Subgroups — C₂×C₃×#66033 #14495378

Order 1920.

2048 conjugacy classes of subgroups.

The subgroup lattice has 488 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66033	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4044	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4044	C₂	1	2	yes	maximal, complemented
5	C₂×C₃×#4043	C₂	1	2	yes	maximal, complemented
6	C₂×C₃×#4042	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4040	C₂	1	2	yes	maximal
8	C₂×C₃×#4034	C₂	1	2	yes	maximal, complemented
9	C₂×C₃×#4021	C₂	1	1	yes	maximal, characteristic
10	C₂×C₃×#4016	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#66033	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
12	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
14	C₂²×C₃×Dic₁₀	C₂²	1	2	yes	—
15	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
16	C₃×C₅×#125	C₂²	1	8	yes	complemented
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
22	C₂×C₃×#685	C₂²	1	2	yes	—
23	C₂×C₃×#685	C₂²	1	2	yes	—
24	C₂×C₃×#685	C₂²	1	2	yes	—
25	C₂×C₃×#685	C₂²	1	2	yes	—
26	C₂×C₃×#685	C₂²	1	2	yes	—
27	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
30	C₂×C₃×#683	C₂²	1	2	yes	—
31	C₂×C₃×#683	C₂²	1	2	yes	—
32	C₂×C₃×#683	C₂²	1	2	yes	—
33	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
34	C₃×#4044	C₂²	1	16	yes	complemented
35	C₃×#4044	C₂²	1	16	yes	complemented
36	C₃×#4043	C₂²	1	16	yes	complemented
37	C₃×#4042	C₂²	1	16	yes	complemented
38	C₃×#4040	C₂²	1	16	yes	—
39	C₃×#4034	C₂²	1	16	yes	complemented
40	C₃×#4021	C₂²	1	8	yes	—
41	C₃×#4016	C₂²	1	8	yes	complemented
42	C₂×C₃×#563	—	5	1	no	maximal, Hall
43	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
44	#66033	C₂×C₃	1	16	yes	direct product factor
45	C₂×#4044	C₂×C₃	1	2	yes	complemented
46	C₂×#4044	C₂×C₃	1	2	yes	complemented
47	C₂×#4043	C₂×C₃	1	2	yes	complemented
48	C₂×#4042	C₂×C₃	1	2	yes	complemented
49	C₂×#4040	C₂×C₃	1	2	yes	—
50	C₂×#4034	C₂×C₃	1	2	yes	complemented
51	C₂×#4021	C₂×C₃	1	1	yes	characteristic
52	C₂×#4016	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂³×C₃×D₅	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×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
60	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
61	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
62	C₂×C₃×D₂₀	—	4	2	no	—
63	C₂×C₃×D₂₀	C₂³	1	4	yes	—
64	C₂×C₃×C₄×D₅	—	4	4	no	—
65	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
66	C₂×C₃×Dic₁₀	—	4	2	no	—
67	C₂×C₃×Dic₁₀	—	4	4	no	—
68	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
69	C₂×C₃×Dic₁₀	C₂³	1	8	yes	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
74	C₃×C₄²×C₅	C₂³	1	4	yes	—
75	C₃×#685	C₂³	1	8	yes	—
76	C₃×#685	C₂³	1	8	yes	—
77	C₃×#685	C₂³	1	8	yes	—
78	C₃×#685	C₂³	1	8	yes	—
79	C₃×#685	C₂³	1	8	yes	—
80	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
81	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
82	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
83	C₃×#683	C₂³	1	8	yes	—
84	C₃×#683	C₂³	1	8	yes	—
85	C₃×#683	C₂³	1	8	yes	—
86	C₃×C₄×Dic₅	C₂³	1	8	yes	—
87	C₃×#563	—	5	16	no	—
88	C₂×C₃×C₄⋊Q₈	—	5	2	no	—
89	C₂×C₃×#126	—	5	2	no	—
90	C₂×C₃×#126	—	5	2	no	—
91	C₂×C₃×#125	—	5	1	no	—
92	C₂×C₃×#125	D₅	1	1	yes	characteristic, complemented
93	C₂×C₃×#124	—	5	1	no	—
94	C₂×C₃×#123	—	5	2	no	—
95	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
96	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
97	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
98	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
99	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
100	C₂²×Dic₁₀	C₂²×C₃	1	2	yes	—
101	C₅×#125	C₂²×C₃	1	8	yes	complemented
102	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×#685	C₂²×C₃	1	2	yes	—
108	C₂×#685	C₂²×C₃	1	2	yes	—
109	C₂×#685	C₂²×C₃	1	2	yes	—
110	C₂×#685	C₂²×C₃	1	2	yes	—
111	C₂×#685	C₂²×C₃	1	2	yes	—
