemented
292	D₂₀	—	5	2	no	—
293	D₂₀	—	5	1	no	—
294	D₂₀	—	5	2	no	—
295	D₂₀	—	5	2	no	—
296	D₂₀	—	5	1	no	—
297	D₂₀	—	5	1	no	—
298	D₂₀	—	5	1	no	—
299	D₂₀	—	10	2	no	—
300	D₂₀	C₂×C₃×D₅	1	1	yes	characteristic, complemented
301	C₄×D₅	—	5	2	no	—
302	C₄×D₅	—	5	1	no	—
303	C₄×D₅	—	5	1	no	—
304	C₄×D₅	—	5	2	no	—
305	C₄×D₅	—	5	2	no	—
306	C₄×D₅	—	10	2	no	—
307	C₄×D₅	C₂×C₃×D₅	1	1	yes	characteristic, complemented
308	C₄×D₅	C₂×C₃×D₅	1	1	yes	characteristic, complemented
309	Dic₁₀	—	5	1	no	—
310	Dic₁₀	—	5	1	no	—
311	Dic₁₀	C₂×C₃×D₅	1	1	yes	characteristic, complemented
312	H(5,𝔽₂)	—	25	1	no	Sylow
313	C₂×C₃×C₅	—	2	2	no	—
314	C₂×C₃×C₅	—	2	2	no	—
315	C₂×C₃×C₅	—	2	2	no	—
316	C₂×C₃×C₅	—	4	4	no	—
317	C₂×C₃×C₅	—	10	1	no	—
318	C₂×C₃×C₅	—	10	2	no	—
319	C₂×C₃×C₅	—	10	1	no	—
320	C₂×C₃×C₅	C₂³×D₅	1	1	yes	characteristic
321	C₂×C₃×C₅	C₂³×D₅	1	1	yes	characteristic
322	C₃×D₅	—	2	1	no	—
323	C₃×D₅	—	2	2	no	—
324	C₃×D₅	—	2	1	no	—
325	C₃×D₅	—	10	2	no	—
326	C₃×D₅	—	10	2	no	—
327	C₃×D₅	—	10	1	no	—
328	C₃×D₅	—	10	2	no	—
329	C₃×D₅	—	10	1	no	—
330	C₃×D₅	—	10	2	no	—
331	C₃×D₅	—	20	4	no	—
332	C₅²	C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
333	C₂³×C₃	—	5	2	no	—
334	C₂³×C₃	—	25	2	no	—
335	C₂³×C₃	—	25	2	no	—
336	C₃×Q₈	—	5	1	no	—
337	C₃×Q₈	—	25	1	no	—
338	C₃×D₄	—	5	2	no	—
339	C₃×D₄	—	5	2	no	—
340	C₃×D₄	—	5	1	no	—
341	C₃×D₄	—	25	1	no	—
342	C₃×D₄	—	25	2	no	—
343	C₃×D₄	—	25	1	no	—
344	C₃×D₄	—	25	2	no	—
345	C₃×D₄	—	25	2	no	—
346	C₃×D₄	—	25	1	no	—
347	C₃×D₄	—	25	2	no	—
348	C₃×D₄	—	25	1	no	—
349	C₃×D₄	D₅²	1	1	yes	characteristic, complemented
350	C₂×C₃×C₄	—	5	2	no	—
351	C₂×C₃×C₄	—	5	1	no	—
352	C₂×C₃×C₄	—	5	1	no	—
353	C₂×C₃×C₄	—	25	2	no	—
354	C₂×C₃×C₄	—	25	2	no	—
355	C₂×C₃×C₄	—	25	1	no	—
356	C₂²×C₅	—	2	4	no	—
357	C₂²×C₅	—	5	2	no	—
358	C₂²×C₅	—	5	1	no	—
359	C₂²×C₅	—	5	1	no	—
360	C₂²×C₅	—	20	2	no	—
361	C₂²×C₅	C₂²×C₃×D₅	1	2	yes	—
362	C₂²×C₅	C₂²×C₃×D₅	1	2	yes	—
363	C₂×D₅	—	4	2	no	—
364	C₂×D₅	—	5	2	no	—
365	C₂×D₅	—	5	1	no	—
366	C₂×D₅	—	5	2	no	—
367	C₂×D₅	—	5	1	no	—
368	C₂×D₅	—	10	2	no	—
369	C₂×D₅	—	10	4	no	—
370	C₂×D₅	—	20	2	no	—
371	C₂×D₅	—	20	2	no	—
372	C₂×D₅	—	20	2	no	—
373	C₂×D₅	—	20	2	no	—
374	C₂×D₅	—	20	4	no	—
375	C₂×D₅	—	20	4	no	—
376	C₂×D₅	C₂²×C₃×D₅	1	2	yes	—
377	C₂×D₅	C₂²×C₃×D₅	1	1	yes	characteristic
