Subgroups — C₅×#73639 #14327663

Order 1920.

1264 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#893	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#872	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4988	C₂	1	1	yes	maximal, characteristic
5	C₅×#4975	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4940	C₂	1	2	yes	maximal, complemented
8	C₅×#4939	C₂	1	1	yes	maximal, characteristic
9	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4669	C₂	1	2	yes	maximal, complemented
11	C₅×#4667	C₂	1	2	yes	maximal, complemented
12	C₅×#2354	—	3	1	no	maximal, Hall
13	C₂²×C₅×D₁₂	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
27	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
28	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
30	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#893	C₄	1	8	yes	complemented
33	C₅×#872	—	2	8	no	—
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₅×C₃⋊#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
37	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
38	#73639	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₄×C₅×D₄	—	3	1	no	—
40	C₂×C₅×#117	—	3	2	no	—
41	C₅×#390	—	3	1	no	—
42	C₅×#390	—	3	1	no	—
43	C₅×#388	—	3	2	no	—
44	C₅×#388	—	3	2	no	—
45	C₅×#384	—	3	1	no	—
46	C₅×#380	—	3	2	no	—
47	C₄×C₅×C₄⋊C₄	—	3	1	no	—
48	C₄×C₅×C₄⋊C₄	—	3	1	no	—
49	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
50	C₂³×C₅×D₃	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
57	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
61	C₂×C₅×D₁₂	—	2	2	no	—
62	C₂×C₅×D₁₂	—	2	2	no	—
63	C₂×C₅×D₁₂	C₂×C₄	1	4	yes	—
64	C₂×C₄×C₅×D₃	—	2	4	no	—
65	C₂×C₄×C₅×D₃	—	2	4	no	—
66	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
69	C₃×C₄²×C₅	—	2	4	no	—
70	C₃×C₄²×C₅	—	2	2	no	—
71	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
72	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
73	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
74	C₅×(C₂×D₃)⋊C₄	—	4	2	no	—
75	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
76	C₅×C₄⋊Dic₃	—	2	2	no	—
77	C₅×Dic₃⋊C₄	—	2	4	no	—
78	C₅×Dic₃⋊C₄	—	2	2	no	—
79	C₅×Dic₃⋊C₄	—	4	2	no	—
80	C₅×Dic₃⋊C₄	D₄	1	4	yes	complemented
81	C₄×C₅×Dic₃	—	2	2	no	—
82	C₄×C₅×Dic₃	—	2	4	no	—
83	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	—
84	C₂×#893	C₂×C₅	1	1	yes	characteristic
85	C₂×#872	C₂×C₅	1	2	yes	complemented
86	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
87	#4988	C₂×C₅	1	1	yes	characteristic
88	#4975	C₂×C₅	1	1	yes	characteristic, complemented
89	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
90	#4940	C₂×C₅	1	2	yes	complemented
91	#4939	C₂×C₅	1	1	yes	characteristic
92	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
93	#4669	C₂×C₅	1	2	yes	complemented
94	#4667	C₂×C₅	1	2	yes	complemented
95	C₂²×C₅×D₄	—	3	1	no	—
96	C₂³×C₄×C₅	—	3	2	no	—
97	C₄×C₅×D₄	—	3	8	no	—
98	C₅×#117	—	6	8	no	—
99	C₂×C₅×C₄⋊C₄	—	3	1	no	—
100	C₂×C₅×C₄⋊C₄	—	3	1	no	—
101	C₂×C₅×C₄⋊C₄	—	3	1	no	—
102	C₂×C₅×C₄⋊C₄	—	3	2	no	—
103	C₂×C₅×C₄⋊C₄	—	3	2	no	—
104	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
