Subgroups — C₅×#73750 #14319660

Order 1920.

1392 conjugacy classes of subgroups.

The subgroup lattice has 580 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#892	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Dic₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal
8	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×Dic₃⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#4666	C₂	1	2	yes	maximal
11	C₅×#4649	C₂	1	2	yes	maximal, complemented
12	C₅×#2274	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
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	2	yes	—
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
23	C₂×C₅×C₄⋊Dic₃	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×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
28	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
30	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
31	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#892	C₄	1	8	yes	complemented
33	C₅×D₃×C₄⋊C₄	C₄	1	8	yes	complemented
34	C₅×#872	C₄	1	8	yes	complemented
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	C₅×C₃⋊#95	C₂²	1	2	yes	—
38	C₅×C₃⋊#95	C₂²	1	2	yes	—
39	#73750	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×#117	—	3	1	no	—
41	C₂×C₅×#117	—	3	1	no	—
42	C₂²×C₅×C₄⋊C₄	—	3	1	no	—
43	C₄×C₅×C₄⋊C₄	—	3	2	no	—
44	C₄×C₅×C₄⋊C₄	—	3	1	no	—
45	C₄×C₅×C₄⋊C₄	—	3	1	no	—
46	C₄×C₅×C₄⋊C₄	—	3	2	no	—
47	C₄×C₅×C₄⋊C₄	—	3	1	no	—
48	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
49	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
50	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
51	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
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	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
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	C₂×C₄×C₅×D₃	—	4	2	no	—
63	C₂×C₄×C₅×D₃	—	4	2	no	—
64	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
65	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
66	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
67	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
68	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	—
69	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
70	C₃×C₄²×C₅	—	4	2	no	—
71	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
72	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
73	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
74	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	—
75	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	—
76	C₅×C₄⋊Dic₃	C₂×C₄	1	4	yes	complemented
77	C₅×Dic₃⋊C₄	C₂×C₄	1	8	yes	—
78	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
79	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
80	C₄×C₅×Dic₃	—	4	2	no	—
81	C₄×C₅×Dic₃	—	4	2	no	—
82	C₄×C₅×Dic₃	—	4	2	no	—
83	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
84	C₄×C₅×Dic₃	C₂×C₄	1	8	yes	complemented
85	C₂×#892	C₂×C₅	1	1	yes	characteristic
86	C₂×D₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
87	C₂×#872	C₂×C₅	1	1	yes	characteristic
88	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
89	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
90	Dic₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
91	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	—
92	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
93	C₄×Dic₃⋊C₄	C₂×C₅	1	2	yes	complemented
94	#4666	C₂×C₅	1	2	yes	—
95	#4649	C₂×C₅	1	2	yes	complemented
