Subgroups — C₂×C₃×#65896 #14481083

Order 1920.

2520 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4084	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#4076	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#4075	C₂	1	2	yes	maximal, complemented
6	C₃×#65896	C₂	1	16	yes	maximal, direct product factor
7	C₂×C₃×#4041	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#4036	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4030	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4029	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₄×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×#4018	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#65896	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
17	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
18	C₂²×C₃×C₂²⋊D₅	C₂²	1	2	yes	—
19	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
20	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
21	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
22	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
23	C₃×C₄×C₅×D₄	C₂²	1	8	yes	complemented
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
28	C₃×#4086	C₂²	1	8	yes	complemented
29	C₃×#4084	C₂²	1	8	yes	complemented
30	C₃×#4076	C₂²	1	16	yes	complemented
31	C₃×#4075	C₂²	1	16	yes	complemented
32	C₂×C₃×#685	C₂²	1	2	yes	—
33	C₂×C₃×#685	C₂²	1	2	yes	—
34	C₂×C₃×#685	C₂²	1	1	yes	characteristic
35	C₂×C₃×#685	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
37	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
38	C₂×C₃×#683	C₂²	1	1	yes	characteristic
39	C₂×C₃×#683	C₂²	1	2	yes	—
40	C₂×C₃×#683	C₂²	1	1	yes	characteristic
41	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
42	C₃×#4041	C₂²	1	8	yes	complemented
43	C₃×#4036	C₂²	1	8	yes	complemented
44	C₃×#4030	C₂²	1	16	yes	complemented
45	C₃×#4029	C₂²	1	16	yes	complemented
46	C₃×C₄×D₂₀	C₂²	1	8	yes	complemented
47	C₃×#4018	C₂²	1	8	yes	complemented
48	C₂×C₃×#540	—	5	1	no	maximal, Hall
49	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#4086	C₂×C₃	1	1	yes	characteristic, complemented
51	C₂×#4084	C₂×C₃	1	1	yes	characteristic, complemented
52	C₂×#4076	C₂×C₃	1	2	yes	complemented
53	C₂×#4075	C₂×C₃	1	2	yes	complemented
54	#65896	C₂×C₃	1	16	yes	direct product factor
55	C₂×#4041	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#4036	C₂×C₃	1	1	yes	characteristic, complemented
57	C₂×#4030	C₂×C₃	1	2	yes	complemented
58	C₂×#4029	C₂×C₃	1	2	yes	complemented
59	C₂×C₄×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×#4018	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
62	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
63	C₂³×C₃×D₅	C₂³	1	2	yes	—
64	C₂×C₃×C₅×D₄	—	2	4	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
66	C₂²×C₃×C₄×C₅	—	4	4	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	8	yes	—
71	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
73	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