106	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
107	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
108	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
109	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
110	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
111	C₂×C₄²×C₅	—	3	1	no	—
112	C₂×C₄²×C₅	—	3	1	no	—
113	C₂×C₄²×C₅	—	3	2	no	—
114	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
115	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
116	C₅×#95	—	3	2	no	—
117	C₅×#95	—	3	1	no	—
118	C₅×#95	—	3	1	no	—
119	C₅×#95	C₂×D₃	1	2	yes	—
120	#2354	—	3	1	no	Sylow
121	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
122	C₂²×C₅×D₃	—	2	2	no	—
123	C₂²×C₅×D₃	—	2	2	no	—
124	C₂²×C₅×D₃	—	2	2	no	—
125	C₂²×C₅×D₃	—	2	2	no	—
126	C₂²×C₅×D₃	—	2	2	no	—
127	C₂²×C₅×D₃	—	2	2	no	—
128	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	1	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	#41	1	2	yes	—
143	C₂×C₃×C₄×C₅	#41	1	2	yes	—
144	C₂×C₅×Dic₃	—	2	1	no	—
145	C₂×C₅×Dic₃	—	2	1	no	—
146	C₂×C₅×Dic₃	—	2	1	no	—
147	C₂×C₅×Dic₃	—	2	1	no	—
148	C₂×C₅×Dic₃	—	2	2	no	—
149	C₂×C₅×Dic₃	—	2	1	no	—
150	C₂×C₅×Dic₃	—	2	1	no	—
151	C₂×C₅×Dic₃	—	2	2	no	—
152	C₂×C₅×Dic₃	—	2	2	no	—
153	C₂×C₅×Dic₃	—	2	1	no	—
154	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
155	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
156	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
157	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
158	C₂×C₅×Dic₃	#41	1	2	yes	—
159	C₅×D₁₂	—	2	8	no	—
160	C₄×C₅×D₃	—	2	16	no	—
161	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
162	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
164	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
167	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
168	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
169	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
170	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
171	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
172	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
173	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
178	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
180	#893	C₄×C₅	1	8	yes	complemented
181	#872	—	2	8	no	—
182	C₃×#95	C₂²×C₅	1	2	yes	—
183	C₃⋊#95	C₂²×C₅	1	2	yes	—
184	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
185	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
186	C₂⁴×C₅	—	3	2	no	—
187	C₂×C₅×D₄	—	3	4	no	—
188	C₂×C₅×D₄	—	6	2	no	—
189	C₂×C₅×D₄	—	6	2	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	1	no	—
192	C₂²×C₄×C₅	—	3	1	no	—
193	C₂²×C₄×C₅	—	3	8	no	—
194	C₂²×C₄×C₅	—	3	2	no	—
195	C₂²×C₄×C₅	—	3	1	no	—
196	C₂²×C₄×C₅	—	6	4	no	—
197	C₂²×C₄×C₅	—	6	4	no	—
198	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
199	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
201	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	3	4	no	—
205	C₅×C₄⋊C₄	—	6	4	no	—
206	C₅×C₄⋊C₄	—	6	2	no	—
207	C₅×C₄⋊C₄	—	6	2	no	—
208	C₅×C₄⋊C₄	—	12	2	no	—
209	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	—
210	C₅×C₂²⋊C₄	—	3	8	no	—
