Subgroups — C₅×#73436 #14319711

Order 1920.

1560 conjugacy classes of subgroups.

The subgroup lattice has 568 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	C₂×C₅×#67⋊C₄	C₂	1	2	yes	maximal
3	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×Dic₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
6	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×Dic₃⋊C₄	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×#4649	C₂	1	1	yes	maximal, characteristic, complemented
11	C₅×#4648	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#2275	—	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	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	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	2	yes	—
28	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
29	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
30	C₅×#67⋊C₄	C₄	1	16	yes	complemented
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	1	yes	characteristic
33	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
34	C₅×C₃⋊#95	C₂²	1	2	yes	—
35	C₅×C₃⋊#95	C₂²	1	1	yes	characteristic
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	C₅×C₃⋊#95	C₂²	1	2	yes	—
38	#73436	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₄×C₅×D₄	—	3	1	no	—
40	C₂×C₄×C₅×D₄	—	3	2	no	—
41	C₄×C₅×C₄⋊C₄	—	3	1	no	—
42	C₄×C₅×C₄⋊C₄	—	3	2	no	—
43	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
44	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
45	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
46	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
47	C₅×#376	—	3	1	no	—
48	C₂×C₅×#95	—	3	1	no	—
49	C₂×C₅×#95	—	3	1	no	—
50	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
51	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	—	4	2	no	—
53	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂×C₅×#67	C₂×C₄	1	8	yes	—
59	C₂×C₅×#67	C₂×C₄	1	4	yes	—
60	C₂²×C₅×Dic₃	—	4	2	no	—
61	C₂²×C₅×Dic₃	—	4	2	no	—
62	C₂²×C₅×Dic₃	C₂×C₄	1	8	yes	complemented
63	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
64	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
65	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
66	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
67	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
68	C₂×C₄×C₅×D₃	—	4	2	no	—
69	C₂×C₄×C₅×D₃	—	4	2	no	—
70	C₂×C₄×C₅×D₃	—	4	2	no	—
71	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
72	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
73	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
74	C₃×C₄²×C₅	—	4	2	no	—
75	C₅×#217	C₂×C₄	1	4	yes	complemented
76	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
77	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
78	C₅×Dic₃⋊C₄	C₂×C₄	1	8	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	C₂×C₄	1	8	yes	complemented
83	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
84	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
85	C₂×#67⋊C₄	C₂×C₅	1	2	yes	—
86	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic, complemented
88	Dic₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
89	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
90	C₄×Dic₃⋊C₄	C₂×C₅	1	2	yes	complemented
91	#4666	C₂×C₅	1	1	yes	characteristic, complemented
92	D₃×#95	C₂×C₅	1	1	yes	characteristic, complemented
93	#4649	C₂×C₅	1	1	yes	characteristic, complemented
94	#4648	C₂×C₅	1	1	yes	characteristic, complemented
95	C₂²×C₅×D₄	—	3	1	no	—
96	C₂³×C₄×C₅	—	3	2	no	—
97	C₂³×C₄×C₅	—	3	1	no	—
