Subgroups — C₃×D₅×#534 #14480288

Order 1920.

3968 conjugacy classes of subgroups.

The subgroup lattice has 768 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×D₄×D₅	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#534	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#66138	C₂	1	2	yes	maximal, complemented
4	C₃×#65987	C₂	1	4	yes	maximal, complemented
5	C₃×D₅×#123	C₂	1	4	yes	maximal, complemented
6	C₃×#65939	C₂	1	4	yes	maximal, complemented
7	C₃×D₅×#121	C₂	1	4	yes	maximal, complemented
8	C₃×#65923	C₂	1	4	yes	maximal, complemented
9	C₃×D₅×#120	C₂	1	4	yes	maximal, complemented
10	C₃×#65827	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×D₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
12	D₅×#534	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
14	C₂⁴×C₃×D₅	C₂²	1	2	yes	complemented
15	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	complemented
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
17	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	complemented
18	C₂×C₃×D₄×D₅	—	2	16	no	—
19	C₂×C₃×D₄×D₅	C₂²	1	4	yes	—
20	C₂×C₃×D₄×D₅	C₂²	1	4	yes	complemented
21	C₂×C₃×D₄×D₅	C₂²	1	4	yes	complemented
22	C₂×C₃×D₄×D₅	C₂²	1	4	yes	complemented
23	C₂×C₃×D₄×D₅	C₂²	1	4	yes	complemented
24	C₂²×C₃×D₂₀	C₂²	1	2	yes	complemented
25	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
26	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	complemented
27	C₃×C₅×#123	C₂²	1	4	yes	complemented
28	C₃×C₅×#121	C₂²	1	4	yes	complemented
29	C₃×C₅×#120	C₂²	1	4	yes	complemented
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic, complemented
31	C₃×#4099	C₂²	1	4	yes	complemented
32	C₂×C₃×C₂²⋊Dic₅	C₂²	1	1	yes	characteristic, complemented
33	C₃×#4085	C₂²	1	8	yes	complemented
34	C₃×#4084	C₂²	1	4	yes	complemented
35	C₃×#4083	C₂²	1	8	yes	complemented
36	C₃×#4083	C₂²	1	4	yes	complemented
37	C₃×#4081	C₂²	1	4	yes	complemented
38	C₃×#4076	C₂²	1	4	yes	complemented
39	C₃×#4075	C₂²	1	4	yes	complemented
40	C₂×C₃×#685	C₂²	1	2	yes	complemented
41	C₃×#4041	C₂²	1	4	yes	complemented
42	C₃×#4040	C₂²	1	8	yes	complemented
43	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	complemented
44	C₃×#4032	C₂²	1	4	yes	complemented
45	C₃×#4030	C₂²	1	8	yes	complemented
46	C₃×#4029	C₂²	1	8	yes	complemented
47	C₃×#4028	C₂²	1	8	yes	complemented
48	C₃×#4028	C₂²	1	4	yes	complemented
49	C₃×D₅×C₂²⋊C₄	C₂²	1	8	yes	complemented
50	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
51	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
52	C₂×C₃×#534	—	5	1	no	maximal, Hall
53	C₂²×D₄×D₅	C₂×C₃	1	2	yes	complemented
54	C₅×#534	C₂×C₃	1	1	yes	characteristic, complemented
55	#66138	C₂×C₃	1	2	yes	complemented
56	#65987	C₂×C₃	1	4	yes	complemented
57	D₅×#123	C₂×C₃	1	4	yes	complemented
58	#65939	C₂×C₃	1	4	yes	complemented
59	D₅×#121	C₂×C₃	1	4	yes	complemented
60	#65923	C₂×C₃	1	4	yes	complemented
61	D₅×#120	C₂×C₃	1	4	yes	complemented
62	#65827	C₂×C₃	1	1	yes	characteristic, complemented
63	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
64	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
65	C₂⁴×C₃×C₅	C₂³	1	2	yes	complemented
66	C₂³×C₃×D₅	—	2	8	no	—
67	C₂³×C₃×D₅	—	4	4	no	—
68	C₂³×C₃×D₅	—	4	8	no	—
69	C₂³×C₃×D₅	D₄	1	8	yes	complemented
70	C₂³×C₃×D₅	C₂³	1	4	yes	—
71	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
72	C₂³×C₃×D₅	C₂³	1	2	yes	—
73	C₂³×C₃×D₅	C₂³	1	2	yes	—
74	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
75	C₂³×C₃×D₅	C₂³	1	2	yes	complemented
76	C₂³×C₃×D₅	C₂³	1	4	yes	complemented
77	C₂×C₃×C₅×D₄	—	2	8	no	—
78	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
79	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
80	C₂×C₃×C₅×D₄	C₂³	1	4	yes	complemented
81	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	complemented
82	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	complemented
83	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
84	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
85	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
86	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	—