74	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
75	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
76	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
77	C₂×C₃×C₂²⋊D₅	C₂³	1	8	yes	—
78	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
79	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
80	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
81	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×D₂₀	—	2	4	no	—
83	C₂×C₃×D₂₀	—	4	4	no	—
84	C₂×C₃×D₂₀	C₂³	1	4	yes	—
85	C₂×C₃×D₂₀	C₂³	1	8	yes	—
86	C₂×C₃×C₄×D₅	—	2	4	no	—
87	C₂×C₃×C₄×D₅	—	4	4	no	—
88	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
89	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
90	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
91	C₃×C₅×C₂²⋊C₄	C₂³	1	8	yes	—
92	C₃×C₄²×C₅	C₂³	1	4	yes	—
93	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
94	C₃×#685	C₂³	1	4	yes	—
95	C₃×#685	C₂³	1	4	yes	—
96	C₃×#685	C₂³	1	8	yes	—
97	C₃×#685	C₂³	1	8	yes	—
98	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
99	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
100	C₃×#683	C₂³	1	4	yes	—
101	C₃×#683	C₂³	1	4	yes	—
102	C₃×#683	C₂³	1	8	yes	—
103	C₃×C₄×Dic₅	C₂³	1	4	yes	—
104	C₃×#540	—	5	16	no	—
105	C₂×C₃×#127	—	5	1	no	—
106	C₂×C₃×#125	—	5	1	no	—
107	C₂×C₃×#123	—	5	2	no	—
108	C₂×C₃×#123	—	5	2	no	—
109	C₂×C₃×#121	—	5	1	no	—
110	C₂×C₃×#121	—	5	2	no	—
111	C₂×C₃×#121	—	5	1	no	—
112	C₂×C₃×#121	—	5	2	no	—
113	C₂×C₃×C₄×D₄	—	5	1	no	—
114	C₂×C₃×C₄×D₄	D₅	1	1	yes	characteristic, complemented
115	C₂×C₃×#117	—	5	1	no	—
116	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
118	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
119	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
120	C₂²×C₂²⋊D₅	C₂²×C₃	1	2	yes	—
121	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
122	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
123	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
124	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
125	C₄×C₅×D₄	C₂²×C₃	1	8	yes	complemented
126	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
128	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
130	#4086	C₂²×C₃	1	8	yes	complemented
131	#4084	C₂²×C₃	1	8	yes	complemented
132	#4076	C₂²×C₃	1	16	yes	complemented
133	#4075	C₂²×C₃	1	16	yes	complemented
134	C₂×#685	C₂²×C₃	1	1	yes	characteristic
135	C₂×#685	C₂²×C₃	1	1	yes	characteristic
136	C₂×#685	C₂²×C₃	1	2	yes	—
137	C₂×#685	C₂²×C₃	1	2	yes	—
138	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
139	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
140	C₂×#683	C₂²×C₃	1	1	yes	characteristic
141	C₂×#683	C₂²×C₃	1	1	yes	characteristic
142	C₂×#683	C₂²×C₃	1	2	yes	—
143	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
144	#4041	C₂²×C₃	1	8	yes	complemented
145	#4036	C₂²×C₃	1	8	yes	complemented
146	#4030	C₂²×C₃	1	16	yes	complemented
147	#4029	C₂²×C₃	1	16	yes	complemented