98	C₂³×C₄×C₅	—	3	2	no	—
99	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
100	C₄×C₅×D₄	—	3	8	no	—
101	C₄×C₅×D₄	—	3	16	no	—
102	C₂×C₅×C₄⋊C₄	—	3	2	no	—
103	C₂×C₅×C₄⋊C₄	—	3	1	no	—
104	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
105	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
106	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
107	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
108	C₂×C₄²×C₅	—	3	1	no	—
109	C₂×C₄²×C₅	—	3	2	no	—
110	C₂×C₄²×C₅	—	3	2	no	—
111	C₂×C₄²×C₅	—	3	2	no	—
112	C₂×C₄²×C₅	C₂×D₃	1	2	yes	—
113	C₅×#95	—	3	1	no	—
114	C₅×#95	—	3	1	no	—
115	C₅×#95	—	3	2	no	—
116	C₅×#95	—	3	2	no	—
117	C₅×#95	—	3	2	no	—
118	C₅×#95	C₂×D₃	1	1	yes	characteristic
119	C₅×#95	C₂×D₃	1	1	yes	characteristic
120	#2275	—	3	1	no	Sylow
121	C₂³×C₃×C₅	—	2	1	no	—
122	C₂³×C₃×C₅	—	2	2	no	—
123	C₂³×C₃×C₅	—	2	1	no	—
124	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
125	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
126	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
127	C₂²×C₅×D₃	—	2	2	no	—
128	C₂²×C₅×D₃	—	2	1	no	—
129	C₂²×C₅×D₃	—	2	1	no	—
130	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
131	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	4	4	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	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
143	C₅×#67	C₄²	1	16	yes	complemented
144	C₂×C₅×Dic₃	—	2	1	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	—	2	2	no	—
149	C₂×C₅×Dic₃	—	2	2	no	—
150	C₂×C₅×Dic₃	—	2	1	no	—
151	C₂×C₅×Dic₃	—	4	8	no	—
152	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
153	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
154	C₂×C₅×Dic₃	C₂²×C₄	1	4	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	2	yes	—
158	C₄×C₅×D₃	—	4	8	no	—
159	C₄×C₅×D₃	—	4	4	no	—
160	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
161	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
162	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
163	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
164	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
165	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
166	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
167	C₂×#217	C₂²×C₅	1	1	yes	characteristic
168	C₄×#67	C₄×C₅	1	8	yes	complemented
169	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
170	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
172	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
174	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
175	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
176	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
177	#67⋊C₄	C₄×C₅	1	16	yes	complemented
178	C₃×#95	C₂²×C₅	1	1	yes	characteristic
179	C₃×#95	C₂²×C₅	1	1	yes	characteristic
180	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
181	C₃⋊#95	C₂²×C₅	1	2	yes	—
182	C₃⋊#95	C₂²×C₅	1	1	yes	characteristic
183	C₃⋊#95	C₂²×C₅	1	2	yes	—
184	C₃⋊#95	C₂²×C₅	1	2	yes	—
185	C₂⁴×C₅	—	3	1	no	—
186	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
187	C₂×C₅×D₄	—	3	4	no	—
188	C₂×C₅×D₄	—	3	8	no	—
189	C₂²×C₄×C₅	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	1	no	—
192	C₂²×C₄×C₅	—	3	2	no	—
193	C₂²×C₄×C₅	—	3	2	no	—
194	C₂²×C₄×C₅	—	3	8	no	—
195	C₂²×C₄×C₅	—	3	8	no	—
196	C₂²×C₄×C₅	—	3	4	no	—
197	C₂²×C₄×C₅	—	4	2	no	—
198	C₂²×C₄×C₅	—	12	2	no	—
199	C₂²×C₄×C₅	—	12	2	no	—
200	C₂²×C₄×C₅	—	12	2	no	—
201	C₂²×C₄×C₅	—	12	2	no	—
202	C₂²×C₄×C₅	—	12	2	no	—
203	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