87	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	complemented
88	C₂×C₃×C₂²⋊D₅	C₂³	1	4	yes	complemented
89	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	complemented
90	C₂²×C₃×Dic₅	C₂³	1	2	yes	complemented
91	C₂²×C₃×Dic₅	C₂³	1	2	yes	complemented
92	C₃×D₄×D₅	—	2	16	no	—
93	C₃×D₄×D₅	—	2	16	no	—
94	C₃×D₄×D₅	—	2	16	no	—
95	C₃×D₄×D₅	—	2	16	no	—
96	C₃×D₄×D₅	—	4	8	no	—
97	C₂×C₃×D₂₀	—	2	8	no	—
98	C₂×C₃×D₂₀	C₂³	1	4	yes	—
99	C₂×C₃×D₂₀	C₂³	1	4	yes	complemented
100	C₂×C₃×D₂₀	C₂³	1	4	yes	complemented
101	C₂×C₃×C₄×D₅	—	2	8	no	—
102	C₂×C₃×C₄×D₅	—	4	4	no	—
103	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
104	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
105	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
106	C₂×C₃×C₄×D₅	C₂³	1	4	yes	complemented
107	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	complemented
108	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	complemented
109	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	complemented
110	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	complemented
111	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	complemented
112	C₃×#685	C₂³	1	8	yes	complemented
113	C₃×#685	C₂³	1	8	yes	complemented
114	C₃×#685	C₂³	1	8	yes	complemented
115	C₃×C₄⋊Dic₅	C₂³	1	4	yes	complemented
116	C₃×#683	C₂³	1	8	yes	complemented
117	C₂³×C₃×D₄	—	5	2	no	—
118	C₃×#534	—	5	2	no	—
119	C₃×#534	—	5	4	no	—
120	C₃×#534	—	5	4	no	—
121	C₃×#534	—	5	4	no	—
122	C₃×#534	—	5	1	no	—
123	C₃×#534	D₅	1	1	yes	characteristic, direct product factor
124	C₂×C₃×#123	—	5	4	no	—
125	C₂×C₃×#121	—	5	4	no	—
126	C₂×C₃×#120	—	5	4	no	—
127	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
128	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
129	C₂⁴×D₅	C₂²×C₃	1	2	yes	complemented
130	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	complemented
131	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
132	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	complemented
133	C₂×D₄×D₅	—	2	16	no	—
134	C₂×D₄×D₅	C₂²×C₃	1	4	yes	—
135	C₂×D₄×D₅	C₂²×C₃	1	4	yes	complemented
136	C₂×D₄×D₅	C₂²×C₃	1	4	yes	complemented
137	C₂×D₄×D₅	C₂²×C₃	1	4	yes	complemented
138	C₂×D₄×D₅	C₂²×C₃	1	4	yes	complemented
139	C₂²×D₂₀	C₂²×C₃	1	2	yes	complemented
140	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
141	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	complemented
142	C₅×#123	C₂²×C₃	1	4	yes	complemented
143	C₅×#121	C₂²×C₃	1	4	yes	complemented
144	C₅×#120	C₂²×C₃	1	4	yes	complemented
145	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic, complemented
146	#4099	C₂²×C₃	1	4	yes	complemented
147	C₂×C₂²⋊Dic₅	C₂²×C₃	1	1	yes	characteristic, complemented
148	#4085	C₂²×C₃	1	8	yes	complemented
149	#4084	C₂²×C₃	1	4	yes	complemented
150	#4083	C₂²×C₃	1	8	yes	complemented
151	#4083	C₂²×C₃	1	4	yes	complemented
152	#4081	C₂²×C₃	1	4	yes	complemented
153	#4076	C₂²×C₃	1	4	yes	complemented
154	#4075	C₂²×C₃	1	4	yes	complemented
155	C₂×#685	C₂²×C₃	1	2	yes	complemented
156	#4041	C₂²×C₃	1	4	yes	complemented
157	#4040	C₂²×C₃	1	8	yes	complemented
158	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	complemented
159	#4032	C₂²×C₃	1	4	yes	complemented
160	#4030	C₂²×C₃	1	8	yes	complemented
161	#4029	C₂²×C₃	1	8	yes	complemented
162	#4028	C₂²×C₃	1	8	yes	complemented
163	#4028	C₂²×C₃	1	4	yes	complemented
164	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
165	D₅×C₂²⋊C₄	C₂²×C₃	1	8	yes	complemented
166	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
167	C₂×#534	—	5	1	no	Sylow
168	C₂³×C₃×C₅	—	2	4	no	—
169	C₂³×C₃×C₅	—	4	2	no	—
170	C₂³×C₃×C₅	—	4	4	no	—
171	C₂³×C₃×C₅	C₂×D₄	1	4	yes	complemented
172	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
173	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
174	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
175	C₂²×C₃×D₅	—	2	4	no	—
176	C₂²×C₃×D₅	—	2	8	no	—
177	C₂²×C₃×D₅	—	2	4	no	—
178	C₂²×C₃×D₅	—	2	8	no	—
179	C₂²×C₃×D₅	—	2	8	no	—
180	C₂²×C₃×D₅	—	2	16	no	—
181	C₂²×C₃×D₅	—	4	16	no	—
182	C₂²×C₃×D₅	—	4	4	no	—
183	C₂²×C₃×D₅	—	4	2	no	—