96	C₂³×C₄×C₅	—	3	1	no	—
97	C₂³×C₄×C₅	—	3	2	no	—
98	C₅×#117	—	3	8	no	—
99	C₅×#117	—	3	8	no	—
100	C₂×C₅×C₄⋊C₄	—	3	2	no	—
101	C₂×C₅×C₄⋊C₄	—	3	1	no	—
102	C₂×C₅×C₄⋊C₄	—	3	1	no	—
103	C₂×C₅×C₄⋊C₄	—	3	1	no	—
104	C₂×C₅×C₄⋊C₄	—	3	1	no	—
105	C₂×C₅×C₄⋊C₄	—	3	8	no	—
106	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
108	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
110	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
111	C₂×C₄²×C₅	—	3	2	no	—
112	C₂×C₄²×C₅	—	3	1	no	—
113	C₂×C₄²×C₅	—	3	2	no	—
114	C₂×C₄²×C₅	—	3	2	no	—
115	C₂×C₄²×C₅	—	3	2	no	—
116	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
117	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
118	C₅×#95	—	3	2	no	—
119	C₅×#95	—	3	2	no	—
120	C₅×#95	—	3	2	no	—
121	C₅×#95	C₂×D₃	1	2	yes	—
122	#2274	—	3	1	no	Sylow
123	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
124	C₂²×C₅×D₃	—	2	1	no	—
125	C₂²×C₅×D₃	—	2	1	no	—
126	C₂²×C₅×D₃	—	2	1	no	—
127	C₂²×C₅×D₃	—	2	1	no	—
128	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
129	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
130	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
140	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
141	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
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	2	no	—
150	C₂×C₅×Dic₃	—	2	2	no	—
151	C₂×C₅×Dic₃	—	2	1	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	C₂²×C₄	1	4	yes	—
157	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
158	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
159	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
160	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
161	C₄×C₅×D₃	—	4	8	no	—
162	C₄×C₅×D₃	C₄²	1	16	yes	complemented
163	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
164	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
168	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
169	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
170	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
171	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
174	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
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	2	yes	—
179	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
180	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
181	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
182	#892	C₄×C₅	1	8	yes	complemented
183	D₃×C₄⋊C₄	C₄×C₅	1	8	yes	complemented
184	#872	C₄×C₅	1	8	yes	complemented
185	C₃×#95	C₂²×C₅	1	2	yes	—
186	C₃⋊#95	C₂²×C₅	1	2	yes	—
187	C₃⋊#95	C₂²×C₅	1	2	yes	—
188	C₃⋊#95	C₂²×C₅	1	2	yes	—
189	C₂⁴×C₅	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	4	no	—
192	C₂²×C₄×C₅	—	3	4	no	—
193	C₂²×C₄×C₅	—	3	4	no	—
194	C₂²×C₄×C₅	—	3	1	no	—
195	C₂²×C₄×C₅	—	3	2	no	—
196	C₂²×C₄×C₅	—	3	1	no	—
197	C₂²×C₄×C₅	—	3	2	no	—
198	C₂²×C₄×C₅	—	3	8	no	—
199	C₂²×C₄×C₅	—	12	2	no	—
200	C₂²×C₄×C₅	—	12	2	no	—
201	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
203	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
204	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
206	C₅×C₄⋊C₄	—	3	8	no	—
207	C₅×C₄⋊C₄	—	3	4	no	—
208	C₅×C₄⋊C₄	—	3	4	no	—
209	C₅×C₄⋊C₄	—	3	4	no	—
210	C₅×C₄⋊C₄	—	3	4	no	—
211	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	—
212	C₅×C₄⋊C₄	C₄×D₃	1	4	yes	complemented
213	C₅×C₂²⋊C₄	—	3	8	no	—
214	C₅×C₂²⋊C₄	—	3	4	no	—
215	C₅×C₂²⋊C₄	—	3	4	no	—
216	C₄²×C₅	—	3	8	no	—
217	C₄²×C₅	—	3	4	no	—