204	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
205	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
206	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
207	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
208	C₅×C₄⋊C₄	—	3	4	no	—
209	C₅×C₄⋊C₄	—	3	8	no	—
210	C₅×C₂²⋊C₄	—	3	4	no	—
211	C₅×C₂²⋊C₄	—	3	4	no	—
212	C₅×C₂²⋊C₄	—	3	8	no	—
213	C₅×C₂²⋊C₄	C₄×D₃	1	8	yes	complemented
214	C₄²×C₅	—	3	4	no	—
215	C₄²×C₅	—	3	8	no	—
216	C₄²×C₅	—	4	2	no	—
217	C₄²×C₅	—	12	2	no	—
218	C₄²×C₅	—	12	2	no	—
219	C₂×C₄×D₄	—	3	1	no	—
220	C₂×C₄×D₄	—	3	2	no	—
221	C₄×C₄⋊C₄	—	3	2	no	—
222	C₄×C₄⋊C₄	—	3	1	no	—
223	C₄×C₂²⋊C₄	—	3	2	no	—
224	C₄×C₂²⋊C₄	—	3	2	no	—
225	C₄×C₂²⋊C₄	—	3	1	no	—
226	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
227	#376	—	3	1	no	—
228	C₂×#95	—	3	1	no	—
229	C₂×#95	—	3	1	no	—
230	C₂²×C₃×C₅	—	2	4	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	4	no	—
234	C₂²×C₃×C₅	C₂×C₄²	1	4	yes	—
235	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
236	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
237	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
238	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
239	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
240	C₂×C₅×D₃	—	2	2	no	—
241	C₂×C₅×D₃	—	2	4	no	—
242	C₂×C₅×D₃	—	2	2	no	—
243	C₂×C₅×D₃	—	2	4	no	—
244	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
245	C₃×C₄×C₅	—	2	2	no	—
246	C₃×C₄×C₅	—	2	4	no	—
247	C₃×C₄×C₅	—	2	2	no	—
248	C₃×C₄×C₅	—	2	4	no	—
249	C₅×Dic₃	—	2	4	no	—
250	C₅×Dic₃	—	2	2	no	—
251	C₅×Dic₃	—	2	4	no	—
252	C₅×Dic₃	—	2	2	no	—
253	C₅×Dic₃	C₂×C₄²	1	4	yes	—
254	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
255	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
256	C₂²×C₃×C₄	—	4	2	no	—
257	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
258	C₂²×C₃×C₄	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	C₂×#67	C₂×C₄×C₅	1	8	yes	—
263	C₂×#67	C₂×C₄×C₅	1	4	yes	—
264	C₂²×Dic₃	—	4	2	no	—
265	C₂²×Dic₃	—	4	2	no	—
266	C₂²×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
267	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
268	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
269	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
270	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
271	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₄×D₃	—	4	2	no	—
273	C₂×C₄×D₃	—	4	2	no	—
274	C₂×C₄×D₃	—	4	2	no	—
275	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
276	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
277	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
278	C₃×C₄²	—	4	2	no	—
279	#217	C₂×C₄×C₅	1	4	yes	complemented
280	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
281	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
282	Dic₃⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
283	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
284	C₄×Dic₃	—	4	2	no	—
285	C₄×Dic₃	—	4	2	no	—
286	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
287	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
288	C₂³×C₅	—	2	2	no	—
289	C₂³×C₅	—	2	1	no	—
290	C₂³×C₅	—	2	1	no	—
291	C₂³×C₅	—	3	2	no	—
292	C₂³×C₅	—	3	4	no	—
293	C₂³×C₅	—	6	2	no	—
294	C₂³×C₅	—	6	1	no	—
295	C₂³×C₅	—	6	1	no	—
296	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
297	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
298	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
299	C₅×D₄	—	3	16	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	3	2	no	—