184	C₂²×C₃×D₅	—	4	8	no	—
185	C₂²×C₃×D₅	—	4	4	no	—
186	C₂²×C₃×D₅	—	4	32	no	—
187	C₂²×C₃×D₅	C₂×D₄	1	8	yes	—
188	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
189	C₂²×C₃×D₅	C₂×D₄	1	8	yes	complemented
190	C₂²×C₃×D₅	C₂×D₄	1	4	yes	complemented
191	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
192	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
193	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
194	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
195	C₃×C₅×D₄	—	2	8	no	—
196	C₃×C₅×D₄	—	2	8	no	—
197	C₃×C₅×D₄	—	4	4	no	—
198	C₂×C₃×C₄×C₅	—	2	4	no	—
199	C₂×C₃×C₄×C₅	—	4	2	no	—
200	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
201	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
202	C₃×C₂²⋊D₅	—	2	8	no	—
203	C₃×C₂²⋊D₅	—	2	8	no	—
204	C₃×C₂²⋊D₅	—	2	8	no	—
205	C₃×C₂²⋊D₅	—	2	8	no	—
206	C₃×C₂²⋊D₅	—	4	8	no	—
207	C₂×C₃×Dic₅	—	2	4	no	—
208	C₂×C₃×Dic₅	—	4	2	no	—
209	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
210	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
211	C₃×D₂₀	—	2	8	no	—
212	C₃×D₂₀	—	2	8	no	—
213	C₃×D₂₀	—	4	4	no	—
214	C₃×C₄×D₅	—	2	8	no	—
215	C₃×C₄×D₅	—	2	8	no	—
216	C₃×C₄×D₅	—	2	8	no	—
217	C₃×C₄×D₅	—	4	4	no	—
218	C₂⁵×C₃	—	5	1	no	—
219	C₂⁵×C₃	—	5	2	no	—
220	C₂²×C₃×D₄	—	5	2	no	—
221	C₂²×C₃×D₄	—	5	2	no	—
222	C₂²×C₃×D₄	—	5	4	no	—
223	C₂²×C₃×D₄	—	5	4	no	—
224	C₂²×C₃×D₄	—	5	4	no	—
225	C₂²×C₃×D₄	—	5	4	no	—
226	C₂²×C₃×D₄	—	5	4	no	—
227	C₂²×C₃×D₄	—	5	2	no	—
228	C₂²×C₃×D₄	—	10	16	no	—
229	C₂²×C₃×D₄	C₂×D₅	1	2	yes	complemented
230	C₂³×C₃×C₄	—	5	2	no	—
231	C₂³×C₃×C₄	—	5	2	no	—
232	C₃×#123	—	5	4	no	—
233	C₃×#123	—	5	4	no	—
234	C₃×#123	—	5	8	no	—
235	C₃×#123	—	5	8	no	—
236	C₃×#123	—	5	4	no	—
237	C₃×#123	C₂×D₅	1	4	yes	complemented
238	C₃×#121	—	5	4	no	—
239	C₃×#121	—	5	8	no	—
240	C₃×#121	—	5	4	no	—
241	C₃×#121	—	5	4	no	—
242	C₃×#121	—	5	8	no	—
243	C₃×#121	C₂×D₅	1	4	yes	complemented
244	C₃×#120	—	5	4	no	—
245	C₃×#120	—	5	4	no	—
246	C₃×#120	—	5	8	no	—
247	C₃×#120	—	5	8	no	—
248	C₃×#120	—	5	4	no	—
249	C₃×#120	C₂×D₅	1	4	yes	complemented
250	C₂×C₃×C₄⋊C₄	—	5	4	no	—
251	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
252	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
253	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
254	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
255	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
256	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	1	yes	characteristic, complemented
257	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
258	C₂⁴×C₅	C₂³×C₃	1	2	yes	complemented
259	C₂³×D₅	—	2	8	no	—
260	C₂³×D₅	—	4	4	no	—
261	C₂³×D₅	—	4	8	no	—
262	C₂³×D₅	C₃×D₄	1	8	yes	complemented
263	C₂³×D₅	C₂³×C₃	1	4	yes	—
264	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
265	C₂³×D₅	C₂³×C₃	1	2	yes	—
266	C₂³×D₅	C₂³×C₃	1	2	yes	—
267	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
268	C₂³×D₅	C₂³×C₃	1	2	yes	complemented
269	C₂³×D₅	C₂³×C₃	1	4	yes	complemented
270	C₂×C₅×D₄	—	2	8	no	—
271	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
272	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
273	C₂×C₅×D₄	C₂³×C₃	1	4	yes	complemented
274	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	complemented
275	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	complemented
276	C₂×C₂²⋊D₅	—	2	8	no	—
277	C₂×C₂²⋊D₅	—	2	8	no	—
278	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
279	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	—
280	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
281	C₂×C₂²⋊D₅	C₂³×C₃	1	4	yes	complemented
282	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	complemented
283	C₂²×Dic₅	C₂³×C₃	1	2	yes	complemented
284	C₂²×Dic₅	C₂³×C₃	1	2	yes	complemented
285	D₄×D₅	—	2	16	no	—
286	D₄×D₅	—	2	16	no	—
287	D₄×D₅	—	2	16	no	—
288	D₄×D₅	—	2	16	no	—
289	D₄×D₅	—	4	8	no	—
290	C₂×D₂₀	—	2	8	no	—
291	C₂×D₂₀	C₂³×C₃	1	4	yes	—
292	C₂×D₂₀	C₂³×C₃	1	4	yes	complemented
293	C₂×D₂₀	C₂³×C₃	1	4	yes	complemented
294	C₂×C₄×D₅	—	2	8	no	—
295	C₂×C₄×D₅	—	4	4	no	—
296	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