148	C₄×D₂₀	C₂²×C₃	1	8	yes	complemented
149	#4018	C₂²×C₃	1	8	yes	complemented
150	C₂×#540	—	5	1	no	Sylow
151	C₂³×C₃×C₅	—	2	4	no	—
152	C₂³×C₃×C₅	—	2	4	no	—
153	C₂³×C₃×C₅	—	2	4	no	—
154	C₂³×C₃×C₅	C₂⁴	1	4	yes	—
155	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
156	C₂²×C₃×D₅	—	2	2	no	—
157	C₂²×C₃×D₅	—	2	4	no	—
158	C₂²×C₃×D₅	—	2	4	no	—
159	C₂²×C₃×D₅	—	2	2	no	—
160	C₂²×C₃×D₅	—	2	4	no	—
161	C₂²×C₃×D₅	—	2	2	no	—
162	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
163	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
164	C₃×C₅×D₄	—	2	8	no	—
165	C₂×C₃×C₄×C₅	—	2	2	no	—
166	C₂×C₃×C₄×C₅	—	2	4	no	—
167	C₂×C₃×C₄×C₅	—	2	2	no	—
168	C₂×C₃×C₄×C₅	—	4	8	no	—
169	C₂×C₃×C₄×C₅	#41	1	4	yes	—
170	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
171	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
172	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
173	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
174	C₃×C₂²⋊D₅	—	4	8	no	—
175	C₃×C₂²⋊D₅	—	4	8	no	—
176	C₃×C₂²⋊D₅	—	4	8	no	—
177	C₂×C₃×Dic₅	—	2	2	no	—
178	C₂×C₃×Dic₅	—	2	4	no	—
179	C₂×C₃×Dic₅	—	2	2	no	—
180	C₂×C₃×Dic₅	—	2	2	no	—
181	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
182	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
183	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
184	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
185	C₃×D₂₀	—	2	8	no	—
186	C₃×D₂₀	—	4	8	no	—
187	C₃×C₄×D₅	—	2	8	no	—
188	C₃×C₄×D₅	—	4	8	no	—
189	C₂²×C₃×D₄	—	5	2	no	—
190	C₂²×C₃×D₄	—	5	2	no	—
191	C₂²×C₃×D₄	—	5	2	no	—
192	C₂²×C₃×D₄	—	5	1	no	—
193	C₂²×C₃×D₄	—	5	2	no	—
194	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
195	C₂³×C₃×C₄	—	5	1	no	—
196	C₂³×C₃×C₄	—	5	2	no	—
197	C₂³×C₃×C₄	C₂×D₅	1	2	yes	—
198	C₃×#127	—	5	8	no	—
199	C₃×#125	—	5	8	no	—
200	C₃×#123	—	5	16	no	—
201	C₃×#123	—	5	16	no	—
202	C₃×#121	—	5	8	no	—
203	C₃×#121	—	5	16	no	—
204	C₃×#121	—	5	8	no	—
205	C₃×#121	—	5	16	no	—
206	C₃×C₄×D₄	—	5	8	no	—
207	C₃×C₄×D₄	C₂×D₅	1	8	yes	complemented
208	C₃×#117	—	5	8	no	—
209	C₂×C₃×C₄⋊C₄	—	5	1	no	—
210	C₂×C₃×C₄⋊C₄	—	5	1	no	—
211	C₂×C₃×C₄⋊C₄	—	5	1	no	—
212	C₂×C₃×C₄⋊C₄	—	5	2	no	—
213	C₂×C₃×C₄⋊C₄	—	5	2	no	—
214	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
215	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
216	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
217	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
218	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
219	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
220	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
221	C₂×C₃×C₄²	—	5	1	no	—
222	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
223	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
224	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
225	C₂³×D₅	C₂³×C₃	1	2	yes	—
226	C₂×C₅×D₄	—	2	4	no	—
227	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
228	C₂²×C₄×C₅	—	4	4	no	—
229	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