307	C₂×C₄×C₅	—	3	4	no	—
308	C₂×C₄×C₅	—	3	2	no	—
309	C₂×C₄×C₅	—	3	4	no	—
310	C₂×C₄×C₅	—	3	2	no	—
311	C₂×C₄×C₅	—	3	4	no	—
312	C₂×C₄×C₅	—	4	4	no	—
313	C₂×C₄×C₅	—	6	2	no	—
314	C₂×C₄×C₅	—	6	2	no	—
315	C₂×C₄×C₅	—	6	2	no	—
316	C₂×C₄×C₅	—	6	1	no	—
317	C₂×C₄×C₅	—	6	2	no	—
318	C₂×C₄×C₅	—	6	2	no	—
319	C₂×C₄×C₅	—	6	1	no	—
320	C₂×C₄×C₅	—	12	4	no	—
321	C₂×C₄×C₅	—	12	8	no	—
322	C₂×C₄×C₅	—	12	8	no	—
323	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
324	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
325	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
326	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
327	C₂²×D₄	—	3	1	no	—
328	C₂³×C₄	—	3	2	no	—
329	C₂³×C₄	—	3	2	no	—
330	C₂³×C₄	—	3	1	no	—
331	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
332	C₄×D₄	—	3	8	no	—
333	C₄×D₄	—	3	16	no	—
334	C₂×C₄⋊C₄	—	3	1	no	—
335	C₂×C₄⋊C₄	—	3	2	no	—
336	C₂×C₂²⋊C₄	—	3	1	no	—
337	C₂×C₂²⋊C₄	—	3	1	no	—
338	C₂×C₂²⋊C₄	—	3	2	no	—
339	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
340	C₂×C₄²	—	3	2	no	—
341	C₂×C₄²	—	3	1	no	—
342	C₂×C₄²	—	3	2	no	—
343	C₂×C₄²	—	3	2	no	—
344	C₂×C₄²	C₂×C₅×D₃	1	2	yes	—
345	#95	—	3	1	no	—
346	#95	—	3	2	no	—
347	#95	—	3	2	no	—
348	#95	—	3	1	no	—
349	#95	—	3	2	no	—
350	#95	C₂×C₅×D₃	1	1	yes	characteristic
351	#95	C₂×C₅×D₃	1	1	yes	characteristic
352	C₂×C₃×C₅	—	2	4	no	—
353	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
354	C₂×C₃×C₅	#518	1	1	yes	characteristic
355	C₂×C₃×C₅	#518	1	2	yes	—
356	C₂×C₃×C₅	#520	1	1	yes	characteristic
357	C₂×C₃×C₅	#520	1	2	yes	—
358	C₅×D₃	—	2	4	no	—
359	C₂³×C₃	—	2	1	no	—
360	C₂³×C₃	—	2	2	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
363	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
364	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
365	C₂²×D₃	—	2	2	no	—
366	C₂²×D₃	—	2	1	no	—
367	C₂²×D₃	—	2	1	no	—
368	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
369	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	4	4	no	—
377	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
378	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
379	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
380	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
381	#67	C₄²×C₅	1	16	yes	complemented
382	C₂×Dic₃	—	2	1	no	—
383	C₂×Dic₃	—	2	2	no	—
384	C₂×Dic₃	—	2	2	no	—
385	C₂×Dic₃	—	2	2	no	—
386	C₂×Dic₃	—	2	2	no	—
387	C₂×Dic₃	—	2	2	no	—
388	C₂×Dic₃	—	2	1	no	—
389	C₂×Dic₃	—	4	8	no	—
390	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
391	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
392	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
393	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
394	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
395	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
396	C₄×D₃	—	4	8	no	—
397	C₄×D₃	—	4	4	no	—
398	C₂²×C₅	—	2	2	no	—
399	C₂²×C₅	—	2	2	no	—
400	C₂²×C₅	—	2	4	no	—
401	C₂²×C₅	—	2	4	no	—
402	C₂²×C₅	—	3	4	no	—
403	C₂²×C₅	—	6	2	no	—
404	C₂²×C₅	—	6	2	no	—
405	C₂²×C₅	—	6	4	no	—
406	C₂²×C₅	—	6	4	no	—
407	C₂²×C₅	C₄²×D₃	1	4	yes	—
408	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
409	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
410	C₂²×C₅	#1004	1	2	yes	—
411	C₂²×C₅	#1009	1	1	yes	characteristic
412	C₂²×C₅	#1010	1	1	yes	characteristic
413	C₄×C₅	—	2	2	no	—
414	C₄×C₅	—	2	2	no	—
415	C₄×C₅	—	2	4	no	—
416	C₄×C₅	—	2	4	no	—
417	C₄×C₅	—	3	4	no	—
418	C₄×C₅	—	6	2	no	—
419	C₄×C₅	—	6	2	no	—
420	C₄×C₅	—	6	4	no	—