112	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
115	C₂×#683	C₂²×C₃	1	2	yes	—
116	C₂×#683	C₂²×C₃	1	2	yes	—
117	C₂×#683	C₂²×C₃	1	2	yes	—
118	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
119	#4044	C₂²×C₃	1	16	yes	complemented
120	#4044	C₂²×C₃	1	16	yes	complemented
121	#4043	C₂²×C₃	1	16	yes	complemented
122	#4042	C₂²×C₃	1	16	yes	complemented
123	#4040	C₂²×C₃	1	16	yes	—
124	#4034	C₂²×C₃	1	16	yes	complemented
125	#4021	C₂²×C₃	1	8	yes	—
126	#4016	C₂²×C₃	1	8	yes	complemented
127	C₂×#563	—	5	1	no	Sylow
128	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
129	C₂²×C₃×D₅	—	2	4	no	—
130	C₂²×C₃×D₅	—	2	4	no	—
131	C₂²×C₃×D₅	—	2	4	no	—
132	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
133	C₂×C₃×C₄×C₅	—	2	4	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	4	no	—
138	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
141	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
142	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
143	C₂×C₃×Dic₅	—	2	4	no	—
144	C₂×C₃×Dic₅	—	2	4	no	—
145	C₂×C₃×Dic₅	—	2	4	no	—
146	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
147	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
148	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
149	C₃×D₂₀	—	4	4	no	—
150	C₃×C₄×D₅	—	4	8	no	—
151	C₃×Dic₁₀	—	4	4	no	—
152	C₃×Dic₁₀	—	4	8	no	—
153	C₂²×C₃×Q₈	—	5	2	no	—
154	C₂²×C₃×Q₈	—	5	1	no	—
155	C₂²×C₃×D₄	—	5	1	no	—
156	C₂³×C₃×C₄	—	5	2	no	—
157	C₃×C₄⋊Q₈	—	5	16	no	—
158	C₃×#126	—	5	16	no	—
159	C₃×#126	—	5	16	no	—
160	C₃×#125	—	5	8	no	—
161	C₃×#125	C₂×D₅	1	8	yes	complemented
162	C₃×#124	—	5	8	no	—
163	C₃×#123	—	5	16	no	—
164	C₃×C₂²⋊Q₈	—	5	16	no	—
165	C₃×C₂²⋊Q₈	—	5	16	no	—
166	C₂×C₃×C₄⋊C₄	—	5	1	no	—
167	C₂×C₃×C₄⋊C₄	—	5	2	no	—
168	C₂×C₃×C₄⋊C₄	—	5	2	no	—
169	C₂×C₃×C₄⋊C₄	—	5	2	no	—
170	C₂×C₃×C₄⋊C₄	—	5	2	no	—
171	C₂×C₃×C₄⋊C₄	—	5	1	no	—
172	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
176	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
177	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
178	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
179	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
180	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
181	C₂×C₃×C₄²	—	5	2	no	—
182	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
183	C₂³×D₅	C₂³×C₃	1	2	yes	—
184	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
188	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
189	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
190	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
191	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
192	C₂×D₂₀	—	4	2	no	—
193	C₂×D₂₀	C₂³×C₃	1	4	yes	—
194	C₂×C₄×D₅	—	4	4	no	—
195	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
196	C₂×Dic₁₀	—	4	2	no	—
197	C₂×Dic₁₀	—	4	4	no	—
198	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
199	C₂×Dic₁₀	C₂³×C₃	1	8	yes	—
200	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
201	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
202	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
203	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
204	C₄²×C₅	C₂³×C₃	1	4	yes	—
205	#685	C₂³×C₃	1	8	yes	—
206	#685	C₂³×C₃	1	8	yes	—
207	#685	C₂³×C₃	1	8	yes	—
208	#685	C₂³×C₃	1	8	yes	—
209	#685	C₂³×C₃	1	8	yes	—
210	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
211	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
212	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
213	#683	C₂³×C₃	1	8	yes	—
214	#683	C₂³×C₃	1	8	yes	—
215	#683	C₂³×C₃	1	8	yes	—
216	C₄×Dic₅	C₂³×C₃	1	8	yes	—
217	#563	—	5	16	no	—
218	C₂×C₄⋊Q₈	—	5	2	no	—
219	C₂×#126	—	5	2	no	—
220	C₂×#126	—	5	2	no	—
221	C₂×#125	—	5	1	no	—
222	C₂×#125	C₃×D₅	1	1	yes	characteristic, complemented
223	C₂×#124	—	5	1	no	—
224	C₂×#123	—	5	2	no	—
225	C₂×C₂²⋊Q₈	—	5	2	no	—
226	C₂×C₂²⋊Q₈	—	5	2	no	—
227	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
