Subgroups — C₅×#74006 #14322985

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5211	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4989	C₂	1	2	yes	maximal, complemented
5	C₅×#4978	C₂	1	2	yes	maximal, complemented
6	C₅×#4956	C₂	1	2	yes	maximal
7	C₅×#4945	C₂	1	2	yes	maximal, complemented
8	C₅×#4666	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₃×#95	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4651	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4650	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2318	—	3	1	no	maximal, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₅×#217	C₂²	1	2	yes	—
20	C₂×C₅×#217	C₂²	1	1	yes	characteristic
21	C₄×C₅×#67	C₄	1	8	yes	complemented
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
27	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
31	C₅×C₃⋊#95	C₂²	1	2	yes	—
32	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
33	C₅×C₃⋊#95	C₂²	1	2	yes	—
34	C₅×C₃⋊#95	C₂²	1	2	yes	—
35	C₅×C₃⋊#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	#74006	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
38	C₂×C₄×C₅×D₄	—	3	1	no	—
39	C₅×#388	—	3	2	no	—
40	C₅×#387	—	3	2	no	—
41	C₅×#386	—	3	2	no	—
42	C₅×#385	—	3	2	no	—
43	C₅×#383	—	3	1	no	—
44	C₅×#382	—	3	1	no	—
45	C₅×#381	—	3	1	no	—
46	C₅×#380	D₃	1	1	yes	characteristic, complemented
47	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
48	C₂×C₅×#95	—	3	1	no	—
49	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
50	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	—	4	2	no	—
52	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	—	2	4	no	—
58	C₂×C₅×#67	C₂×C₄	1	4	yes	—
59	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
60	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
61	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
62	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
63	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
64	C₂×C₄×C₅×D₃	—	2	4	no	—
65	C₂×C₄×C₅×D₃	—	4	2	no	—
66	C₂×C₄×C₅×D₃	—	4	2	no	—
67	C₂×C₄×C₅×D₃	—	4	2	no	—
68	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
69	C₃×C₅×C₄⋊C₄	—	4	2	no	—
70	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
71	C₅×#217	—	4	2	no	—
72	C₅×#217	C₂×C₄	1	4	yes	complemented
73	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
74	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
75	C₅×Dic₃⋊C₄	—	4	2	no	—
76	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
77	C₄×C₅×Dic₃	—	4	2	no	—
78	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
79	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
80	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
81	#5211	C₂×C₅	1	1	yes	characteristic, complemented
82	#4989	C₂×C₅	1	2	yes	complemented
83	#4978	C₂×C₅	1	2	yes	complemented
84	#4956	C₂×C₅	1	2	yes	—
85	#4945	C₂×C₅	1	2	yes	complemented
86	#4666	C₂×C₅	1	1	yes	characteristic, complemented
87	D₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
88	#4651	C₂×C₅	1	1	yes	characteristic, complemented
89	#4650	C₂×C₅	1	1	yes	characteristic, complemented
90	C₂²×C₅×D₄	—	3	1	no	—
91	C₂³×C₄×C₅	—	3	1	no	—
92	C₂³×C₄×C₅	—	3	2	no	—
93	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
94	C₄×C₅×D₄	—	3	8	no	—
95	C₂×C₅×C₄⋊C₄	—	3	1	no	—
96	C₂×C₅×C₄⋊C₄	—	3	2	no	—
97	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
98	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
99	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
100	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
101	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