230	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
231	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
232	C₂²×C₄×C₅	C₂³×C₃	1	8	yes	—
233	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
234	C₂×C₂²⋊D₅	—	4	4	no	—
235	C₂×C₂²⋊D₅	—	4	4	no	—
236	C₂×C₂²⋊D₅	—	4	4	no	—
237	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
238	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
239	C₂×C₂²⋊D₅	C₂³×C₃	1	8	yes	—
240	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
241	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
242	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
243	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
244	C₂×D₂₀	—	2	4	no	—
245	C₂×D₂₀	—	4	4	no	—
246	C₂×D₂₀	C₂³×C₃	1	4	yes	—
247	C₂×D₂₀	C₂³×C₃	1	8	yes	—
248	C₂×C₄×D₅	—	2	4	no	—
249	C₂×C₄×D₅	—	4	4	no	—
250	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
251	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
252	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
253	C₅×C₂²⋊C₄	C₂³×C₃	1	8	yes	—
254	C₄²×C₅	C₂³×C₃	1	4	yes	—
255	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
256	#685	C₂³×C₃	1	4	yes	—
257	#685	C₂³×C₃	1	4	yes	—
258	#685	C₂³×C₃	1	8	yes	—
259	#685	C₂³×C₃	1	8	yes	—
260	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
261	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
262	#683	C₂³×C₃	1	4	yes	—
263	#683	C₂³×C₃	1	4	yes	—
264	#683	C₂³×C₃	1	8	yes	—
265	C₄×Dic₅	C₂³×C₃	1	4	yes	—
266	#540	—	5	16	no	—
267	C₂×#127	—	5	1	no	—
268	C₂×#125	—	5	1	no	—
269	C₂×#123	—	5	2	no	—
270	C₂×#123	—	5	2	no	—
271	C₂×#121	—	5	1	no	—
272	C₂×#121	—	5	2	no	—
273	C₂×#121	—	5	1	no	—
274	C₂×#121	—	5	2	no	—
275	C₂×C₄×D₄	—	5	1	no	—
276	C₂×C₄×D₄	C₃×D₅	1	1	yes	characteristic, complemented
277	C₂×#117	—	5	1	no	—
278	C₂²×C₃×C₅	—	2	4	no	—
279	C₂²×C₃×C₅	—	2	4	no	—
280	C₂²×C₃×C₅	—	2	4	no	—
281	C₂²×C₃×C₅	—	4	8	no	—
282	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
283	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
284	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
285	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
286	C₂×C₃×D₅	—	2	2	no	—
287	C₂×C₃×D₅	—	2	4	no	—
288	C₂×C₃×D₅	—	2	4	no	—
289	C₂×C₃×D₅	—	2	2	no	—
290	C₂×C₃×D₅	—	2	4	no	—
291	C₂×C₃×D₅	—	2	2	no	—
292	C₂×C₃×D₅	—	4	4	no	—
293	C₂×C₃×D₅	—	4	8	no	—
294	C₃×C₄×C₅	—	2	2	no	—
295	C₃×C₄×C₅	—	2	4	no	—
296	C₃×C₄×C₅	—	2	2	no	—
297	C₃×C₄×C₅	C₂×#41	1	4	yes	—
298	C₃×Dic₅	—	2	2	no	—
299	C₃×Dic₅	—	2	4	no	—
300	C₃×Dic₅	—	2	2	no	—
301	C₃×Dic₅	—	2	2	no	—
302	C₂⁴×C₃	—	5	1	no	—
303	C₂⁴×C₃	—	5	2	no	—
304	C₂⁴×C₃	C₂²×D₅	1	2	yes	—
305	C₂×C₃×D₄	—	2	4	no	—
306	C₂×C₃×D₄	—	5	8	no	—
307	C₂×C₃×D₄	—	5	8	no	—
308	C₂×C₃×D₄	—	5	8	no	—
309	C₂×C₃×D₄	—	5	4	no	—
310	C₂×C₃×D₄	—	5	8	no	—
311	C₂×C₃×D₄	—	10	4	no	—
312	C₂×C₃×D₄	—	20	4	no	—
313	C₂×C₃×D₄	—	20	4	no	—
314	C₂×C₃×D₄	—	20	4	no	—
315	C₂×C₃×D₄	—	20	4	no	—
316	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