297	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
298	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
299	C₂×C₄×D₅	C₂³×C₃	1	4	yes	complemented
300	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	complemented
301	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	complemented
302	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	complemented
303	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	complemented
304	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	complemented
305	#685	C₂³×C₃	1	8	yes	complemented
306	#685	C₂³×C₃	1	8	yes	complemented
307	#685	C₂³×C₃	1	8	yes	complemented
308	C₄⋊Dic₅	C₂³×C₃	1	4	yes	complemented
309	#683	C₂³×C₃	1	8	yes	complemented
310	C₂³×D₄	—	5	2	no	—
311	#534	—	5	2	no	—
312	#534	—	5	4	no	—
313	#534	—	5	4	no	—
314	#534	—	5	4	no	—
315	#534	—	5	1	no	—
316	#534	C₃×D₅	1	1	yes	characteristic, direct product factor
317	C₂×#123	—	5	4	no	—
318	C₂×#121	—	5	4	no	—
319	C₂×#120	—	5	4	no	—
320	C₂²×C₂²⋊C₄	—	5	1	no	—
321	C₂²×C₃×C₅	—	2	2	no	—
322	C₂²×C₃×C₅	—	2	4	no	—
323	C₂²×C₃×C₅	—	2	4	no	—
324	C₂²×C₃×C₅	—	2	8	no	—
325	C₂²×C₃×C₅	—	4	4	no	—
326	C₂²×C₃×C₅	—	4	8	no	—
327	C₂²×C₃×C₅	C₂²×D₄	1	4	yes	—
328	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
329	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
330	C₂×C₃×D₅	—	2	2	no	—
331	C₂×C₃×D₅	—	2	4	no	—
332	C₂×C₃×D₅	—	2	16	no	—
333	C₂×C₃×D₅	—	2	8	no	—
334	C₂×C₃×D₅	—	2	4	no	—
335	C₂×C₃×D₅	—	2	8	no	—
336	C₂×C₃×D₅	—	4	4	no	—
337	C₂×C₃×D₅	—	4	8	no	—
338	C₂×C₃×D₅	—	4	16	no	—
339	C₂×C₃×D₅	—	4	8	no	—
340	C₂×C₃×D₅	—	4	16	no	—
341	C₂×C₃×D₅	C₂²×D₄	1	4	yes	—
342	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
343	C₂×C₃×D₅	C₂²×D₄	1	2	yes	—
344	C₂×C₃×D₅	H(5,𝔽₂)	1	4	yes	—
345	C₃×C₄×C₅	—	2	4	no	—
346	C₃×C₄×C₅	—	2	4	no	—
347	C₃×Dic₅	—	2	4	no	—
348	C₃×Dic₅	—	2	4	no	—
349	C₂⁴×C₃	—	5	2	no	—
350	C₂⁴×C₃	—	5	1	no	—
351	C₂⁴×C₃	—	5	8	no	—
352	C₂⁴×C₃	—	5	1	no	—
353	C₂⁴×C₃	—	5	2	no	—
354	C₂⁴×C₃	—	5	4	no	—
355	C₂⁴×C₃	—	5	4	no	—
356	C₂⁴×C₃	—	5	2	no	—
357	C₂⁴×C₃	—	10	8	no	—
358	C₂⁴×C₃	—	20	4	no	—
359	C₂⁴×C₃	—	20	8	no	—
360	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
361	C₂⁴×C₃	C₂²×D₅	1	2	yes	complemented
362	C₂×C₃×D₄	—	2	8	no	—
363	C₂×C₃×D₄	—	5	4	no	—
364	C₂×C₃×D₄	—	5	4	no	—
365	C₂×C₃×D₄	—	5	4	no	—
366	C₂×C₃×D₄	—	5	4	no	—
367	C₂×C₃×D₄	—	5	8	no	—
368	C₂×C₃×D₄	—	5	4	no	—
369	C₂×C₃×D₄	—	5	4	no	—
370	C₂×C₃×D₄	—	5	4	no	—
371	C₂×C₃×D₄	—	10	8	no	—
372	C₂×C₃×D₄	—	10	16	no	—
373	C₂×C₃×D₄	—	10	16	no	—
374	C₂×C₃×D₄	—	10	16	no	—
375	C₂×C₃×D₄	—	10	16	no	—
376	C₂×C₃×D₄	—	10	8	no	—
377	C₂×C₃×D₄	—	10	8	no	—
378	C₂×C₃×D₄	—	20	8	no	—
379	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
380	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
381	C₂×C₃×D₄	C₂²×D₅	1	4	yes	complemented
382	C₂²×C₃×C₄	—	5	2	no	—
383	C₂²×C₃×C₄	—	5	2	no	—
384	C₂²×C₃×C₄	—	5	4	no	—
385	C₂²×C₃×C₄	—	5	4	no	—
386	C₂²×C₃×C₄	—	5	4	no	—
387	C₂²×C₃×C₄	—	5	4	no	—
388	C₂²×C₃×C₄	—	10	8	no	—
389	C₂²×C₃×C₄	—	20	4	no	—
390	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	complemented
391	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	complemented
392	C₃×C₄⋊C₄	—	5	8	no	—
393	C₃×C₄⋊C₄	—	5	4	no	—
394	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	complemented
395	C₃×C₂²⋊C₄	—	5	4	no	—
396	C₃×C₂²⋊C₄	—	5	8	no	—
397	C₃×C₂²⋊C₄	—	5	8	no	—
398	C₃×C₂²⋊C₄	—	5	8	no	—
399	C₃×C₂²⋊C₄	—	5	8	no	—
400	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	complemented
401	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	complemented
402	C₂³×C₅	—	2	4	no	—
403	C₂³×C₅	—	4	2	no	—
404	C₂³×C₅	—	4	4	no	—
405	C₂³×C₅	C₂×C₃×D₄	1	4	yes	complemented
406	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
407	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
408	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
409	C₂²×D₅	—	2	4	no	—
410	C₂²×D₅	—	2	8	no	—
411	C₂²×D₅	—	2	4	no	—
412	C₂²×D₅	—	2	8	no	—
413	C₂²×D₅	—	2	8	no	—
414	C₂²×D₅	—	2	16	no	—
415	C₂²×D₅	—	4	16	no	—
416	C₂²×D₅	—	4	4	no	—
417	C₂²×D₅	—	4	2	no	—
418	C₂²×D₅	—	4	8	no	—
419	C₂²×D₅	—	4	4	no	—
420	C₂²×D₅	—	4	32	no	—