102	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
103	C₂×C₄²×C₅	—	3	1	no	—
104	C₂×C₄²×C₅	—	3	2	no	—
105	C₅×#95	—	3	1	no	—
106	C₅×#95	—	3	2	no	—
107	C₅×#95	—	3	1	no	—
108	C₅×#95	—	3	2	no	—
109	C₅×#95	—	3	2	no	—
110	C₅×#95	—	3	2	no	—
111	C₅×#95	—	3	2	no	—
112	C₅×#95	C₂×D₃	1	1	yes	characteristic
113	C₅×#95	C₂×D₃	1	1	yes	characteristic
114	#2318	—	3	1	no	Sylow
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	1	no	—
118	C₂³×C₃×C₅	—	2	1	no	—
119	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
120	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
121	C₂²×C₅×D₃	—	2	2	no	—
122	C₂²×C₅×D₃	—	2	1	no	—
123	C₂²×C₅×D₃	—	2	1	no	—
124	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
125	C₂²×C₅×D₃	#41	1	4	yes	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	4	4	no	—
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₅×#67	—	2	8	no	—
138	C₂×C₅×Dic₃	—	2	2	no	—
139	C₂×C₅×Dic₃	—	2	2	no	—
140	C₂×C₅×Dic₃	—	2	1	no	—
141	C₂×C₅×Dic₃	—	2	1	no	—
142	C₂×C₅×Dic₃	—	2	2	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	—	2	2	no	—
146	C₂×C₅×Dic₃	—	2	2	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
149	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
150	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
151	C₄×C₅×D₃	—	4	4	no	—
152	C₄×C₅×D₃	—	4	8	no	—
153	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
154	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
156	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×#217	C₂²×C₅	1	2	yes	—
160	C₂×#217	C₂²×C₅	1	1	yes	characteristic
161	C₄×#67	C₄×C₅	1	8	yes	complemented
162	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
165	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
167	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
168	C₃×#95	C₂²×C₅	1	1	yes	characteristic
169	C₃×#95	C₂²×C₅	1	1	yes	characteristic
170	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
171	C₃⋊#95	C₂²×C₅	1	2	yes	—
172	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
173	C₃⋊#95	C₂²×C₅	1	2	yes	—
174	C₃⋊#95	C₂²×C₅	1	2	yes	—
175	C₃⋊#95	C₂²×C₅	1	2	yes	—
176	C₃⋊#95	C₂²×C₅	1	2	yes	—
177	C₂⁴×C₅	—	3	1	no	—
178	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
179	C₂×C₅×D₄	—	3	4	no	—
180	C₂×C₅×D₄	—	6	4	no	—
181	C₂²×C₄×C₅	—	3	1	no	—
182	C₂²×C₄×C₅	—	3	1	no	—
183	C₂²×C₄×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	4	no	—
185	C₂²×C₄×C₅	—	3	2	no	—
186	C₂²×C₄×C₅	—	3	2	no	—
187	C₂²×C₄×C₅	—	4	2	no	—
188	C₂²×C₄×C₅	—	6	4	no	—
189	C₂²×C₄×C₅	—	12	2	no	—
190	C₂²×C₄×C₅	—	12	2	no	—
191	C₂²×C₄×C₅	—	12	2	no	—
192	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
193	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
194	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
195	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₅×C₄⋊C₄	—	3	4	no	—
198	C₅×C₄⋊C₄	—	4	2	no	—
199	C₅×C₄⋊C₄	—	12	2	no	—
200	C₅×C₂²⋊C₄	—	3	4	no	—
201	C₅×C₂²⋊C₄	—	3	4	no	—
202	C₅×C₂²⋊C₄	—	4	2	no	—
203	C₅×C₂²⋊C₄	—	6	4	no	—
204	C₅×C₂²⋊C₄	—	12	2	no	—
205	C₄²×C₅	—	3	4	no	—
206	C₄²×C₅	—	12	2	no	—
207	C₂×C₄×D₄	—	3	1	no	—
208	#388	—	3	2	no	—
209	#387	—	3	2	no	—
210	#386	—	3	2	no	—
211	#385	—	3	2	no	—
212	#383	—	3	1	no	—
213	#382	—	3	1	no	—
214	#381	—	3	1	no	—
215	#380	C₅×D₃	1	1	yes	characteristic, complemented
216	C₄×C₂²⋊C₄	—	3	1	no	—
217	C₂×#95	—	3	1	no	—
218	C₂²×C₃×C₅	—	2	2	no	—
219	C₂²×C₃×C₅	—	2	2	no	—
220	C₂²×C₃×C₅	—	2	2	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
224	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
225	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