317	C₂²×C₃×C₄	—	4	4	no	—
318	C₂²×C₃×C₄	—	5	1	no	—
319	C₂²×C₃×C₄	—	5	1	no	—
320	C₂²×C₃×C₄	—	5	1	no	—
321	C₂²×C₃×C₄	—	5	2	no	—
322	C₂²×C₃×C₄	—	5	4	no	—
323	C₂²×C₃×C₄	—	5	8	no	—
324	C₂²×C₃×C₄	—	10	4	no	—
325	C₂²×C₃×C₄	—	20	4	no	—
326	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
327	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
328	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
329	C₂²×C₃×C₄	C₂²×D₅	1	8	yes	—
330	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
331	C₃×C₄⋊C₄	—	5	4	no	—
332	C₃×C₄⋊C₄	—	5	4	no	—
333	C₃×C₄⋊C₄	—	5	8	no	—
334	C₃×C₄⋊C₄	—	5	4	no	—
335	C₃×C₄⋊C₄	—	5	8	no	—
336	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
337	C₃×C₂²⋊C₄	—	5	8	no	—
338	C₃×C₂²⋊C₄	—	5	4	no	—
339	C₃×C₂²⋊C₄	—	5	4	no	—
340	C₃×C₂²⋊C₄	—	5	8	no	—
341	C₃×C₂²⋊C₄	—	5	8	no	—
342	C₃×C₂²⋊C₄	C₂²×D₅	1	8	yes	—
343	C₃×C₄²	—	5	4	no	—
344	C₃×C₄²	C₂²×D₅	1	4	yes	—
345	C₂³×C₅	—	2	4	no	—
346	C₂³×C₅	—	2	4	no	—
347	C₂³×C₅	—	2	4	no	—
348	C₂³×C₅	C₂⁴×C₃	1	4	yes	—
349	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
350	C₂²×D₅	—	2	2	no	—
351	C₂²×D₅	—	2	4	no	—
352	C₂²×D₅	—	2	4	no	—
353	C₂²×D₅	—	2	2	no	—
354	C₂²×D₅	—	2	4	no	—
355	C₂²×D₅	—	2	2	no	—
356	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
357	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
358	C₅×D₄	—	2	8	no	—
359	C₂×C₄×C₅	—	2	2	no	—
360	C₂×C₄×C₅	—	2	4	no	—
361	C₂×C₄×C₅	—	2	2	no	—
362	C₂×C₄×C₅	—	4	8	no	—
363	C₂×C₄×C₅	C₃×#41	1	4	yes	—
364	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
365	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
366	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
367	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
368	C₂²⋊D₅	—	4	8	no	—
369	C₂²⋊D₅	—	4	8	no	—
370	C₂²⋊D₅	—	4	8	no	—
371	C₂×Dic₅	—	2	2	no	—
372	C₂×Dic₅	—	2	4	no	—
373	C₂×Dic₅	—	2	2	no	—
374	C₂×Dic₅	—	2	2	no	—
375	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
376	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
377	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
378	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
379	D₂₀	—	2	8	no	—
380	D₂₀	—	4	8	no	—
381	C₄×D₅	—	2	8	no	—
382	C₄×D₅	—	4	8	no	—
383	C₂²×D₄	—	5	2	no	—
384	C₂²×D₄	—	5	2	no	—
385	C₂²×D₄	—	5	2	no	—
386	C₂²×D₄	—	5	1	no	—
387	C₂²×D₄	—	5	2	no	—
388	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
389	C₂³×C₄	—	5	1	no	—
390	C₂³×C₄	—	5	2	no	—
391	C₂³×C₄	C₂×C₃×D₅	1	2	yes	—
392	#127	—	5	8	no	—
393	#125	—	5	8	no	—
394	#123	—	5	16	no	—
395	#123	—	5	16	no	—
396	#121	—	5	8	no	—
397	#121	—	5	16	no	—
398	#121	—	5	8	no	—
399	#121	—	5	16	no	—
400	C₄×D₄	—	5	8	no	—
401	C₄×D₄	C₂×C₃×D₅	1	8	yes	complemented
402	#117	—	5	8	no	—
403	C₂×C₄⋊C₄	—	5	1	no	—
404	C₂×C₄⋊C₄	—	5	1	no	—
405	C₂×C₄⋊C₄	—	5	1	no	—
406	C₂×C₄⋊C₄	—	5	2	no	—
407	C₂×C₄⋊C₄	—	5	2	no	—
408	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
409	C₂×C₂²⋊C₄	—	5	2	no	—
410	C₂×C₂²⋊C₄	—	5	1	no	—
411	C₂×C₂²⋊C₄	—	5	1	no	—
412	C₂×C₂²⋊C₄	—	5	2	no	—