421	C₂²×D₅	C₂×C₃×D₄	1	8	yes	—
422	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
423	C₂²×D₅	C₂×C₃×D₄	1	8	yes	complemented
424	C₂²×D₅	C₂×C₃×D₄	1	4	yes	complemented
425	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
426	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
427	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
428	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
429	C₅×D₄	—	2	8	no	—
430	C₅×D₄	—	2	8	no	—
431	C₅×D₄	—	4	4	no	—
432	C₂×C₄×C₅	—	2	4	no	—
433	C₂×C₄×C₅	—	4	2	no	—
434	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
435	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
436	C₂²⋊D₅	—	2	8	no	—
437	C₂²⋊D₅	—	2	8	no	—
438	C₂²⋊D₅	—	2	8	no	—
439	C₂²⋊D₅	—	2	8	no	—
440	C₂²⋊D₅	—	4	8	no	—
441	C₂×Dic₅	—	2	4	no	—
442	C₂×Dic₅	—	4	2	no	—
443	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
444	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
445	D₂₀	—	2	8	no	—
446	D₂₀	—	2	8	no	—
447	D₂₀	—	4	4	no	—
448	C₄×D₅	—	2	8	no	—
449	C₄×D₅	—	2	8	no	—
450	C₄×D₅	—	2	8	no	—
451	C₄×D₅	—	4	4	no	—
452	C₂⁵	—	5	1	no	—
453	C₂⁵	—	5	2	no	—
454	C₂²×D₄	—	5	2	no	—
455	C₂²×D₄	—	5	2	no	—
456	C₂²×D₄	—	5	4	no	—
457	C₂²×D₄	—	5	4	no	—
458	C₂²×D₄	—	5	4	no	—
459	C₂²×D₄	—	5	4	no	—
460	C₂²×D₄	—	5	4	no	—
461	C₂²×D₄	—	5	2	no	—
462	C₂²×D₄	—	10	16	no	—
463	C₂²×D₄	C₂×C₃×D₅	1	2	yes	complemented
464	C₂³×C₄	—	5	2	no	—
465	C₂³×C₄	—	5	2	no	—
466	#123	—	5	4	no	—
467	#123	—	5	4	no	—
468	#123	—	5	8	no	—
469	#123	—	5	8	no	—
470	#123	—	5	4	no	—
471	#123	C₂×C₃×D₅	1	4	yes	complemented
472	#121	—	5	4	no	—
473	#121	—	5	8	no	—
474	#121	—	5	4	no	—
475	#121	—	5	4	no	—
476	#121	—	5	8	no	—
477	#121	C₂×C₃×D₅	1	4	yes	complemented
478	#120	—	5	4	no	—
479	#120	—	5	4	no	—
480	#120	—	5	8	no	—
481	#120	—	5	8	no	—
482	#120	—	5	4	no	—
483	#120	C₂×C₃×D₅	1	4	yes	complemented
484	C₂×C₄⋊C₄	—	5	4	no	—
485	C₂×C₂²⋊C₄	—	5	1	no	—
486	C₂×C₂²⋊C₄	—	5	2	no	—
487	C₂×C₂²⋊C₄	—	5	4	no	—
488	C₂×C₂²⋊C₄	—	5	4	no	—
489	C₂×C₂²⋊C₄	—	5	8	no	—
490	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic, complemented
491	C₂×C₃×C₅	—	2	4	no	—
492	C₂×C₃×C₅	—	2	2	no	—
493	C₂×C₃×C₅	—	4	4	no	—
494	C₂×C₃×C₅	C₂³×D₄	1	1	yes	characteristic
495	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	2	yes	—
496	C₃×D₅	—	2	4	no	—
497	C₃×D₅	—	2	2	no	—
498	C₃×D₅	—	4	4	no	—
499	C₃×D₅	#534	1	4	yes	direct product factor
500	C₂³×C₃	—	2	4	no	—
501	C₂³×C₃	—	4	2	no	—
502	C₂³×C₃	—	4	4	no	—
503	C₂³×C₃	—	5	1	no	—
504	C₂³×C₃	—	5	8	no	—
505	C₂³×C₃	—	5	4	no	—
506	C₂³×C₃	—	5	2	no	—
507	C₂³×C₃	—	5	1	no	—
508	C₂³×C₃	—	5	4	no	—
509	C₂³×C₃	—	5	8	no	—
510	C₂³×C₃	—	5	4	no	—
511	C₂³×C₃	—	10	4	no	—
512	C₂³×C₃	—	10	8	no	—
513	C₂³×C₃	—	10	8	no	—
514	C₂³×C₃	—	10	8	no	—
515	C₂³×C₃	—	10	16	no	—
516	C₂³×C₃	—	10	4	no	—
517	C₂³×C₃	—	20	2	no	—
518	C₂³×C₃	—	20	4	no	—
519	C₂³×C₃	—	20	4	no	—
520	C₂³×C₃	—	20	8	no	—
521	C₂³×C₃	—	20	16	no	—
522	C₂³×C₃	—	20	32	no	—
523	C₂³×C₃	D₄×D₅	1	4	yes	complemented
524	C₂³×C₃	C₂³×D₅	1	4	yes	—
525	C₂³×C₃	C₂³×D₅	1	2	yes	—
526	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
527	C₃×D₄	—	2	8	no	—
528	C₃×D₄	—	2	8	no	—
529	C₃×D₄	—	4	4	no	—
530	C₃×D₄	—	10	8	no	—
531	C₃×D₄	—	10	8	no	—
532	C₃×D₄	—	10	8	no	—
533	C₃×D₄	—	10	8	no	—
534	C₃×D₄	—	10	8	no	—
535	C₃×D₄	—	10	8	no	—
536	C₃×D₄	—	20	4	no	—
537	C₃×D₄	—	20	8	no	—
538	C₂×C₃×C₄	—	2	4	no	—
539	C₂×C₃×C₄	—	4	2	no	—
540	C₂×C₃×C₄	—	5	4	no	—
541	C₂×C₃×C₄	—	5	4	no	—
542	C₂×C₃×C₄	—	10	8	no	—
543	C₂×C₃×C₄	—	10	8	no	—
544	C₂×C₃×C₄	—	10	8	no	—
545	C₂×C₃×C₄	—	10	4	no	—
546	C₂×C₃×C₄	—	20	4	no	—
547	C₂×C₃×C₄	—	20	2	no	—
548	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
549	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
550	C₂²×C₅	—	2	2	no	—
551	C₂²×C₅	—	2	4	no	—
552	C₂²×C₅	—	2	4	no	—
553	C₂²×C₅	—	2	8	no	—
554	C₂²×C₅	—	4	4	no	—
555	C₂²×C₅	—	4	8	no	—
556	C₂²×C₅	C₂²×C₃×D₄	1	4	yes	—
557	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
558	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
559	C₂×D₅	—	2	2	no	—
560	C₂×D₅	—	2	4	no	—
561	C₂×D₅	—	2	16	no	—
562	C₂×D₅	—	2	8	no	—
563	C₂×D₅	—	2	4	no	—
564	C₂×D₅	—	2	8	no	—
565	C₂×D₅	—	4	4	no	—