378	C₂×D₅	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	5	1	no	—
381	C₄×C₅	—	5	1	no	—
382	C₄×C₅	—	5	2	no	—
383	C₄×C₅	C₂²×C₃×D₅	1	1	yes	characteristic
384	C₄×C₅	C₂²×C₃×D₅	1	1	yes	characteristic
385	Dic₅	—	5	1	no	—
386	Dic₅	—	5	1	no	—
387	Dic₅	—	10	2	no	—
388	Dic₅	C₂²×C₃×D₅	1	1	yes	characteristic
389	Dic₅	C₂²×C₃×D₅	1	1	yes	characteristic
390	Dic₅	C₂²×C₃×D₅	1	2	yes	—
391	#41	—	5	1	no	—
392	#41	—	25	1	no	—
393	#41	—	25	2	no	—
394	#41	—	25	1	no	—
395	#41	—	25	1	no	—
396	C₂×D₄	—	5	1	no	—
397	C₂×D₄	—	25	1	no	—
398	C₂×D₄	—	25	2	no	—
399	C₂×D₄	—	25	2	no	—
400	C₂×D₄	—	25	2	no	—
401	C₂×D₄	—	25	1	no	—
402	C₃×C₅	—	2	2	no	—
403	C₃×C₅	#4144	1	1	yes	characteristic, complemented
404	C₃×C₅	#4149	1	1	yes	characteristic, complemented
405	C₂²×C₃	—	5	1	no	—
406	C₂²×C₃	—	5	1	no	—
407	C₂²×C₃	—	5	2	no	—
408	C₂²×C₃	—	20	2	no	—
409	C₂²×C₃	—	25	1	no	—
410	C₂²×C₃	—	25	2	no	—
411	C₂²×C₃	—	100	2	no	—
412	C₂²×C₃	—	100	2	no	—
413	C₂²×C₃	C₂×D₅²	1	2	yes	—
414	C₃×C₄	—	5	1	no	—
415	C₃×C₄	—	5	1	no	—
416	C₃×C₄	—	5	2	no	—
417	C₃×C₄	—	25	1	no	—
418	C₃×C₄	C₂×D₅²	1	1	yes	characteristic
419	C₂×C₅	—	2	2	no	—
420	C₂×C₅	—	2	2	no	—
421	C₂×C₅	—	2	2	no	—
422	C₂×C₅	—	4	4	no	—
423	C₂×C₅	—	10	1	no	—
424	C₂×C₅	—	10	2	no	—
425	C₂×C₅	—	10	1	no	—
426	C₂×C₅	C₂³×C₃×D₅	1	1	yes	characteristic
427	C₂×C₅	C₂³×C₃×D₅	1	1	yes	characteristic
428	D₅	—	2	1	no	—
429	D₅	—	2	2	no	—
430	D₅	—	2	1	no	—
431	D₅	—	10	2	no	—
432	D₅	—	10	2	no	—
433	D₅	—	10	1	no	—
434	D₅	—	10	2	no	—
435	D₅	—	10	1	no	—
436	D₅	—	10	2	no	—
437	D₅	—	20	4	no	—
438	C₂³	—	5	2	no	—
439	C₂³	—	25	2	no	—
440	C₂³	—	25	2	no	—
441	Q₈	—	5	1	no	—
442	Q₈	—	25	1	no	—
443	D₄	—	5	2	no	—
444	D₄	—	5	2	no	—
445	D₄	—	5	1	no	—
446	D₄	—	25	1	no	—
447	D₄	—	25	2	no	—
448	D₄	—	25	1	no	—
449	D₄	—	25	2	no	—
450	D₄	—	25	2	no	—
451	D₄	—	25	1	no	—
452	D₄	—	25	2	no	—
453	D₄	—	25	1	no	—
454	D₄	C₃×D₅²	1	1	yes	characteristic, complemented
455	C₂×C₄	—	5	2	no	—
456	C₂×C₄	—	5	1	no	—
457	C₂×C₄	—	5	1	no	—
458	C₂×C₄	—	25	2	no	—
459	C₂×C₄	—	25	2	no	—
460	C₂×C₄	—	25	1	no	—
461	C₂×C₃	—	2	2	no	—
462	C₂×C₃	—	10	1	no	—
463	C₂×C₃	—	10	2	no	—
464	C₂×C₃	—	10	1	no	—
465	C₂×C₃	—	50	1	no	—
466	C₂×C₃	—	50	2	no	—
467	C₂×C₃	C₂²×D₅²	1	1	yes	characteristic