421	C₄×C₅	—	6	4	no	—
422	C₂⁴	—	3	1	no	—
423	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
424	C₂×D₄	—	3	4	no	—
425	C₂×D₄	—	3	8	no	—
426	C₂²×C₄	—	3	1	no	—
427	C₂²×C₄	—	3	2	no	—
428	C₂²×C₄	—	3	1	no	—
429	C₂²×C₄	—	3	1	no	—
430	C₂²×C₄	—	3	2	no	—
431	C₂²×C₄	—	3	8	no	—
432	C₂²×C₄	—	3	8	no	—
433	C₂²×C₄	—	3	4	no	—
434	C₂²×C₄	—	4	2	no	—
435	C₂²×C₄	—	12	2	no	—
436	C₂²×C₄	—	12	2	no	—
437	C₂²×C₄	—	12	2	no	—
438	C₂²×C₄	—	12	2	no	—
439	C₂²×C₄	—	12	2	no	—
440	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
441	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
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	C₄⋊C₄	—	3	4	no	—
446	C₄⋊C₄	—	3	8	no	—
447	C₂²⋊C₄	—	3	4	no	—
448	C₂²⋊C₄	—	3	4	no	—
449	C₂²⋊C₄	—	3	8	no	—
450	C₂²⋊C₄	C₄×C₅×D₃	1	8	yes	complemented
451	C₄²	—	3	4	no	—
452	C₄²	—	3	8	no	—
453	C₄²	—	4	2	no	—
454	C₄²	—	12	2	no	—
455	C₄²	—	12	2	no	—
456	C₃×C₅	#2275	1	1	yes	characteristic, complemented, Hall
457	C₂²×C₃	—	2	4	no	—
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	4	no	—
461	C₂²×C₃	C₂×C₄²×C₅	1	4	yes	—
462	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
463	C₂²×C₃	C₂³×C₄×C₅	1	2	yes	—
464	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
465	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
466	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
467	C₂×D₃	—	2	2	no	—
468	C₂×D₃	—	2	4	no	—
469	C₂×D₃	—	2	2	no	—
470	C₂×D₃	—	2	4	no	—
471	C₂×D₃	C₂×C₄²×C₅	1	4	yes	—
472	C₃×C₄	—	2	2	no	—
473	C₃×C₄	—	2	4	no	—
474	C₃×C₄	—	2	2	no	—
475	C₃×C₄	—	2	4	no	—
476	Dic₃	—	2	4	no	—
477	Dic₃	—	2	2	no	—
478	Dic₃	—	2	4	no	—
479	Dic₃	—	2	2	no	—
480	Dic₃	C₂×C₄²×C₅	1	4	yes	—
481	C₂×C₅	—	2	4	no	—
482	C₂×C₅	—	6	4	no	—
483	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
484	C₂×C₅	#5486	1	1	yes	characteristic
485	C₂×C₅	#5523	1	1	yes	characteristic
486	C₂×C₅	#5545	1	2	yes	—
487	C₂×C₅	#5546	1	2	yes	—
488	C₂³	—	2	2	no	—
489	C₂³	—	2	1	no	—
490	C₂³	—	2	1	no	—
491	C₂³	—	3	2	no	—
492	C₂³	—	3	4	no	—
493	C₂³	—	6	2	no	—
494	C₂³	—	6	1	no	—
495	C₂³	—	6	1	no	—
496	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
497	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
498	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
499	D₄	—	3	16	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	3	2	no	—
507	C₂×C₄	—	3	4	no	—
508	C₂×C₄	—	3	2	no	—
509	C₂×C₄	—	3	4	no	—
510	C₂×C₄	—	3	2	no	—
511	C₂×C₄	—	3	4	no	—
512	C₂×C₄	—	4	4	no	—
513	C₂×C₄	—	6	2	no	—
514	C₂×C₄	—	6	2	no	—
515	C₂×C₄	—	6	2	no	—
516	C₂×C₄	—	6	1	no	—
517	C₂×C₄	—	6	2	no	—
518	C₂×C₄	—	6	2	no	—
519	C₂×C₄	—	6	1	no	—
520	C₂×C₄	—	12	4	no	—
521	C₂×C₄	—	12	8	no	—
522	C₂×C₄	—	12	8	no	—
523	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
524	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
525	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
526	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
527	C₂×C₃	—	2	4	no	—
528	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
529	C₂×C₃	C₅×#518	1	1	yes	characteristic
530	C₂×C₃	C₅×#518	1	2	yes	—
531	C₂×C₃	C₅×#520	1	1	yes	characteristic
532	C₂×C₃	C₅×#520	1	2	yes	—
533	D₃	—	2	4	no	—
534	C₅	#73436	1	1	yes	characteristic, direct product factor, Sylow
535	C₂²	—	2	2	no	—
536	C₂²	—	2	2	no	—
537	C₂²	—	2	4	no	—
538	C₂²	—	2	4	no	—
539	C₂²	—	3	4	no	—
540	C₂²	—	6	2	no	—
541	C₂²	—	6	2	no	—
542	C₂²	—	6	4	no	—
543	C₂²	—	6	4	no	—
544	C₂²	C₄²×C₅×D₃	1	4	yes	—
545	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
546	C₂²	C₂²×C₄×C₅×D₃	1	2	yes	—