566	C₂×D₅	—	4	8	no	—
567	C₂×D₅	—	4	16	no	—
568	C₂×D₅	—	4	8	no	—
569	C₂×D₅	—	4	16	no	—
570	C₂×D₅	C₂²×C₃×D₄	1	4	yes	—
571	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
572	C₂×D₅	C₂²×C₃×D₄	1	2	yes	—
573	C₂×D₅	C₃×H(5,𝔽₂)	1	4	yes	—
574	C₄×C₅	—	2	4	no	—
575	C₄×C₅	—	2	4	no	—
576	Dic₅	—	2	4	no	—
577	Dic₅	—	2	4	no	—
578	C₂⁴	—	5	2	no	—
579	C₂⁴	—	5	1	no	—
580	C₂⁴	—	5	8	no	—
581	C₂⁴	—	5	1	no	—
582	C₂⁴	—	5	2	no	—
583	C₂⁴	—	5	4	no	—
584	C₂⁴	—	5	4	no	—
585	C₂⁴	—	5	2	no	—
586	C₂⁴	—	10	8	no	—
587	C₂⁴	—	20	4	no	—
588	C₂⁴	—	20	8	no	—
589	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
590	C₂⁴	C₂²×C₃×D₅	1	2	yes	complemented
591	C₂×D₄	—	2	8	no	—
592	C₂×D₄	—	5	4	no	—
593	C₂×D₄	—	5	4	no	—
594	C₂×D₄	—	5	4	no	—
595	C₂×D₄	—	5	4	no	—
596	C₂×D₄	—	5	8	no	—
597	C₂×D₄	—	5	4	no	—
598	C₂×D₄	—	5	4	no	—
599	C₂×D₄	—	5	4	no	—
600	C₂×D₄	—	10	8	no	—
601	C₂×D₄	—	10	16	no	—
602	C₂×D₄	—	10	16	no	—
603	C₂×D₄	—	10	16	no	—
604	C₂×D₄	—	10	16	no	—
605	C₂×D₄	—	10	8	no	—
606	C₂×D₄	—	10	8	no	—
607	C₂×D₄	—	20	8	no	—
608	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
609	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
610	C₂×D₄	C₂²×C₃×D₅	1	4	yes	complemented
611	C₂²×C₄	—	5	2	no	—
612	C₂²×C₄	—	5	2	no	—
613	C₂²×C₄	—	5	4	no	—
614	C₂²×C₄	—	5	4	no	—
615	C₂²×C₄	—	5	4	no	—
616	C₂²×C₄	—	5	4	no	—
617	C₂²×C₄	—	10	8	no	—
618	C₂²×C₄	—	20	4	no	—
619	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	complemented
620	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	complemented
621	C₄⋊C₄	—	5	8	no	—
622	C₄⋊C₄	—	5	4	no	—
623	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
624	C₂²⋊C₄	—	5	4	no	—
625	C₂²⋊C₄	—	5	8	no	—
626	C₂²⋊C₄	—	5	8	no	—
627	C₂²⋊C₄	—	5	8	no	—
628	C₂²⋊C₄	—	5	8	no	—
629	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	complemented
630	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	complemented
631	C₃×C₅	C₂×#534	1	1	yes	characteristic, complemented, Hall
632	C₂²×C₃	—	2	2	no	—
633	C₂²×C₃	—	2	4	no	—
634	C₂²×C₃	—	2	4	no	—
635	C₂²×C₃	—	2	8	no	—
636	C₂²×C₃	—	4	4	no	—
637	C₂²×C₃	—	4	8	no	—
638	C₂²×C₃	—	5	2	no	—
639	C₂²×C₃	—	5	4	no	—
640	C₂²×C₃	—	5	4	no	—
641	C₂²×C₃	—	5	2	no	—
642	C₂²×C₃	—	10	8	no	—
643	C₂²×C₃	—	10	16	no	—
644	C₂²×C₃	—	10	2	no	—
645	C₂²×C₃	—	10	4	no	—
646	C₂²×C₃	—	10	4	no	—
647	C₂²×C₃	—	10	8	no	—
648	C₂²×C₃	—	20	8	no	—
649	C₂²×C₃	—	20	4	no	—
650	C₂²×C₃	—	20	8	no	—
651	C₂²×C₃	—	20	16	no	—
652	C₂²×C₃	—	20	16	no	—
653	C₂²×C₃	C₂×D₄×D₅	1	4	yes	—
654	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
655	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
656	C₃×C₄	—	2	4	no	—
657	C₃×C₄	—	2	4	no	—
658	C₃×C₄	—	10	4	no	—
659	C₃×C₄	—	10	4	no	—
660	C₂×C₅	—	2	4	no	—
661	C₂×C₅	—	2	2	no	—
662	C₂×C₅	—	4	4	no	—
663	C₂×C₅	C₂³×C₃×D₄	1	1	yes	characteristic
664	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	2	yes	—
665	D₅	—	2	4	no	—
666	D₅	—	2	2	no	—
667	D₅	—	4	4	no	—
668	D₅	C₃×#534	1	4	yes	direct product factor
669	C₂³	—	2	4	no	—
670	C₂³	—	4	2	no	—
671	C₂³	—	4	4	no	—
672	C₂³	—	5	1	no	—
673	C₂³	—	5	8	no	—
674	C₂³	—	5	4	no	—
675	C₂³	—	5	2	no	—
676	C₂³	—	5	1	no	—
677	C₂³	—	5	4	no	—
678	C₂³	—	5	8	no	—
679	C₂³	—	5	4	no	—
680	C₂³	—	10	4	no	—
681	C₂³	—	10	8	no	—
682	C₂³	—	10	8	no	—
683	C₂³	—	10	8	no	—
684	C₂³	—	10	16	no	—
685	C₂³	—	10	4	no	—
686	C₂³	—	20	2	no	—
687	C₂³	—	20	4	no	—
688	C₂³	—	20	4	no	—
689	C₂³	—	20	8	no	—
690	C₂³	—	20	16	no	—
691	C₂³	—	20	32	no	—
692	C₂³	C₃×D₄×D₅	1	4	yes	complemented
693	C₂³	C₂³×C₃×D₅	1	4	yes	—
694	C₂³	C₂³×C₃×D₅	1	2	yes	—
695	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
696	D₄	—	2	8	no	—
697	D₄	—	2	8	no	—
698	D₄	—	4	4	no	—
699	D₄	—	10	8	no	—
700	D₄	—	10	8	no	—
701	D₄	—	10	8	no	—
702	D₄	—	10	8	no	—
703	D₄	—	10	8	no	—
704	D₄	—	10	8	no	—
705	D₄	—	20	4	no	—
706	D₄	—	20	8	no	—
707	C₂×C₄	—	2	4	no	—
708	C₂×C₄	—	4	2	no	—
709	C₂×C₄	—	5	4	no	—
710	C₂×C₄	—	5	4	no	—
711	C₂×C₄	—	10	8	no	—
712	C₂×C₄	—	10	8	no	—
713	C₂×C₄	—	10	8	no	—
714	C₂×C₄	—	10	4	no	—
715	C₂×C₄	—	20	4	no	—
716	C₂×C₄	—	20	2	no	—
717	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
718	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