218	C₄²×C₅	—	4	2	no	—
219	C₄²×C₅	—	12	2	no	—
220	C₄²×C₅	—	12	2	no	—
221	C₄²×C₅	—	12	2	no	—
222	C₄²×C₅	C₄×D₃	1	4	yes	complemented
223	C₂×#117	—	3	1	no	—
224	C₂×#117	—	3	1	no	—
225	C₂²×C₄⋊C₄	—	3	1	no	—
226	C₄×C₄⋊C₄	—	3	1	no	—
227	C₄×C₄⋊C₄	—	3	1	no	—
228	C₄×C₄⋊C₄	—	3	2	no	—
229	C₄×C₄⋊C₄	—	3	1	no	—
230	C₄×C₄⋊C₄	—	3	2	no	—
231	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
232	C₄×C₂²⋊C₄	—	3	2	no	—
233	C₄×C₂²⋊C₄	—	3	2	no	—
234	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
235	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
237	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
238	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
240	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
241	C₂×C₅×D₃	—	2	2	no	—
242	C₂×C₅×D₃	—	2	2	no	—
243	C₂×C₅×D₃	—	2	2	no	—
244	C₂×C₅×D₃	—	2	2	no	—
245	C₂×C₅×D₃	—	2	2	no	—
246	C₂×C₅×D₃	—	2	2	no	—
247	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
248	C₃×C₄×C₅	—	2	4	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	2	4	no	—
252	C₃×C₄×C₅	C₂×C₄²	1	4	yes	—
253	C₅×Dic₃	—	2	4	no	—
254	C₅×Dic₃	—	2	2	no	—
255	C₅×Dic₃	—	2	2	no	—
256	C₅×Dic₃	—	2	4	no	—
257	C₅×Dic₃	C₂×C₄²	1	4	yes	—
258	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
261	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
262	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
263	C₂²×C₃×C₄	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	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
267	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
268	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₄×D₃	—	4	2	no	—
270	C₂×C₄×D₃	—	4	2	no	—
271	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
272	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
273	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
274	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
275	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	—
276	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
277	C₃×C₄²	—	4	2	no	—
278	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
279	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
280	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
281	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	—
282	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	—
283	C₄⋊Dic₃	C₂×C₄×C₅	1	4	yes	complemented
284	Dic₃⋊C₄	C₂×C₄×C₅	1	8	yes	—
285	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
286	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
287	C₄×Dic₃	—	4	2	no	—
288	C₄×Dic₃	—	4	2	no	—
289	C₄×Dic₃	—	4	2	no	—
290	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
291	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
292	C₂³×C₅	—	3	2	no	—
293	C₂³×C₅	—	3	2	no	—
294	C₂³×C₅	—	3	2	no	—
295	C₂³×C₅	—	6	1	no	—
296	C₂³×C₅	—	6	1	no	—
297	C₂³×C₅	—	6	1	no	—
298	C₂³×C₅	—	6	1	no	—
299	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	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	16	no	—
312	C₂×C₄×C₅	—	3	2	no	—
313	C₂×C₄×C₅	—	3	2	no	—
314	C₂×C₄×C₅	—	3	4	no	—
315	C₂×C₄×C₅	—	3	4	no	—
316	C₂×C₄×C₅	—	6	1	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	—	6	1	no	—
319	C₂×C₄×C₅	—	6	2	no	—
320	C₂×C₄×C₅	—	6	1	no	—
321	C₂×C₄×C₅	—	6	2	no	—
322	C₂×C₄×C₅	—	6	2	no	—
323	C₂×C₄×C₅	—	6	1	no	—
324	C₂×C₄×C₅	—	12	8	no	—
325	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
326	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
327	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