226	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
227	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
228	C₂×C₅×D₃	—	2	2	no	—
229	C₂×C₅×D₃	—	2	2	no	—
230	C₂×C₅×D₃	—	2	4	no	—
231	C₂×C₅×D₃	—	2	4	no	—
232	C₂×C₅×D₃	#117	1	4	yes	—
233	C₃×C₄×C₅	—	2	2	no	—
234	C₃×C₄×C₅	—	2	2	no	—
235	C₃×C₄×C₅	—	4	2	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₅×Dic₃	—	2	2	no	—
238	C₅×Dic₃	—	2	2	no	—
239	C₅×Dic₃	—	2	2	no	—
240	C₅×Dic₃	—	4	2	no	—
241	C₅×Dic₃	—	4	2	no	—
242	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
243	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	—	4	2	no	—
245	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
246	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
247	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂×#67	—	2	4	no	—
251	C₂×#67	C₂×C₄×C₅	1	4	yes	—
252	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
253	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
254	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
255	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
256	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
257	C₂×C₄×D₃	—	2	4	no	—
258	C₂×C₄×D₃	—	4	2	no	—
259	C₂×C₄×D₃	—	4	2	no	—
260	C₂×C₄×D₃	—	4	2	no	—
261	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
262	C₃×C₄⋊C₄	—	4	2	no	—
263	C₃×C₂²⋊C₄	—	4	2	no	—
264	#217	—	4	2	no	—
265	#217	C₂×C₄×C₅	1	4	yes	complemented
266	(C₂×D₃)⋊C₄	—	2	4	no	—
267	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
268	Dic₃⋊C₄	—	4	2	no	—
269	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
270	C₄×Dic₃	—	4	2	no	—
271	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
272	C₂³×C₅	—	2	1	no	—
273	C₂³×C₅	—	2	2	no	—
274	C₂³×C₅	—	2	1	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	3	2	no	—
277	C₂³×C₅	—	3	4	no	—
278	C₂³×C₅	—	6	2	no	—
279	C₂³×C₅	—	6	1	no	—
280	C₂³×C₅	—	6	1	no	—
281	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
282	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
283	C₅×D₄	—	6	8	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	3	2	no	—
293	C₂×C₄×C₅	—	3	2	no	—
294	C₂×C₄×C₅	—	3	2	no	—
295	C₂×C₄×C₅	—	4	4	no	—
296	C₂×C₄×C₅	—	6	2	no	—
297	C₂×C₄×C₅	—	6	1	no	—
298	C₂×C₄×C₅	—	6	1	no	—
299	C₂×C₄×C₅	—	6	2	no	—
300	C₂×C₄×C₅	—	6	2	no	—
301	C₂×C₄×C₅	—	6	2	no	—
302	C₂×C₄×C₅	—	6	2	no	—
303	C₂×C₄×C₅	—	6	2	no	—
304	C₂×C₄×C₅	—	6	2	no	—
305	C₂×C₄×C₅	—	6	2	no	—
306	C₂×C₄×C₅	—	12	4	no	—
307	C₂×C₄×C₅	—	12	8	no	—
308	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
309	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
310	C₂²×D₄	—	3	1	no	—
311	C₂³×C₄	—	3	1	no	—
312	C₂³×C₄	—	3	2	no	—
313	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
314	C₄×D₄	—	3	8	no	—
315	C₂×C₄⋊C₄	—	3	1	no	—
316	C₂×C₄⋊C₄	—	3	2	no	—
317	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
318	C₂×C₂²⋊C₄	—	3	1	no	—
319	C₂×C₂²⋊C₄	—	3	1	no	—
320	C₂×C₂²⋊C₄	—	3	2	no	—
321	C₂×C₂²⋊C₄	—	3	2	no	—
322	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
323	C₂×C₄²	—	3	1	no	—
324	C₂×C₄²	—	3	2	no	—
325	#95	—	3	1	no	—
326	#95	—	3	2	no	—
327	#95	—	3	1	no	—
328	#95	—	3	2	no	—
329	#95	—	3	2	no	—
330	#95	—	3	2	no	—
331	#95	—	3	2	no	—
332	#95	C₂×C₅×D₃	1	1	yes	characteristic
333	#95	C₂×C₅×D₃	1	1	yes	characteristic
334	C₂×C₃×C₅	—	4	2	no	—
335	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
336	C₂×C₃×C₅	#518	1	1	yes	characteristic
337	C₂×C₃×C₅	#520	1	1	yes	characteristic
338	C₂×C₃×C₅	#538	1	2	yes	—
339	C₂×C₃×C₅	#539	1	2	yes	—
340	C₅×D₃	—	2	4	no	—
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	2	no	—
343	C₂³×C₃	—	2	1	no	—
344	C₂³×C₃	—	2	1	no	—