413	C₂×C₂²⋊C₄	—	5	2	no	—
414	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
415	C₂×C₄²	—	5	1	no	—
416	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
417	C₂×C₃×C₅	—	4	4	no	—
418	C₂×C₃×C₅	#540	1	4	yes	complemented
419	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
420	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
421	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
422	C₃×D₅	—	4	2	no	—
423	C₃×D₅	—	4	4	no	—
424	C₂³×C₃	—	2	4	no	—
425	C₂³×C₃	—	2	4	no	—
426	C₂³×C₃	—	2	4	no	—
427	C₂³×C₃	—	5	2	no	—
428	C₂³×C₃	—	5	4	no	—
429	C₂³×C₃	—	10	2	no	—
430	C₂³×C₃	—	10	4	no	—
431	C₂³×C₃	—	10	2	no	—
432	C₂³×C₃	—	10	4	no	—
433	C₂³×C₃	—	10	4	no	—
434	C₂³×C₃	—	10	2	no	—
435	C₂³×C₃	C₂³×D₅	1	4	yes	—
436	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
437	C₃×D₄	—	2	8	no	—
438	C₃×D₄	—	10	8	no	—
439	C₃×D₄	—	20	8	no	—
440	C₃×D₄	—	20	8	no	—
441	C₃×D₄	—	20	8	no	—
442	C₃×D₄	—	20	8	no	—
443	C₂×C₃×C₄	—	2	2	no	—
444	C₂×C₃×C₄	—	2	4	no	—
445	C₂×C₃×C₄	—	2	2	no	—
446	C₂×C₃×C₄	—	4	8	no	—
447	C₂×C₃×C₄	—	5	2	no	—
448	C₂×C₃×C₄	—	5	2	no	—
449	C₂×C₃×C₄	—	5	2	no	—
450	C₂×C₃×C₄	—	5	4	no	—
451	C₂×C₃×C₄	—	10	2	no	—
452	C₂×C₃×C₄	—	10	2	no	—
453	C₂×C₃×C₄	—	10	4	no	—
454	C₂×C₃×C₄	—	10	2	no	—
455	C₂×C₃×C₄	—	10	8	no	—
456	C₂×C₃×C₄	—	20	8	no	—
457	C₂×C₃×C₄	#709	1	4	yes	—
458	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
459	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
460	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
461	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
462	C₂²×C₅	—	2	4	no	—
463	C₂²×C₅	—	2	4	no	—
464	C₂²×C₅	—	2	4	no	—
465	C₂²×C₅	—	4	8	no	—
466	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
467	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
468	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
469	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
470	C₂×D₅	—	2	2	no	—
471	C₂×D₅	—	2	4	no	—
472	C₂×D₅	—	2	4	no	—
473	C₂×D₅	—	2	2	no	—
474	C₂×D₅	—	2	4	no	—
475	C₂×D₅	—	2	2	no	—
476	C₂×D₅	—	4	4	no	—
477	C₂×D₅	—	4	8	no	—
478	C₄×C₅	—	2	2	no	—
479	C₄×C₅	—	2	4	no	—
480	C₄×C₅	—	2	2	no	—
481	C₄×C₅	C₂×C₃×#41	1	4	yes	—
482	Dic₅	—	2	2	no	—
483	Dic₅	—	2	4	no	—
484	Dic₅	—	2	2	no	—
485	Dic₅	—	2	2	no	—
486	C₂⁴	—	5	1	no	—
487	C₂⁴	—	5	2	no	—
488	C₂⁴	C₂²×C₃×D₅	1	2	yes	—
489	C₂×D₄	—	2	4	no	—
490	C₂×D₄	—	5	8	no	—
491	C₂×D₄	—	5	8	no	—
492	C₂×D₄	—	5	8	no	—
493	C₂×D₄	—	5	4	no	—
494	C₂×D₄	—	5	8	no	—
495	C₂×D₄	—	10	4	no	—
496	C₂×D₄	—	20	4	no	—
497	C₂×D₄	—	20	4	no	—
498	C₂×D₄	—	20	4	no	—
499	C₂×D₄	—	20	4	no	—
500	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
501	C₂²×C₄	—	4	4	no	—
502	C₂²×C₄	—	5	1	no	—
503	C₂²×C₄	—	5	1	no	—
504	C₂²×C₄	—	5	1	no	—
505	C₂²×C₄	—	5	2	no	—
506	C₂²×C₄	—	5	4	no	—
507	C₂²×C₄	—	5	8	no	—
508	C₂²×C₄	—	10	4	no	—
509	C₂²×C₄	—	20	4	no	—
510	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
511	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
512	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