211	C₅×C₂²⋊C₄	—	6	4	no	—
212	C₅×C₂²⋊C₄	—	6	4	no	—
213	C₅×C₂²⋊C₄	—	12	2	no	—
214	C₅×C₂²⋊C₄	—	12	2	no	—
215	C₄²×C₅	—	2	2	no	—
216	C₄²×C₅	—	2	4	no	—
217	C₄²×C₅	—	3	4	no	—
218	C₄²×C₅	—	6	4	no	—
219	C₄²×C₅	—	6	2	no	—
220	C₂×C₄×D₄	—	3	1	no	—
221	C₂×#117	—	3	2	no	—
222	#390	—	3	1	no	—
223	#390	—	3	1	no	—
224	#388	—	3	2	no	—
225	#388	—	3	2	no	—
226	#384	—	3	1	no	—
227	#380	—	3	2	no	—
228	C₄×C₄⋊C₄	—	3	1	no	—
229	C₄×C₄⋊C₄	—	3	1	no	—
230	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
231	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
232	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
233	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
234	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
235	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
236	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
237	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
238	C₂×C₅×D₃	—	2	4	no	—
239	C₂×C₅×D₃	—	2	4	no	—
240	C₂×C₅×D₃	—	2	4	no	—
241	C₂×C₅×D₃	—	4	2	no	—
242	C₂×C₅×D₃	—	4	2	no	—
243	C₂×C₅×D₃	—	4	2	no	—
244	C₂×C₅×D₃	—	4	2	no	—
245	C₃×C₄×C₅	—	2	4	no	—
246	C₃×C₄×C₅	—	2	2	no	—
247	C₃×C₄×C₅	—	4	2	no	—
248	C₃×C₄×C₅	—	4	1	no	—
249	C₃×C₄×C₅	#117	1	4	yes	complemented
250	C₅×Dic₃	—	2	2	no	—
251	C₅×Dic₃	—	2	2	no	—
252	C₅×Dic₃	—	4	2	no	—
253	C₅×Dic₃	—	4	1	no	—
254	C₅×Dic₃	C₄×D₄	1	4	yes	—
255	C₂³×D₃	C₂³×C₅	1	2	yes	—
256	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
258	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
259	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
262	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
263	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
264	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
265	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
266	C₂×D₁₂	—	2	2	no	—
267	C₂×D₁₂	—	2	2	no	—
268	C₂×D₁₂	C₂×C₄×C₅	1	4	yes	—
269	C₂×C₄×D₃	—	2	4	no	—
270	C₂×C₄×D₃	—	2	4	no	—
271	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
272	C₃×C₄⋊C₄	—	2	2	no	—
273	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
274	C₃×C₄²	—	2	4	no	—
275	C₃×C₄²	—	2	2	no	—
276	(C₂×D₃)⋊C₄	—	2	4	no	—
277	(C₂×D₃)⋊C₄	—	2	4	no	—
278	(C₂×D₃)⋊C₄	—	4	2	no	—
279	(C₂×D₃)⋊C₄	—	4	2	no	—
280	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
281	C₄⋊Dic₃	—	2	2	no	—
282	Dic₃⋊C₄	—	2	4	no	—
283	Dic₃⋊C₄	—	2	2	no	—
284	Dic₃⋊C₄	—	4	2	no	—
285	Dic₃⋊C₄	C₅×D₄	1	4	yes	complemented
286	C₄×Dic₃	—	2	2	no	—
287	C₄×Dic₃	—	2	4	no	—
288	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	—
289	C₂³×C₅	—	3	4	no	—
290	C₂³×C₅	—	6	2	no	—
291	C₂³×C₅	—	6	2	no	—
292	C₂³×C₅	—	6	2	no	—
293	C₂³×C₅	—	6	2	no	—
294	C₂³×C₅	—	6	2	no	—
295	C₂³×C₅	—	6	2	no	—
296	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
297	C₅×D₄	—	6	8	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	3	2	no	—
309	C₂×C₄×C₅	—	3	2	no	—
310	C₂×C₄×C₅	—	3	2	no	—
311	C₂×C₄×C₅	—	3	2	no	—
312	C₂×C₄×C₅	—	3	2	no	—
313	C₂×C₄×C₅	—	6	16	no	—
314	C₂×C₄×C₅	—	6	1	no	—
315	C₂×C₄×C₅	—	6	1	no	—
316	C₂×C₄×C₅	—	6	1	no	—
317	C₂×C₄×C₅	—	6	1	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	6	2	no	—
321	C₂×C₄×C₅	—	6	1	no	—