328	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
329	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
330	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
331	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
332	C₂³×C₄	—	3	1	no	—
333	C₂³×C₄	—	3	2	no	—
334	#117	—	3	8	no	—
335	#117	—	3	8	no	—
336	C₂×C₄⋊C₄	—	3	2	no	—
337	C₂×C₄⋊C₄	—	3	1	no	—
338	C₂×C₄⋊C₄	—	3	1	no	—
339	C₂×C₄⋊C₄	—	3	1	no	—
340	C₂×C₄⋊C₄	—	3	1	no	—
341	C₂×C₄⋊C₄	—	3	8	no	—
342	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
343	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
344	C₂×C₂²⋊C₄	—	3	1	no	—
345	C₂×C₂²⋊C₄	—	3	2	no	—
346	C₂×C₂²⋊C₄	—	3	1	no	—
347	C₂×C₄²	—	3	2	no	—
348	C₂×C₄²	—	3	1	no	—
349	C₂×C₄²	—	3	2	no	—
350	C₂×C₄²	—	3	2	no	—
351	C₂×C₄²	—	3	2	no	—
352	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
353	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
354	#95	—	3	2	no	—
355	#95	—	3	2	no	—
356	#95	—	3	2	no	—
357	#95	C₂×C₅×D₃	1	2	yes	—
358	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
359	C₂×C₃×C₅	#518	1	1	yes	characteristic
360	C₂×C₃×C₅	#519	1	1	yes	characteristic
361	C₂×C₃×C₅	#520	1	1	yes	characteristic
362	C₂×C₃×C₅	#520	1	1	yes	characteristic
363	C₂×C₃×C₅	#520	1	1	yes	characteristic
364	C₂×C₃×C₅	#520	1	1	yes	characteristic
365	C₅×D₃	—	2	4	no	—
366	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
367	C₂²×D₃	—	2	1	no	—
368	C₂²×D₃	—	2	1	no	—
369	C₂²×D₃	—	2	1	no	—
370	C₂²×D₃	—	2	1	no	—
371	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
372	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
373	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	2	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	2	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
383	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
384	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
385	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
386	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
387	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
388	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
389	C₂×Dic₃	—	2	1	no	—
390	C₂×Dic₃	—	2	1	no	—
391	C₂×Dic₃	—	2	2	no	—
392	C₂×Dic₃	—	2	2	no	—
393	C₂×Dic₃	—	2	2	no	—
394	C₂×Dic₃	—	2	1	no	—
395	C₂×Dic₃	—	2	2	no	—
396	C₂×Dic₃	—	2	1	no	—
397	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
398	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
399	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
400	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
401	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
402	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
403	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
404	C₄×D₃	—	4	8	no	—
405	C₄×D₃	C₄²×C₅	1	16	yes	complemented
406	C₂²×C₅	—	3	4	no	—
407	C₂²×C₅	—	6	2	no	—
408	C₂²×C₅	—	6	2	no	—
409	C₂²×C₅	—	6	2	no	—
410	C₂²×C₅	—	6	2	no	—
411	C₂²×C₅	—	6	2	no	—
412	C₂²×C₅	—	6	2	no	—
413	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
414	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
415	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
416	C₂²×C₅	#1004	1	1	yes	characteristic
417	C₂²×C₅	#1007	1	1	yes	characteristic
418	C₂²×C₅	#1009	1	1	yes	characteristic
419	C₂²×C₅	#1010	1	1	yes	characteristic
420	C₄×C₅	—	2	2	no	—
421	C₄×C₅	—	2	2	no	—
422	C₄×C₅	—	2	4	no	—
423	C₄×C₅	—	2	4	no	—
424	C₄×C₅	—	3	4	no	—
425	C₄×C₅	—	6	2	no	—
426	C₄×C₅	—	6	2	no	—
427	C₄×C₅	—	6	4	no	—
428	C₄×C₅	—	6	4	no	—