719	C₂×C₃	—	2	4	no	—
720	C₂×C₃	—	2	2	no	—
721	C₂×C₃	—	4	4	no	—
722	C₂×C₃	—	5	4	no	—
723	C₂×C₃	—	10	4	no	—
724	C₂×C₃	—	10	2	no	—
725	C₂×C₃	—	20	4	no	—
726	C₂×C₃	C₂²×D₄×D₅	1	1	yes	characteristic
727	C₂×C₃	D₅×H(5,𝔽₂)	1	2	yes	—
728	C₅	C₂×C₃×#534	1	1	yes	characteristic, complemented, Sylow
729	C₂²	—	2	2	no	—
730	C₂²	—	2	4	no	—
731	C₂²	—	2	4	no	—
732	C₂²	—	2	8	no	—
733	C₂²	—	4	4	no	—
734	C₂²	—	4	8	no	—
735	C₂²	—	5	2	no	—
736	C₂²	—	5	4	no	—
737	C₂²	—	5	4	no	—
738	C₂²	—	5	2	no	—
739	C₂²	—	10	16	no	—
740	C₂²	—	10	8	no	—
741	C₂²	—	10	2	no	—
742	C₂²	—	10	4	no	—
743	C₂²	—	10	4	no	—
744	C₂²	—	10	8	no	—
745	C₂²	—	20	8	no	—
746	C₂²	—	20	4	no	—
747	C₂²	—	20	8	no	—
748	C₂²	—	20	16	no	—
749	C₂²	—	20	16	no	—
750	C₂²	C₂×C₃×D₄×D₅	1	4	yes	—
751	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
752	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
753	C₄	—	2	4	no	—
754	C₄	—	2	4	no	—
755	C₄	—	10	4	no	—
756	C₄	—	10	4	no	—
757	C₃	D₅×#534	1	1	yes	characteristic, direct product factor, Sylow
758	C₂	—	2	4	no	—
759	C₂	—	2	2	no	—
760	C₂	—	4	4	no	—
761	C₂	—	5	4	no	—
762	C₂	—	10	4	no	—
763	C₂	—	10	2	no	—
764	C₂	—	20	4	no	—
765	C₂	C₂²×C₃×D₄×D₅	1	1	yes	characteristic
766	C₂	C₃×D₅×H(5,𝔽₂)	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#534	C₂
socle	C₂²×C₃×C₅	C₂⁵
hypercenter	C₃×#534	D₅
hypocenter	C₅	C₂×C₃×#534
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#534

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×D₄×D₅	C₂	semidirect
2. C₃×C₅×#534	C₂	semidirect
3. C₃×#66138	C₂	semidirect
4. C₃×#65987	C₂	semidirect
5. C₃×D₅×#123	C₂	semidirect
6. C₃×#65939	C₂	semidirect
7. C₃×D₅×#121	C₂	semidirect
8. C₃×#65923	C₂	semidirect
9. C₃×D₅×#120	C₂	semidirect
10. C₃×#65827	C₂	semidirect
11. C₂×C₃×D₅×C₂²⋊C₄	C₂	semidirect
12. D₅×#534	C₃	direct (N × H)
14. C₂⁴×C₃×D₅	C₂²	semidirect
15. C₂²×C₃×C₅×D₄	C₂²	semidirect
16. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
17. C₂²×C₃×C₂²⋊D₅	C₂²	semidirect
20. C₂×C₃×D₄×D₅	C₂²	semidirect
21. C₂×C₃×D₄×D₅	C₂²	semidirect
22. C₂×C₃×D₄×D₅	C₂²	semidirect
23. C₂×C₃×D₄×D₅	C₂²	semidirect
24. C₂²×C₃×D₂₀	C₂²	semidirect
25. C₂²×C₃×C₄×D₅	C₂²	semidirect
26. C₂²×C₃×C₄×D₅	C₂²	semidirect
27. C₃×C₅×#123	C₂²	semidirect
28. C₃×C₅×#121	C₂²	semidirect
29. C₃×C₅×#120	C₂²	semidirect
30. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
31. C₃×#4099	C₂²	semidirect
32. C₂×C₃×C₂²⋊Dic₅	C₂²	semidirect
33. C₃×#4085	C₂²	semidirect
34. C₃×#4084	C₂²	semidirect
35. C₃×#4083	C₂²	semidirect
36. C₃×#4083	C₂²	semidirect
37. C₃×#4081	C₂²	semidirect
38. C₃×#4076	C₂²	semidirect
39. C₃×#4075	C₂²	semidirect
40. C₂×C₃×#685	C₂²	semidirect
41. C₃×#4041	C₂²	semidirect
42. C₃×#4040	C₂²	semidirect
43. C₃×D₅×C₄⋊C₄	C₂²	semidirect
44. C₃×#4032	C₂²	semidirect
45. C₃×#4030	C₂²	semidirect
46. C₃×#4029	C₂²	semidirect
47. C₃×#4028	C₂²	semidirect
48. C₃×#4028	C₂²	semidirect
49. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
50. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
51. C₃×D₅×C₂²⋊C₄	C₂²	semidirect
53. C₂²×D₄×D₅	C₂×C₃	semidirect
54. C₅×#534	C₂×C₃	semidirect
55. #66138	C₂×C₃	semidirect
56. #65987	C₂×C₃	semidirect
57. D₅×#123	C₂×C₃	semidirect
58. #65939	C₂×C₃	semidirect
59. D₅×#121	C₂×C₃	semidirect
60. #65923	C₂×C₃	semidirect
61. D₅×#120	C₂×C₃	semidirect
62. #65827	C₂×C₃	semidirect
63. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
65. C₂⁴×C₃×C₅	C₂³	semidirect
69. C₂³×C₃×D₅	D₄	semidirect
75. C₂³×C₃×D₅	C₂³	semidirect
76. C₂³×C₃×D₅	C₂³	semidirect
79. C₂×C₃×C₅×D₄	C₂³	semidirect
80. C₂×C₃×C₅×D₄	C₂³	semidirect
81. C₂²×C₃×C₄×C₅	C₂³	semidirect
82. C₂²×C₃×C₄×C₅	C₂³	semidirect
87. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
88. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
89. C₂×C₃×C₂²⋊D₅	C₂³	semidirect
90. C₂²×C₃×Dic₅	C₂³	semidirect
91. C₂²×C₃×Dic₅	C₂³	semidirect
99. C₂×C₃×D₂₀	C₂³	semidirect
100. C₂×C₃×D₂₀	C₂³	semidirect
105. C₂×C₃×C₄×D₅	C₂³	semidirect
106. C₂×C₃×C₄×D₅	C₂³	semidirect
107. C₃×C₅×C₄⋊C₄	C₂³	semidirect
108. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
109. C₃×C₅×C₂²⋊C₄	C₂³	semidirect