322	C₂×C₄×C₅	—	6	1	no	—
323	C₂×C₄×C₅	—	6	2	no	—
324	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
325	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
326	C₂×C₄×C₅	#235	1	2	yes	—
327	C₂×C₄×C₅	#235	1	2	yes	—
328	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
329	C₂²×D₄	—	3	1	no	—
330	C₂³×C₄	—	3	2	no	—
331	C₄×D₄	—	3	8	no	—
332	#117	—	6	8	no	—
333	C₂×C₄⋊C₄	—	3	1	no	—
334	C₂×C₄⋊C₄	—	3	2	no	—
335	C₂×C₄⋊C₄	—	3	1	no	—
336	C₂×C₄⋊C₄	—	3	1	no	—
337	C₂×C₄⋊C₄	—	3	2	no	—
338	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
339	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
340	C₂×C₂²⋊C₄	—	3	2	no	—
341	C₂×C₂²⋊C₄	—	3	2	no	—
342	C₂×C₂²⋊C₄	—	3	2	no	—
343	C₂×C₂²⋊C₄	—	3	2	no	—
344	C₂×C₂²⋊C₄	—	3	2	no	—
345	C₂×C₄²	—	3	1	no	—
346	C₂×C₄²	—	3	2	no	—
347	C₂×C₄²	—	3	1	no	—
348	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
349	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
350	#95	—	3	2	no	—
351	#95	—	3	1	no	—
352	#95	—	3	1	no	—
353	#95	C₂×C₅×D₃	1	2	yes	—
354	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
355	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
356	C₂×C₃×C₅	#520	1	1	yes	characteristic
357	C₂×C₃×C₅	#547	1	1	yes	characteristic
358	C₂×C₃×C₅	#550	1	1	yes	characteristic
359	C₂×C₃×C₅	#555	1	1	yes	characteristic
360	C₂×C₃×C₅	#556	1	1	yes	characteristic
361	C₅×D₃	—	4	4	no	—
362	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
363	C₂²×D₃	—	2	2	no	—
364	C₂²×D₃	—	2	2	no	—
365	C₂²×D₃	—	2	2	no	—
366	C₂²×D₃	—	2	2	no	—
367	C₂²×D₃	—	2	2	no	—
368	C₂²×D₃	—	2	2	no	—
369	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	1	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	1	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
381	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
382	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
383	C₂×C₃×C₄	C₅×#41	1	2	yes	—
384	C₂×C₃×C₄	C₅×#41	1	2	yes	—
385	C₂×Dic₃	—	2	1	no	—
386	C₂×Dic₃	—	2	1	no	—
387	C₂×Dic₃	—	2	1	no	—
388	C₂×Dic₃	—	2	1	no	—
389	C₂×Dic₃	—	2	2	no	—
390	C₂×Dic₃	—	2	1	no	—
391	C₂×Dic₃	—	2	1	no	—
392	C₂×Dic₃	—	2	2	no	—
393	C₂×Dic₃	—	2	2	no	—
394	C₂×Dic₃	—	2	1	no	—
395	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
396	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
397	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
398	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
399	C₂×Dic₃	C₅×#41	1	2	yes	—
400	D₁₂	—	2	8	no	—
401	C₄×D₃	—	2	16	no	—
402	C₂²×C₅	—	6	4	no	—
403	C₂²×C₅	—	6	4	no	—
404	C₂²×C₅	—	6	4	no	—
405	C₂²×C₅	—	12	2	no	—
406	C₂²×C₅	—	12	2	no	—
407	C₂²×C₅	—	12	2	no	—
408	C₂²×C₅	—	12	2	no	—
409	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
410	C₂²×C₅	C₂×#235	1	1	yes	characteristic
411	C₂²×C₅	C₂×#235	1	1	yes	characteristic
412	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
413	C₂²×C₅	#1007	1	1	yes	characteristic
414	C₂²×C₅	D₃×#41	1	1	yes	characteristic
415	C₂²×C₅	#1009	1	1	yes	characteristic
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	4	no	—
418	C₄×C₅	—	3	4	no	—
419	C₄×C₅	—	4	1	no	—
420	C₄×C₅	—	4	2	no	—
421	C₄×C₅	—	6	2	no	—
422	C₄×C₅	—	6	2	no	—