547	C₂²	C₅×#1004	1	2	yes	—
548	C₂²	C₅×#1009	1	1	yes	characteristic
549	C₂²	C₅×#1010	1	1	yes	characteristic
550	C₄	—	2	2	no	—
551	C₄	—	2	2	no	—
552	C₄	—	2	4	no	—
553	C₄	—	2	4	no	—
554	C₄	—	3	4	no	—
555	C₄	—	6	2	no	—
556	C₄	—	6	2	no	—
557	C₄	—	6	4	no	—
558	C₄	—	6	4	no	—
559	C₃	C₅×#2275	1	1	yes	characteristic, complemented, Sylow
560	C₂	—	2	4	no	—
561	C₂	—	6	4	no	—
562	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
563	C₂	C₅×#5486	1	1	yes	characteristic
564	C₂	C₅×#5523	1	1	yes	characteristic
565	C₂	C₅×#5545	1	2	yes	—
566	C₂	C₅×#5546	1	2	yes	—

	subgroup	G/H
center	C₂³×C₅	C₂³×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₅×#2275
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂³×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
4. C₂×C₅×C₃⋊#95	C₂	semidirect
5. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
6. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
7. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
8. C₅×#4666	C₂	semidirect
9. C₅×D₃×#95	C₂	semidirect
10. C₅×#4649	C₂	semidirect
11. C₅×#4648	C₂	semidirect
21. C₄×C₅×#67	C₄	semidirect
30. C₅×#67⋊C₄	C₄	semidirect
38. #73436	C₅	direct (N × H)
46. C₄×C₅×C₂²⋊C₄	D₃	semidirect
53. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
62. C₂²×C₅×Dic₃	C₂×C₄	semidirect
71. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
72. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
73. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
75. C₅×#217	C₂×C₄	semidirect
76. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
77. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
78. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
79. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
82. C₄×C₅×Dic₃	C₂×C₄	semidirect
83. C₄×C₅×Dic₃	C₂×C₄	semidirect
86. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
87. C₂×C₃⋊#95	C₂×C₅	semidirect
88. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
89. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
90. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
91. #4666	C₂×C₅	semidirect
92. D₃×#95	C₂×C₅	semidirect
93. #4649	C₂×C₅	semidirect
94. #4648	C₂×C₅	semidirect
143. C₅×#67	C₄²	semidirect
168. C₄×#67	C₄×C₅	semidirect
177. #67⋊C₄	C₄×C₅	semidirect
203. C₂²×C₄×C₅	C₄×D₃	semidirect
213. C₅×C₂²⋊C₄	C₄×D₃	semidirect
226. C₄×C₂²⋊C₄	C₅×D₃	semidirect
257. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
266. C₂²×Dic₃	C₂×C₄×C₅	semidirect
275. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
276. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
277. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
279. #217	C₂×C₄×C₅	semidirect
280. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
281. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
282. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
283. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
286. C₄×Dic₃	C₂×C₄×C₅	semidirect
287. C₄×Dic₃	C₂×C₄×C₅	semidirect
381. #67	C₄²×C₅	semidirect
440. C₂²×C₄	C₄×C₅×D₃	semidirect
450. C₂²⋊C₄	C₄×C₅×D₃	semidirect
456. C₃×C₅	#2275	semidirect
534. C₅	#73436	direct (N × H)
559. C₃	C₅×#2275	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
C₂×C₅×#67⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₂×C₅×C₃⋊#95	2
C₅×Dic₃×C₂²⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4666	2
C₅×D₃×#95	2
C₅×#4649	2
C₅×#4648	2
C₅×#2275	3
#73436	5

Subgroups — C5×#73436 #14319711

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73436 #14319711