468	C₅	—	2	2	no	—
469	C₅	C₃×#4144	1	1	yes	characteristic, complemented
470	C₅	C₃×#4149	1	1	yes	characteristic, complemented
471	C₂²	—	5	1	no	—
472	C₂²	—	5	1	no	—
473	C₂²	—	5	2	no	—
474	C₂²	—	20	2	no	—
475	C₂²	—	25	1	no	—
476	C₂²	—	25	2	no	—
477	C₂²	—	100	2	no	—
478	C₂²	—	100	2	no	—
479	C₂²	C₂×C₃×D₅²	1	2	yes	—
480	C₄	—	5	1	no	—
481	C₄	—	5	1	no	—
482	C₄	—	5	2	no	—
483	C₄	—	25	1	no	—
484	C₄	C₂×C₃×D₅²	1	1	yes	characteristic
485	C₃	#11717479	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	2	2	no	—
487	C₂	—	10	1	no	—
488	C₂	—	10	2	no	—
489	C₂	—	10	1	no	—
490	C₂	—	50	1	no	—
491	C₂	—	50	2	no	—
492	C₂	C₂²×C₃×D₅²	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	C₂²×D₅²
commutator, cosocle	C₂×C₅²	C₂⁴×C₃
Frattini	C₂	C₂²×C₃×D₅²
Fitting	C₃×C₅²×D₄	C₂²
socle	C₂×C₃×C₅²	C₂⁴
hypercenter	C₃×D₄	D₅²
hypocenter	C₅²	C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₅² ▷ C₅²
UCS	C₁ ◁ C₂×C₃ ◁ C₃×D₄

Complements

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

N	H ≅ G/N	type
1. C₃×D₄×C₅⋊D₅	C₂	semidirect
2. C₃×C₅×#711	C₂	semidirect
3. C₃×C₅×D₄×D₅	C₂	semidirect
4. C₃×#87886	C₂	semidirect
5. C₃×D₅×C₂²⋊D₅	C₂	semidirect
6. C₂×C₃×#6038	C₂	semidirect
7. C₃×#87879	C₂	semidirect
8. C₃×D₅×D₂₀	C₂	semidirect
9. C₃×#87874	C₂	semidirect
10. C₃×#87873	C₂	semidirect
11. C₃×#87871	C₂	semidirect
12. #11717479	C₃	direct (N × H)
13. C₂²×C₃×C₅⋊D₅	C₂²	semidirect
14. C₂²×C₃×C₅×D₅	C₂²	semidirect
15. C₂×C₃×D₅²	C₂²	semidirect
16. C₃×C₅²×D₄	C₂²	semidirect
17. C₃×C₂²⋊(C₅⋊D₅)	C₂²	semidirect
18. C₃×C₄⋊(C₅⋊D₅)	C₂²	semidirect
19. C₃×C₄×C₅⋊D₅	C₂²	semidirect
20. C₃×C₅×C₂²⋊D₅	C₂²	semidirect
21. C₃×C₅×C₂²⋊D₅	C₂²	semidirect
22. C₂×C₃×C₅×Dic₅	C₂²	semidirect
23. C₃×C₅×D₂₀	C₂²	semidirect
24. C₃×C₄×C₅×D₅	C₂²	semidirect
25. C₃×C₄×C₅×D₅	C₂²	semidirect
26. C₃×C₅×Dic₁₀	C₂²	semidirect
27. C₃×#6039	C₂²	semidirect
28. C₃×#6038	C₂²	semidirect
29. C₃×#6038	C₂²	semidirect
30. C₃×#6038	C₂²	semidirect
31. C₃×#6038	C₂²	semidirect
32. C₃×#6038	C₂²	semidirect
33. C₃×#6037	C₂²	semidirect
34. C₃×#6036	C₂²	semidirect
35. C₃×D₅×Dic₅	C₂²	semidirect
38. D₄×C₅⋊D₅	C₂×C₃	semidirect
39. C₅×#711	C₂×C₃	semidirect
40. C₅×D₄×D₅	C₂×C₃	semidirect
41. #87886	C₂×C₃	semidirect
42. D₅×C₂²⋊D₅	C₂×C₃	semidirect