423	C₄×C₅	—	12	1	no	—
424	C₄×C₅	—	12	2	no	—
425	C₄×C₅	#872	1	4	yes	complemented
426	C₂⁴	—	3	2	no	—
427	C₂×D₄	—	3	4	no	—
428	C₂×D₄	—	6	2	no	—
429	C₂×D₄	—	6	2	no	—
430	C₂²×C₄	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	1	no	—
433	C₂²×C₄	—	3	8	no	—
434	C₂²×C₄	—	3	1	no	—
435	C₂²×C₄	—	3	2	no	—
436	C₂²×C₄	—	6	4	no	—
437	C₂²×C₄	—	6	4	no	—
438	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
439	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
440	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
441	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
442	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	3	4	no	—
445	C₄⋊C₄	—	6	4	no	—
446	C₄⋊C₄	—	6	2	no	—
447	C₄⋊C₄	—	6	2	no	—
448	C₄⋊C₄	—	12	2	no	—
449	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	—
450	C₂²⋊C₄	—	3	8	no	—
451	C₂²⋊C₄	—	6	4	no	—
452	C₂²⋊C₄	—	6	4	no	—
453	C₂²⋊C₄	—	12	2	no	—
454	C₂²⋊C₄	—	12	2	no	—
455	C₄²	—	2	2	no	—
456	C₄²	—	2	4	no	—
457	C₄²	—	3	4	no	—
458	C₄²	—	6	4	no	—
459	C₄²	—	6	2	no	—
460	C₃×C₅	#2354	1	1	yes	characteristic, complemented, Hall
461	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
462	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
463	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
464	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
465	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
466	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
467	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
468	C₂×D₃	—	2	4	no	—
469	C₂×D₃	—	2	4	no	—
470	C₂×D₃	—	2	4	no	—
471	C₂×D₃	—	4	2	no	—
472	C₂×D₃	—	4	2	no	—
473	C₂×D₃	—	4	2	no	—
474	C₂×D₃	—	4	2	no	—
475	C₃×C₄	—	2	4	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	4	2	no	—
478	C₃×C₄	—	4	1	no	—
479	C₃×C₄	C₅×#117	1	4	yes	complemented
480	Dic₃	—	2	2	no	—
481	Dic₃	—	2	2	no	—
482	Dic₃	—	4	2	no	—
483	Dic₃	—	4	1	no	—
484	Dic₃	C₄×C₅×D₄	1	4	yes	—
485	C₂×C₅	—	12	4	no	—
486	C₂×C₅	C₂×#872	1	1	yes	characteristic
487	C₂×C₅	#5507	1	1	yes	characteristic
488	C₂×C₅	#5532	1	1	yes	characteristic
489	C₂×C₅	C₄×D₃×D₄	1	1	yes	characteristic
490	C₂×C₅	#5553	1	1	yes	characteristic
491	C₂×C₅	#5568	1	1	yes	characteristic
492	C₂×C₅	#5574	1	1	yes	characteristic
493	C₂³	—	3	4	no	—
494	C₂³	—	6	2	no	—
495	C₂³	—	6	2	no	—
496	C₂³	—	6	2	no	—
497	C₂³	—	6	2	no	—
498	C₂³	—	6	2	no	—
499	C₂³	—	6	2	no	—
500	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
501	D₄	—	6	8	no	—
502	C₂×C₄	—	2	1	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	1	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	1	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	1	no	—
511	C₂×C₄	—	2	2	no	—
512	C₂×C₄	—	3	2	no	—
513	C₂×C₄	—	3	2	no	—
514	C₂×C₄	—	3	2	no	—
515	C₂×C₄	—	3	2	no	—
516	C₂×C₄	—	3	2	no	—
517	C₂×C₄	—	6	16	no	—
518	C₂×C₄	—	6	1	no	—
519	C₂×C₄	—	6	1	no	—
520	C₂×C₄	—	6	1	no	—
521	C₂×C₄	—	6	1	no	—
522	C₂×C₄	—	6	1	no	—
523	C₂×C₄	—	6	2	no	—
524	C₂×C₄	—	6	2	no	—
525	C₂×C₄	—	6	1	no	—
526	C₂×C₄	—	6	1	no	—
527	C₂×C₄	—	6	2	no	—
528	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
529	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