513	C₂²×C₄	C₂²×C₃×D₅	1	8	yes	—
514	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
515	C₄⋊C₄	—	5	4	no	—
516	C₄⋊C₄	—	5	4	no	—
517	C₄⋊C₄	—	5	4	no	—
518	C₄⋊C₄	—	5	8	no	—
519	C₄⋊C₄	—	5	8	no	—
520	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
521	C₂²⋊C₄	—	5	8	no	—
522	C₂²⋊C₄	—	5	4	no	—
523	C₂²⋊C₄	—	5	4	no	—
524	C₂²⋊C₄	—	5	8	no	—
525	C₂²⋊C₄	—	5	8	no	—
526	C₂²⋊C₄	C₂²×C₃×D₅	1	8	yes	—
527	C₄²	—	5	4	no	—
528	C₄²	C₂²×C₃×D₅	1	4	yes	—
529	C₃×C₅	C₂×#540	1	1	yes	characteristic, complemented, Hall
530	C₂²×C₃	—	2	4	no	—
531	C₂²×C₃	—	2	4	no	—
532	C₂²×C₃	—	2	4	no	—
533	C₂²×C₃	—	4	8	no	—
534	C₂²×C₃	—	10	2	no	—
535	C₂²×C₃	—	10	4	no	—
536	C₂²×C₃	—	10	2	no	—
537	C₂²×C₃	—	10	4	no	—
538	C₂²×C₃	—	10	4	no	—
539	C₂²×C₃	—	10	2	no	—
540	C₂²×C₃	—	20	4	no	—
541	C₂²×C₃	—	20	8	no	—
542	C₂²×C₃	C₂×#709	1	2	yes	—
543	C₂²×C₃	#4144	1	2	yes	—
544	C₂²×C₃	#4149	1	2	yes	—
545	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
546	C₃×C₄	—	2	2	no	—
547	C₃×C₄	—	2	4	no	—
548	C₃×C₄	—	2	2	no	—
549	C₃×C₄	—	10	2	no	—
550	C₃×C₄	—	10	2	no	—
551	C₃×C₄	—	10	4	no	—
552	C₃×C₄	—	10	2	no	—
553	C₃×C₄	C₂×#709	1	4	yes	—
554	C₂×C₅	—	4	4	no	—
555	C₂×C₅	C₃×#540	1	4	yes	complemented
556	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
557	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
558	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
559	D₅	—	4	2	no	—
560	D₅	—	4	4	no	—
561	C₂³	—	2	4	no	—
562	C₂³	—	2	4	no	—
563	C₂³	—	2	4	no	—
564	C₂³	—	5	2	no	—
565	C₂³	—	5	4	no	—
566	C₂³	—	10	2	no	—
567	C₂³	—	10	4	no	—
568	C₂³	—	10	2	no	—
569	C₂³	—	10	4	no	—
570	C₂³	—	10	4	no	—
571	C₂³	—	10	2	no	—
572	C₂³	C₂³×C₃×D₅	1	4	yes	—
573	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
574	D₄	—	2	8	no	—
575	D₄	—	10	8	no	—
576	D₄	—	20	8	no	—
577	D₄	—	20	8	no	—
578	D₄	—	20	8	no	—
579	D₄	—	20	8	no	—
580	C₂×C₄	—	2	2	no	—
581	C₂×C₄	—	2	4	no	—
582	C₂×C₄	—	2	2	no	—
583	C₂×C₄	—	4	8	no	—
584	C₂×C₄	—	5	2	no	—
585	C₂×C₄	—	5	2	no	—
586	C₂×C₄	—	5	2	no	—
587	C₂×C₄	—	5	4	no	—
588	C₂×C₄	—	10	2	no	—
589	C₂×C₄	—	10	2	no	—
590	C₂×C₄	—	10	4	no	—
591	C₂×C₄	—	10	2	no	—
592	C₂×C₄	—	10	8	no	—
593	C₂×C₄	—	20	8	no	—
594	C₂×C₄	C₃×#709	1	4	yes	—
595	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
596	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
597	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
598	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
599	C₂×C₃	—	4	4	no	—
600	C₂×C₃	—	20	2	no	—
601	C₂×C₃	—	20	4	no	—
602	C₂×C₃	#65896	1	4	yes	direct product factor
603	C₂×C₃	C₂²×#709	1	1	yes	characteristic
604	C₂×C₃	C₂×#4144	1	1	yes	characteristic
605	C₂×C₃	C₂×#4149	1	1	yes	characteristic
606	C₅	C₂×C₃×#540	1	1	yes	characteristic, complemented, Sylow
607	C₂²	—	2	4	no	—
608	C₂²	—	2	4	no	—
609	C₂²	—	2	4	no	—
610	C₂²	—	4	8	no	—
611	C₂²	—	10	2	no	—
612	C₂²	—	10	4	no	—
613	C₂²	—	10	2	no	—
614	C₂²	—	10	4	no	—
615	C₂²	—	10	4	no	—
616	C₂²	—	10	2	no	—
617	C₂²	—	20	4	no	—