110. C₃×C₂²⋊Dic₅	C₂³	semidirect
111. C₃×C₂²⋊Dic₅	C₂³	semidirect
112. C₃×#685	C₂³	semidirect
113. C₃×#685	C₂³	semidirect
114. C₃×#685	C₂³	semidirect
115. C₃×C₄⋊Dic₅	C₂³	semidirect
116. C₃×#683	C₂³	semidirect
123. C₃×#534	D₅	direct (N × H)
129. C₂⁴×D₅	C₂²×C₃	semidirect
130. C₂²×C₅×D₄	C₂²×C₃	semidirect
131. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
132. C₂²×C₂²⋊D₅	C₂²×C₃	semidirect
135. C₂×D₄×D₅	C₂²×C₃	semidirect
136. C₂×D₄×D₅	C₂²×C₃	semidirect
137. C₂×D₄×D₅	C₂²×C₃	semidirect
138. C₂×D₄×D₅	C₂²×C₃	semidirect
139. C₂²×D₂₀	C₂²×C₃	semidirect
140. C₂²×C₄×D₅	C₂²×C₃	semidirect
141. C₂²×C₄×D₅	C₂²×C₃	semidirect
142. C₅×#123	C₂²×C₃	semidirect
143. C₅×#121	C₂²×C₃	semidirect
144. C₅×#120	C₂²×C₃	semidirect
145. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
146. #4099	C₂²×C₃	semidirect
147. C₂×C₂²⋊Dic₅	C₂²×C₃	semidirect
148. #4085	C₂²×C₃	semidirect
149. #4084	C₂²×C₃	semidirect
150. #4083	C₂²×C₃	semidirect
151. #4083	C₂²×C₃	semidirect
152. #4081	C₂²×C₃	semidirect
153. #4076	C₂²×C₃	semidirect
154. #4075	C₂²×C₃	semidirect
155. C₂×#685	C₂²×C₃	semidirect
156. #4041	C₂²×C₃	semidirect
157. #4040	C₂²×C₃	semidirect
158. D₅×C₄⋊C₄	C₂²×C₃	semidirect
159. #4032	C₂²×C₃	semidirect
160. #4030	C₂²×C₃	semidirect
161. #4029	C₂²×C₃	semidirect
162. #4028	C₂²×C₃	semidirect
163. #4028	C₂²×C₃	semidirect
164. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
165. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
166. D₅×C₂²⋊C₄	C₂²×C₃	semidirect
171. C₂³×C₃×C₅	C₂×D₄	semidirect
189. C₂²×C₃×D₅	C₂×D₄	semidirect
190. C₂²×C₃×D₅	C₂×D₄	semidirect
229. C₂²×C₃×D₄	C₂×D₅	semidirect
237. C₃×#123	C₂×D₅	semidirect
243. C₃×#121	C₂×D₅	semidirect
249. C₃×#120	C₂×D₅	semidirect
256. C₂×C₃×C₂²⋊C₄	C₂×D₅	semidirect
258. C₂⁴×C₅	C₂³×C₃	semidirect
262. C₂³×D₅	C₃×D₄	semidirect
268. C₂³×D₅	C₂³×C₃	semidirect
269. C₂³×D₅	C₂³×C₃	semidirect
272. C₂×C₅×D₄	C₂³×C₃	semidirect
273. C₂×C₅×D₄	C₂³×C₃	semidirect
274. C₂²×C₄×C₅	C₂³×C₃	semidirect
275. C₂²×C₄×C₅	C₂³×C₃	semidirect
280. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
281. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
282. C₂×C₂²⋊D₅	C₂³×C₃	semidirect
283. C₂²×Dic₅	C₂³×C₃	semidirect
284. C₂²×Dic₅	C₂³×C₃	semidirect
292. C₂×D₂₀	C₂³×C₃	semidirect
293. C₂×D₂₀	C₂³×C₃	semidirect
298. C₂×C₄×D₅	C₂³×C₃	semidirect
299. C₂×C₄×D₅	C₂³×C₃	semidirect
300. C₅×C₄⋊C₄	C₂³×C₃	semidirect
301. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
302. C₅×C₂²⋊C₄	C₂³×C₃	semidirect
303. C₂²⋊Dic₅	C₂³×C₃	semidirect
304. C₂²⋊Dic₅	C₂³×C₃	semidirect
305. #685	C₂³×C₃	semidirect
306. #685	C₂³×C₃	semidirect
307. #685	C₂³×C₃	semidirect
308. C₄⋊Dic₅	C₂³×C₃	semidirect
309. #683	C₂³×C₃	semidirect
316. #534	C₃×D₅	direct (N × H)
361. C₂⁴×C₃	C₂²×D₅	semidirect
380. C₂×C₃×D₄	C₂²×D₅	semidirect
381. C₂×C₃×D₄	C₂²×D₅	semidirect
390. C₂²×C₃×C₄	C₂²×D₅	semidirect
391. C₂²×C₃×C₄	C₂²×D₅	semidirect
394. C₃×C₄⋊C₄	C₂²×D₅	semidirect
400. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
401. C₃×C₂²⋊C₄	C₂²×D₅	semidirect
405. C₂³×C₅	C₂×C₃×D₄	semidirect
423. C₂²×D₅	C₂×C₃×D₄	semidirect
424. C₂²×D₅	C₂×C₃×D₄	semidirect
463. C₂²×D₄	C₂×C₃×D₅	semidirect
471. #123	C₂×C₃×D₅	semidirect
477. #121	C₂×C₃×D₅	semidirect
483. #120	C₂×C₃×D₅	semidirect
490. C₂×C₂²⋊C₄	C₂×C₃×D₅	semidirect
499. C₃×D₅	#534	direct (N × H)
523. C₂³×C₃	D₄×D₅	semidirect
590. C₂⁴	C₂²×C₃×D₅	semidirect
609. C₂×D₄	C₂²×C₃×D₅	semidirect
610. C₂×D₄	C₂²×C₃×D₅	semidirect
619. C₂²×C₄	C₂²×C₃×D₅	semidirect
620. C₂²×C₄	C₂²×C₃×D₅	semidirect
623. C₄⋊C₄	C₂²×C₃×D₅	semidirect
629. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
630. C₂²⋊C₄	C₂²×C₃×D₅	semidirect
631. C₃×C₅	C₂×#534	semidirect
668. D₅	C₃×#534	direct (N × H)
692. C₂³	C₃×D₄×D₅	semidirect
728. C₅	C₂×C₃×#534	semidirect
757. C₃	D₅×#534	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×D₄×D₅	2
C₃×C₅×#534	2
C₃×#66138	2
C₃×#65987	2
C₃×D₅×#123	2
C₃×#65939	2
C₃×D₅×#121	2
C₃×#65923	2
C₃×D₅×#120	2
C₃×#65827	2
C₂×C₃×D₅×C₂²⋊C₄	2
D₅×#534	3
C₂×C₃×#534	5

Subgroups — C3×D5×#534 #14480288

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#534 #14480288