530	C₂×C₄	C₅×#235	1	2	yes	—
531	C₂×C₄	C₅×#235	1	2	yes	—
532	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
533	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
534	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
535	C₂×C₃	C₅×#520	1	1	yes	characteristic
536	C₂×C₃	C₅×#547	1	1	yes	characteristic
537	C₂×C₃	C₅×#550	1	1	yes	characteristic
538	C₂×C₃	C₅×#555	1	1	yes	characteristic
539	C₂×C₃	C₅×#556	1	1	yes	characteristic
540	D₃	—	4	4	no	—
541	C₅	#73639	1	1	yes	characteristic, direct product factor, Sylow
542	C₂²	—	6	4	no	—
543	C₂²	—	6	4	no	—
544	C₂²	—	6	4	no	—
545	C₂²	—	12	2	no	—
546	C₂²	—	12	2	no	—
547	C₂²	—	12	2	no	—
548	C₂²	—	12	2	no	—
549	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
550	C₂²	C₂×C₅×#235	1	1	yes	characteristic
551	C₂²	C₂×C₅×#235	1	1	yes	characteristic
552	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
553	C₂²	C₅×#1007	1	1	yes	characteristic
554	C₂²	C₅×D₃×#41	1	1	yes	characteristic
555	C₂²	C₅×#1009	1	1	yes	characteristic
556	C₄	—	2	2	no	—
557	C₄	—	2	4	no	—
558	C₄	—	3	4	no	—
559	C₄	—	4	1	no	—
560	C₄	—	4	2	no	—
561	C₄	—	6	2	no	—
562	C₄	—	6	2	no	—
563	C₄	—	12	1	no	—
564	C₄	—	12	2	no	—
565	C₄	C₅×#872	1	4	yes	complemented
566	C₃	C₅×#2354	1	1	yes	characteristic, complemented, Sylow
567	C₂	—	12	4	no	—
568	C₂	C₂×C₅×#872	1	1	yes	characteristic
569	C₂	C₅×#5507	1	1	yes	characteristic
570	C₂	C₅×#5532	1	1	yes	characteristic
571	C₂	C₄×C₅×D₃×D₄	1	1	yes	characteristic
572	C₂	C₅×#5553	1	1	yes	characteristic
573	C₂	C₅×#5568	1	1	yes	characteristic
574	C₂	C₅×#5574	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×D₁₂	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2354
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
2. C₂×C₅×#872	C₂	semidirect
3. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₅×#4975	C₂	semidirect
6. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
7. C₅×#4940	C₂	semidirect
9. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
10. C₅×#4669	C₂	semidirect
11. C₅×#4667	C₂	semidirect
32. C₅×#893	C₄	semidirect
38. #73639	C₅	direct (N × H)
49. C₄×C₅×C₄⋊C₄	D₃	semidirect
80. C₅×Dic₃⋊C₄	D₄	semidirect
85. C₂×#872	C₂×C₅	semidirect
86. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
88. #4975	C₂×C₅	semidirect
89. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
90. #4940	C₂×C₅	semidirect
92. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
93. #4669	C₂×C₅	semidirect
94. #4667	C₂×C₅	semidirect
180. #893	C₄×C₅	semidirect
230. C₄×C₄⋊C₄	C₅×D₃	semidirect
249. C₃×C₄×C₅	#117	semidirect
285. Dic₃⋊C₄	C₅×D₄	semidirect
425. C₄×C₅	#872	semidirect
460. C₃×C₅	#2354	semidirect
479. C₃×C₄	C₅×#117	semidirect
541. C₅	#73639	direct (N × H)
565. C₄	C₅×#872	semidirect
566. C₃	C₅×#2354	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#893	2
C₂×C₅×#872	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4988	2
C₅×#4975	2
C₅×Dic₃×C₄⋊C₄	2
C₅×#4940	2
C₅×#4939	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4669	2
C₅×#4667	2
C₅×#2354	3
#73639	5

Subgroups — C5×#73639 #14327663

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73639 #14327663