618	C₂²	—	20	8	no	—
619	C₂²	C₂×C₃×#709	1	2	yes	—
620	C₂²	C₃×#4144	1	2	yes	—
621	C₂²	C₃×#4149	1	2	yes	—
622	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
623	C₄	—	2	2	no	—
624	C₄	—	2	4	no	—
625	C₄	—	2	2	no	—
626	C₄	—	10	2	no	—
627	C₄	—	10	2	no	—
628	C₄	—	10	4	no	—
629	C₄	—	10	2	no	—
630	C₄	C₂×C₃×#709	1	4	yes	—
631	C₃	C₂×#65896	1	1	yes	characteristic, direct product factor, Sylow
632	C₂	—	4	4	no	—
633	C₂	—	20	2	no	—
634	C₂	—	20	4	no	—
635	C₂	C₃×#65896	1	4	yes	direct product factor
636	C₂	C₂²×C₃×#709	1	1	yes	characteristic
637	C₂	C₂×C₃×#4144	1	1	yes	characteristic
638	C₂	C₂×C₃×#4149	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₂×C₃×C₄×C₅×D₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
hypercenter	C₂×C₃×C₄×D₄	D₅
hypocenter	C₅	C₂×C₃×#540
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
2. C₂×C₃×#4086	C₂	semidirect
3. C₂×C₃×#4084	C₂	semidirect
4. C₂×C₃×#4076	C₂	semidirect
5. C₂×C₃×#4075	C₂	semidirect
6. C₃×#65896	C₂	direct (N × H)
7. C₂×C₃×#4041	C₂	semidirect
8. C₂×C₃×#4036	C₂	semidirect
9. C₂×C₃×#4030	C₂	semidirect
10. C₂×C₃×#4029	C₂	semidirect
11. C₂×C₃×C₄×D₂₀	C₂	semidirect
12. C₂×C₃×#4018	C₂	semidirect
13. C₂×#65896	C₃	direct (N × H)
23. C₃×C₄×C₅×D₄	C₂²	semidirect
28. C₃×#4086	C₂²	semidirect
29. C₃×#4084	C₂²	semidirect
30. C₃×#4076	C₂²	semidirect
31. C₃×#4075	C₂²	semidirect
42. C₃×#4041	C₂²	semidirect
43. C₃×#4036	C₂²	semidirect
44. C₃×#4030	C₂²	semidirect
45. C₃×#4029	C₂²	semidirect
46. C₃×C₄×D₂₀	C₂²	semidirect
47. C₃×#4018	C₂²	semidirect
49. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
50. C₂×#4086	C₂×C₃	semidirect
51. C₂×#4084	C₂×C₃	semidirect
52. C₂×#4076	C₂×C₃	semidirect
53. C₂×#4075	C₂×C₃	semidirect
54. #65896	C₂×C₃	direct (N × H)
55. C₂×#4041	C₂×C₃	semidirect
56. C₂×#4036	C₂×C₃	semidirect
57. C₂×#4030	C₂×C₃	semidirect
58. C₂×#4029	C₂×C₃	semidirect
59. C₂×C₄×D₂₀	C₂×C₃	semidirect
60. C₂×#4018	C₂×C₃	semidirect
114. C₂×C₃×C₄×D₄	D₅	semidirect
125. C₄×C₅×D₄	C₂²×C₃	semidirect
130. #4086	C₂²×C₃	semidirect
131. #4084	C₂²×C₃	semidirect
132. #4076	C₂²×C₃	semidirect
133. #4075	C₂²×C₃	semidirect
144. #4041	C₂²×C₃	semidirect
145. #4036	C₂²×C₃	semidirect
146. #4030	C₂²×C₃	semidirect
147. #4029	C₂²×C₃	semidirect
148. C₄×D₂₀	C₂²×C₃	semidirect
149. #4018	C₂²×C₃	semidirect
207. C₃×C₄×D₄	C₂×D₅	semidirect
276. C₂×C₄×D₄	C₃×D₅	semidirect
401. C₄×D₄	C₂×C₃×D₅	semidirect
418. C₂×C₃×C₅	#540	semidirect
529. C₃×C₅	C₂×#540	semidirect
555. C₂×C₅	C₃×#540	semidirect
602. C₂×C₃	#65896	direct (N × H)
606. C₅	C₂×C₃×#540	semidirect
631. C₃	C₂×#65896	direct (N × H)
635. C₂	C₃×#65896	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₄×C₅×D₄	2
C₂×C₃×#4086	2
C₂×C₃×#4084	2
C₂×C₃×#4076	2
C₂×C₃×#4075	2
C₃×#65896	2
C₂×C₃×#4041	2
C₂×C₃×#4036	2
C₂×C₃×#4030	2
C₂×C₃×#4029	2
C₂×C₃×C₄×D₂₀	2
C₂×C₃×#4018	2
C₂×#65896	3
C₂×C₃×#540	5

Subgroups — C2×C3×#65896 #14481083

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65896 #14481083