429	C₄×C₅	C₄²×D₃	1	4	yes	—
430	C₂⁴	—	3	1	no	—
431	C₂²×C₄	—	3	1	no	—
432	C₂²×C₄	—	3	4	no	—
433	C₂²×C₄	—	3	4	no	—
434	C₂²×C₄	—	3	4	no	—
435	C₂²×C₄	—	3	1	no	—
436	C₂²×C₄	—	3	2	no	—
437	C₂²×C₄	—	3	1	no	—
438	C₂²×C₄	—	3	2	no	—
439	C₂²×C₄	—	3	8	no	—
440	C₂²×C₄	—	12	2	no	—
441	C₂²×C₄	—	12	2	no	—
442	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
443	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
444	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
445	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
446	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
447	C₄⋊C₄	—	3	8	no	—
448	C₄⋊C₄	—	3	4	no	—
449	C₄⋊C₄	—	3	4	no	—
450	C₄⋊C₄	—	3	4	no	—
451	C₄⋊C₄	—	3	4	no	—
452	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	—
453	C₄⋊C₄	C₄×C₅×D₃	1	4	yes	complemented
454	C₂²⋊C₄	—	3	8	no	—
455	C₂²⋊C₄	—	3	4	no	—
456	C₂²⋊C₄	—	3	4	no	—
457	C₄²	—	3	8	no	—
458	C₄²	—	3	4	no	—
459	C₄²	—	4	2	no	—
460	C₄²	—	12	2	no	—
461	C₄²	—	12	2	no	—
462	C₄²	—	12	2	no	—
463	C₄²	C₄×C₅×D₃	1	4	yes	complemented
464	C₃×C₅	#2274	1	1	yes	characteristic, complemented, Hall
465	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
466	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
467	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
468	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
469	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
470	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
471	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
472	C₂×D₃	—	2	2	no	—
473	C₂×D₃	—	2	2	no	—
474	C₂×D₃	—	2	2	no	—
475	C₂×D₃	—	2	2	no	—
476	C₂×D₃	—	2	2	no	—
477	C₂×D₃	—	2	2	no	—
478	C₂×D₃	C₂×C₄²×C₅	1	4	yes	—
479	C₃×C₄	—	2	4	no	—
480	C₃×C₄	—	2	2	no	—
481	C₃×C₄	—	2	2	no	—
482	C₃×C₄	—	2	4	no	—
483	C₃×C₄	C₂×C₄²×C₅	1	4	yes	—
484	Dic₃	—	2	4	no	—
485	Dic₃	—	2	2	no	—
486	Dic₃	—	2	2	no	—
487	Dic₃	—	2	4	no	—
488	Dic₃	C₂×C₄²×C₅	1	4	yes	—
489	C₂×C₅	—	6	4	no	—
490	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
491	C₂×C₅	#5504	1	1	yes	characteristic
492	C₂×C₅	#5523	1	1	yes	characteristic
493	C₂×C₅	#5545	1	1	yes	characteristic
494	C₂×C₅	#5546	1	1	yes	characteristic
495	C₂×C₅	#5572	1	1	yes	characteristic
496	C₂×C₅	#5574	1	1	yes	characteristic
497	C₂³	—	3	2	no	—
498	C₂³	—	3	2	no	—
499	C₂³	—	3	2	no	—
500	C₂³	—	6	1	no	—
501	C₂³	—	6	1	no	—
502	C₂³	—	6	1	no	—
503	C₂³	—	6	1	no	—
504	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
505	C₂×C₄	—	2	1	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	2	no	—
513	C₂×C₄	—	3	2	no	—
514	C₂×C₄	—	3	2	no	—
515	C₂×C₄	—	3	2	no	—
516	C₂×C₄	—	3	16	no	—
517	C₂×C₄	—	3	2	no	—
518	C₂×C₄	—	3	2	no	—
519	C₂×C₄	—	3	4	no	—
520	C₂×C₄	—	3	4	no	—
521	C₂×C₄	—	6	1	no	—
522	C₂×C₄	—	6	2	no	—
523	C₂×C₄	—	6	1	no	—
524	C₂×C₄	—	6	2	no	—
525	C₂×C₄	—	6	1	no	—
526	C₂×C₄	—	6	2	no	—
527	C₂×C₄	—	6	2	no	—
528	C₂×C₄	—	6	1	no	—
529	C₂×C₄	—	12	8	no	—
530	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
531	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
532	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
533	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
534	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
535	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
536	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
537	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
538	C₂×C₃	C₅×#518	1	1	yes	characteristic
539	C₂×C₃	C₅×#519	1	1	yes	characteristic
540	C₂×C₃	C₅×#520	1	1	yes	characteristic