345	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
346	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
347	C₂²×D₃	—	2	2	no	—
348	C₂²×D₃	—	2	1	no	—
349	C₂²×D₃	—	2	1	no	—
350	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
351	C₂²×D₃	C₅×#41	1	4	yes	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	4	4	no	—
361	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
362	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
363	#67	—	2	8	no	—
364	C₂×Dic₃	—	2	2	no	—
365	C₂×Dic₃	—	2	2	no	—
366	C₂×Dic₃	—	2	1	no	—
367	C₂×Dic₃	—	2	1	no	—
368	C₂×Dic₃	—	2	2	no	—
369	C₂×Dic₃	—	2	2	no	—
370	C₂×Dic₃	—	2	2	no	—
371	C₂×Dic₃	—	2	2	no	—
372	C₂×Dic₃	—	2	2	no	—
373	C₂×Dic₃	—	2	2	no	—
374	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
375	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
376	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
377	C₄×D₃	—	4	4	no	—
378	C₄×D₃	—	4	8	no	—
379	C₂²×C₅	—	2	2	no	—
380	C₂²×C₅	—	2	2	no	—
381	C₂²×C₅	—	2	2	no	—
382	C₂²×C₅	—	3	4	no	—
383	C₂²×C₅	—	4	2	no	—
384	C₂²×C₅	—	4	2	no	—
385	C₂²×C₅	—	6	4	no	—
386	C₂²×C₅	—	6	2	no	—
387	C₂²×C₅	—	6	2	no	—
388	C₂²×C₅	—	6	4	no	—
389	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
390	C₂²×C₅	#1004	1	2	yes	—
391	C₂²×C₅	#1004	1	1	yes	characteristic
392	C₂²×C₅	#1007	1	1	yes	characteristic
393	C₂²×C₅	D₃×#41	1	2	yes	—
394	C₄×C₅	—	2	2	no	—
395	C₄×C₅	—	2	2	no	—
396	C₄×C₅	—	4	2	no	—
397	C₄×C₅	—	4	2	no	—
398	C₄×C₅	—	6	2	no	—
399	C₄×C₅	—	6	2	no	—
400	C₄×C₅	—	6	2	no	—
401	C₄×C₅	—	12	2	no	—
402	C₄×C₅	—	12	2	no	—
403	C₂⁴	—	3	1	no	—
404	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
405	C₂×D₄	—	3	4	no	—
406	C₂×D₄	—	6	4	no	—
407	C₂²×C₄	—	3	1	no	—
408	C₂²×C₄	—	3	1	no	—
409	C₂²×C₄	—	3	1	no	—
410	C₂²×C₄	—	3	4	no	—
411	C₂²×C₄	—	3	2	no	—
412	C₂²×C₄	—	3	2	no	—
413	C₂²×C₄	—	4	2	no	—
414	C₂²×C₄	—	6	4	no	—
415	C₂²×C₄	—	12	2	no	—
416	C₂²×C₄	—	12	2	no	—
417	C₂²×C₄	—	12	2	no	—
418	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
419	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
420	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
421	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
422	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₄⋊C₄	—	3	4	no	—
424	C₄⋊C₄	—	4	2	no	—
425	C₄⋊C₄	—	12	2	no	—
426	C₂²⋊C₄	—	3	4	no	—
427	C₂²⋊C₄	—	3	4	no	—
428	C₂²⋊C₄	—	4	2	no	—
429	C₂²⋊C₄	—	6	4	no	—
430	C₂²⋊C₄	—	12	2	no	—
431	C₄²	—	3	4	no	—
432	C₄²	—	12	2	no	—
433	C₃×C₅	#2318	1	1	yes	characteristic, complemented, Hall
434	C₂²×C₃	—	2	2	no	—
435	C₂²×C₃	—	2	2	no	—
436	C₂²×C₃	—	2	2	no	—
437	C₂²×C₃	—	4	2	no	—
438	C₂²×C₃	—	4	2	no	—
439	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
440	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
441	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
442	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
443	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
444	C₂×D₃	—	2	2	no	—
445	C₂×D₃	—	2	2	no	—
446	C₂×D₃	—	2	4	no	—
447	C₂×D₃	—	2	4	no	—
448	C₂×D₃	C₅×#117	1	4	yes	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	2	no	—
451	C₃×C₄	—	4	2	no	—
452	C₃×C₄	—	4	2	no	—
453	Dic₃	—	2	2	no	—
454	Dic₃	—	2	2	no	—
455	Dic₃	—	2	2	no	—
456	Dic₃	—	4	2	no	—
457	Dic₃	—	4	2	no	—
458	C₂×C₅	—	4	2	no	—
459	C₂×C₅	—	6	4	no	—
460	C₂×C₅	#5486	1	1	yes	characteristic
461	C₂×C₅	#5504	1	1	yes	characteristic
462	C₂×C₅	D₃×#117	1	1	yes	characteristic
463	C₂×C₅	#5613	1	2	yes	—
464	C₂×C₅	#5638	1	2	yes	—
465	C₂³	—	2	1	no	—
466	C₂³	—	2	2	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	2	2	no	—
469	C₂³	—	3	2	no	—
470	C₂³	—	3	4	no	—