43. C₂×#6038	C₂×C₃	semidirect
44. #87879	C₂×C₃	semidirect
45. D₅×D₂₀	C₂×C₃	semidirect
46. #87874	C₂×C₃	semidirect
47. #87873	C₂×C₃	semidirect
48. #87871	C₂×C₃	semidirect
71. C₃×#711	D₅	semidirect
79. C₃×D₄×D₅	D₅	semidirect
86. C₂²×C₅⋊D₅	C₂²×C₃	semidirect
87. C₂²×C₅×D₅	C₂²×C₃	semidirect
88. C₂×D₅²	C₂²×C₃	semidirect
89. C₅²×D₄	C₂²×C₃	semidirect
90. C₂²⋊(C₅⋊D₅)	C₂²×C₃	semidirect
91. C₄⋊(C₅⋊D₅)	C₂²×C₃	semidirect
92. C₄×C₅⋊D₅	C₂²×C₃	semidirect
93. C₅×C₂²⋊D₅	C₂²×C₃	semidirect
94. C₅×C₂²⋊D₅	C₂²×C₃	semidirect
95. C₂×C₅×Dic₅	C₂²×C₃	semidirect
96. C₅×D₂₀	C₂²×C₃	semidirect
97. C₄×C₅×D₅	C₂²×C₃	semidirect
98. C₄×C₅×D₅	C₂²×C₃	semidirect
99. C₅×Dic₁₀	C₂²×C₃	semidirect
100. #6039	C₂²×C₃	semidirect
101. #6038	C₂²×C₃	semidirect
102. #6038	C₂²×C₃	semidirect
103. #6038	C₂²×C₃	semidirect
104. #6038	C₂²×C₃	semidirect
105. #6038	C₂²×C₃	semidirect
106. #6037	C₂²×C₃	semidirect
107. #6036	C₂²×C₃	semidirect
108. D₅×Dic₅	C₂²×C₃	semidirect
124. C₂²×C₃×D₅	C₂×D₅	semidirect
130. C₃×C₅×D₄	C₂×D₅	semidirect
131. C₃×C₅×D₄	C₂×D₅	semidirect
145. C₃×C₂²⋊D₅	C₂×D₅	semidirect
146. C₃×C₂²⋊D₅	C₂×D₅	semidirect
148. C₂×C₃×Dic₅	C₂×D₅	semidirect
157. C₃×D₂₀	C₂×D₅	semidirect
164. C₃×C₄×D₅	C₂×D₅	semidirect
165. C₃×C₄×D₅	C₂×D₅	semidirect
168. C₃×Dic₁₀	C₂×D₅	semidirect
192. #711	C₃×D₅	semidirect
200. D₄×D₅	C₃×D₅	semidirect
207. C₃×C₅²	H(5,𝔽₂)	semidirect
267. C₂²×D₅	C₂×C₃×D₅	semidirect
273. C₅×D₄	C₂×C₃×D₅	semidirect
274. C₅×D₄	C₂×C₃×D₅	semidirect
288. C₂²⋊D₅	C₂×C₃×D₅	semidirect
289. C₂²⋊D₅	C₂×C₃×D₅	semidirect
291. C₂×Dic₅	C₂×C₃×D₅	semidirect
300. D₂₀	C₂×C₃×D₅	semidirect
307. C₄×D₅	C₂×C₃×D₅	semidirect
308. C₄×D₅	C₂×C₃×D₅	semidirect
311. Dic₁₀	C₂×C₃×D₅	semidirect
332. C₅²	C₃×H(5,𝔽₂)	semidirect
349. C₃×D₄	D₅²	semidirect
403. C₃×C₅	#4144	semidirect
404. C₃×C₅	#4149	semidirect
454. D₄	C₃×D₅²	semidirect
469. C₅	C₃×#4144	semidirect
470. C₅	C₃×#4149	semidirect
485. C₃	#11717479	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×D₄×C₅⋊D₅	2
C₃×C₅×#711	2
C₃×C₅×D₄×D₅	2
C₃×#87886	2
C₃×D₅×C₂²⋊D₅	2
C₂×C₃×#6038	2
C₃×#87879	2
C₃×D₅×D₂₀	2
C₃×#87874	2
C₃×#87873	2
C₃×#87871	2
#11717479	3
C₃×#4149	5
C₃×#4144	5

Subgroups — C3×#11717479 #72231621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#11717479 #72231621