541	C₂×C₃	C₅×#520	1	1	yes	characteristic
542	C₂×C₃	C₅×#520	1	1	yes	characteristic
543	C₂×C₃	C₅×#520	1	1	yes	characteristic
544	D₃	—	2	4	no	—
545	C₅	#73750	1	1	yes	characteristic, direct product factor, Sylow
546	C₂²	—	3	4	no	—
547	C₂²	—	6	2	no	—
548	C₂²	—	6	2	no	—
549	C₂²	—	6	2	no	—
550	C₂²	—	6	2	no	—
551	C₂²	—	6	2	no	—
552	C₂²	—	6	2	no	—
553	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
554	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
555	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
556	C₂²	C₅×#1004	1	1	yes	characteristic
557	C₂²	C₅×#1007	1	1	yes	characteristic
558	C₂²	C₅×#1009	1	1	yes	characteristic
559	C₂²	C₅×#1010	1	1	yes	characteristic
560	C₄	—	2	2	no	—
561	C₄	—	2	2	no	—
562	C₄	—	2	4	no	—
563	C₄	—	2	4	no	—
564	C₄	—	3	4	no	—
565	C₄	—	6	2	no	—
566	C₄	—	6	2	no	—
567	C₄	—	6	4	no	—
568	C₄	—	6	4	no	—
569	C₄	C₄²×C₅×D₃	1	4	yes	—
570	C₃	C₅×#2274	1	1	yes	characteristic, complemented, Sylow
571	C₂	—	6	4	no	—
572	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
573	C₂	C₅×#5504	1	1	yes	characteristic
574	C₂	C₅×#5523	1	1	yes	characteristic
575	C₂	C₅×#5545	1	1	yes	characteristic
576	C₂	C₅×#5546	1	1	yes	characteristic
577	C₂	C₅×#5572	1	1	yes	characteristic
578	C₂	C₅×#5574	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2274
LCS	G ▷ C₂×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
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
5. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
6. C₅×Dic₃×C₄⋊C₄	C₂	semidirect
8. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
9. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
11. C₅×#4649	C₂	semidirect
32. C₅×#892	C₄	semidirect
33. C₅×D₃×C₄⋊C₄	C₄	semidirect
34. C₅×#872	C₄	semidirect
39. #73750	C₅	direct (N × H)
48. C₄×C₅×C₄⋊C₄	D₃	semidirect
69. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
71. C₃×C₄²×C₅	C₂×C₄	semidirect
76. C₅×C₄⋊Dic₃	C₂×C₄	semidirect
78. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
79. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
83. C₄×C₅×Dic₃	C₂×C₄	semidirect
84. C₄×C₅×Dic₃	C₂×C₄	semidirect
88. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
89. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
90. Dic₃×C₄⋊C₄	C₂×C₅	semidirect
92. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
93. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
95. #4649	C₂×C₅	semidirect
162. C₄×C₅×D₃	C₄²	semidirect
182. #892	C₄×C₅	semidirect
183. D₃×C₄⋊C₄	C₄×C₅	semidirect
184. #872	C₄×C₅	semidirect
212. C₅×C₄⋊C₄	C₄×D₃	semidirect
222. C₄²×C₅	C₄×D₃	semidirect
231. C₄×C₄⋊C₄	C₅×D₃	semidirect
276. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
278. C₃×C₄²	C₂×C₄×C₅	semidirect
283. C₄⋊Dic₃	C₂×C₄×C₅	semidirect
285. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
286. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
290. C₄×Dic₃	C₂×C₄×C₅	semidirect
291. C₄×Dic₃	C₂×C₄×C₅	semidirect
405. C₄×D₃	C₄²×C₅	semidirect
453. C₄⋊C₄	C₄×C₅×D₃	semidirect
463. C₄²	C₄×C₅×D₃	semidirect
464. C₃×C₅	#2274	semidirect
545. C₅	#73750	direct (N × H)
570. C₃	C₅×#2274	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#892	2
C₂×C₅×D₃×C₄⋊C₄	2
C₂×C₅×#872	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×Dic₃×C₄⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×C₄⋊Dic₃	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4666	2
C₅×#4649	2
C₅×#2274	3
#73750	5

Subgroups — C5×#73750 #14319660

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73750 #14319660