471	C₂³	—	6	2	no	—
472	C₂³	—	6	1	no	—
473	C₂³	—	6	1	no	—
474	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
475	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
476	D₄	—	6	8	no	—
477	C₂×C₄	—	2	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	3	2	no	—
486	C₂×C₄	—	3	2	no	—
487	C₂×C₄	—	3	2	no	—
488	C₂×C₄	—	4	4	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	—	6	1	no	—
491	C₂×C₄	—	6	1	no	—
492	C₂×C₄	—	6	2	no	—
493	C₂×C₄	—	6	2	no	—
494	C₂×C₄	—	6	2	no	—
495	C₂×C₄	—	6	2	no	—
496	C₂×C₄	—	6	2	no	—
497	C₂×C₄	—	6	2	no	—
498	C₂×C₄	—	6	2	no	—
499	C₂×C₄	—	12	4	no	—
500	C₂×C₄	—	12	8	no	—
501	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
502	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
503	C₂×C₃	—	4	2	no	—
504	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
505	C₂×C₃	C₅×#518	1	1	yes	characteristic
506	C₂×C₃	C₅×#520	1	1	yes	characteristic
507	C₂×C₃	C₅×#538	1	2	yes	—
508	C₂×C₃	C₅×#539	1	2	yes	—
509	D₃	—	2	4	no	—
510	C₅	#74006	1	1	yes	characteristic, direct product factor, Sylow
511	C₂²	—	2	2	no	—
512	C₂²	—	2	2	no	—
513	C₂²	—	2	2	no	—
514	C₂²	—	3	4	no	—
515	C₂²	—	4	2	no	—
516	C₂²	—	4	2	no	—
517	C₂²	—	6	2	no	—
518	C₂²	—	6	2	no	—
519	C₂²	—	6	4	no	—
520	C₂²	—	6	4	no	—
521	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
522	C₂²	C₅×#1004	1	2	yes	—
523	C₂²	C₅×#1004	1	1	yes	characteristic
524	C₂²	C₅×#1007	1	1	yes	characteristic
525	C₂²	C₅×D₃×#41	1	2	yes	—
526	C₄	—	2	2	no	—
527	C₄	—	2	2	no	—
528	C₄	—	4	2	no	—
529	C₄	—	4	2	no	—
530	C₄	—	6	2	no	—
531	C₄	—	6	2	no	—
532	C₄	—	6	2	no	—
533	C₄	—	12	2	no	—
534	C₄	—	12	2	no	—
535	C₃	C₅×#2318	1	1	yes	characteristic, complemented, Sylow
536	C₂	—	4	2	no	—
537	C₂	—	6	4	no	—
538	C₂	C₅×#5486	1	1	yes	characteristic
539	C₂	C₅×#5504	1	1	yes	characteristic
540	C₂	C₅×D₃×#117	1	1	yes	characteristic
541	C₂	C₅×#5613	1	2	yes	—
542	C₂	C₅×#5638	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₅×#380	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₅×#380	D₃
hypocenter	C₃	C₅×#2318
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₅×#380

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#380	C₂	semidirect
3. C₅×#5211	C₂	semidirect
4. C₅×#4989	C₂	semidirect
5. C₅×#4978	C₂	semidirect
7. C₅×#4945	C₂	semidirect
8. C₅×#4666	C₂	semidirect
9. C₅×D₃×#95	C₂	semidirect
10. C₅×#4651	C₂	semidirect
11. C₅×#4650	C₂	semidirect
21. C₄×C₅×#67	C₄	semidirect
37. #74006	C₅	direct (N × H)
46. C₅×#380	D₃	semidirect
52. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
72. C₅×#217	C₂×C₄	semidirect
76. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
78. C₄×C₅×Dic₃	C₂×C₄	semidirect
80. C₃×#380	C₂×C₅	semidirect
81. #5211	C₂×C₅	semidirect
82. #4989	C₂×C₅	semidirect
83. #4978	C₂×C₅	semidirect
85. #4945	C₂×C₅	semidirect
86. #4666	C₂×C₅	semidirect
87. D₃×#95	C₂×C₅	semidirect
88. #4651	C₂×C₅	semidirect
89. #4650	C₂×C₅	semidirect
161. C₄×#67	C₄×C₅	semidirect
192. C₂²×C₄×C₅	C₄×D₃	semidirect
215. #380	C₅×D₃	semidirect
245. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
265. #217	C₂×C₄×C₅	semidirect
269. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
271. C₄×Dic₃	C₂×C₄×C₅	semidirect
418. C₂²×C₄	C₄×C₅×D₃	semidirect
433. C₃×C₅	#2318	semidirect
510. C₅	#74006	direct (N × H)
535. C₃	C₅×#2318	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×#67	2
C₃×C₅×#380	2
C₅×#5211	2
C₅×#4989	2
C₅×#4978	2
C₅×#4956	2
C₅×#4945	2
C₅×#4666	2
C₅×D₃×#95	2
C₅×#4651	2
C₅×#4650	2
C₅×#2318	3
#74006	5

Subgroups — C5×#74006 #14322985

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#74006 #14322985