228	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
229	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
230	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
231	C₂×C₃×D₅	—	2	4	no	—
232	C₂×C₃×D₅	—	2	4	no	—
233	C₂×C₃×D₅	—	2	4	no	—
234	C₂×C₃×D₅	—	4	8	no	—
235	C₃×C₄×C₅	—	2	4	no	—
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	4	no	—
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×Dic₅	—	2	4	no	—
241	C₃×Dic₅	—	2	4	no	—
242	C₃×Dic₅	—	2	4	no	—
243	C₂⁴×C₃	—	5	2	no	—
244	C₂×C₃×Q₈	—	5	8	no	—
245	C₂×C₃×Q₈	—	5	4	no	—
246	C₂×C₃×Q₈	—	20	4	no	—
247	C₂×C₃×Q₈	—	20	2	no	—
248	C₂×C₃×D₄	—	5	4	no	—
249	C₂×C₃×D₄	—	20	2	no	—
250	C₂²×C₃×C₄	—	5	2	no	—
251	C₂²×C₃×C₄	—	5	2	no	—
252	C₂²×C₃×C₄	—	5	2	no	—
253	C₂²×C₃×C₄	—	5	8	no	—
254	C₂²×C₃×C₄	—	20	4	no	—
255	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
256	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
258	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
259	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
260	C₃×C₄⋊C₄	—	5	8	no	—
261	C₃×C₄⋊C₄	—	5	8	no	—
262	C₃×C₄⋊C₄	—	5	8	no	—
263	C₃×C₄⋊C₄	—	5	4	no	—
264	C₃×C₄⋊C₄	—	5	8	no	—
265	C₃×C₄⋊C₄	—	5	4	no	—
266	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
267	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
268	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
269	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
270	C₃×C₂²⋊C₄	—	5	8	no	—
271	C₃×C₂²⋊C₄	—	5	8	no	—
272	C₃×C₂²⋊C₄	—	5	8	no	—
273	C₃×C₂²⋊C₄	—	5	8	no	—
274	C₃×C₂²⋊C₄	—	5	8	no	—
275	C₃×C₄²	—	5	8	no	—
276	C₃×C₄²	C₂²×D₅	1	4	yes	—
277	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
278	C₂²×D₅	—	2	4	no	—
279	C₂²×D₅	—	2	4	no	—
280	C₂²×D₅	—	2	4	no	—
281	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
282	C₂×C₄×C₅	—	2	4	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	4	no	—
287	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
288	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
289	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
290	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
291	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
292	C₂×Dic₅	—	2	4	no	—
293	C₂×Dic₅	—	2	4	no	—
294	C₂×Dic₅	—	2	4	no	—
295	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
296	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
297	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
298	D₂₀	—	4	4	no	—
299	C₄×D₅	—	4	8	no	—
300	Dic₁₀	—	4	4	no	—
301	Dic₁₀	—	4	8	no	—
302	C₂²×Q₈	—	5	2	no	—
303	C₂²×Q₈	—	5	1	no	—
304	C₂²×D₄	—	5	1	no	—
305	C₂³×C₄	—	5	2	no	—
306	C₄⋊Q₈	—	5	16	no	—
307	#126	—	5	16	no	—
308	#126	—	5	16	no	—
309	#125	—	5	8	no	—
310	#125	C₂×C₃×D₅	1	8	yes	complemented
311	#124	—	5	8	no	—
312	#123	—	5	16	no	—
313	C₂²⋊Q₈	—	5	16	no	—
314	C₂²⋊Q₈	—	5	16	no	—
315	C₂×C₄⋊C₄	—	5	1	no	—
316	C₂×C₄⋊C₄	—	5	2	no	—
317	C₂×C₄⋊C₄	—	5	2	no	—
318	C₂×C₄⋊C₄	—	5	2	no	—
319	C₂×C₄⋊C₄	—	5	2	no	—
320	C₂×C₄⋊C₄	—	5	1	no	—
321	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
322	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
323	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
324	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
325	C₂×C₂²⋊C₄	—	5	2	no	—
326	C₂×C₂²⋊C₄	—	5	2	no	—
327	C₂×C₂²⋊C₄	—	5	2	no	—
328	C₂×C₂²⋊C₄	—	5	2	no	—
329	C₂×C₂²⋊C₄	—	5	2	no	—
330	C₂×C₄²	—	5	2	no	—
331	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
332	C₂×C₃×C₅	#563	1	4	yes	complemented
333	C₂×C₃×C₅	C₂×H(5,𝔽₂)	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
336	C₃×D₅	—	4	4	no	—
337	C₂³×C₃	—	5	4	no	—
338	C₂³×C₃	—	10	4	no	—
339	C₂³×C₃	—	10	4	no	—
340	C₂³×C₃	—	10	4	no	—
341	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
342	C₃×Q₈	—	20	8	no	—
343	C₃×Q₈	—	20	4	no	—
344	C₃×D₄	—	20	4	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	4	no	—
347	C₂×C₃×C₄	—	2	2	no	—
348	C₂×C₃×C₄	—	2	4	no	—
349	C₂×C₃×C₄	—	2	2	no	—
350	C₂×C₃×C₄	—	5	4	no	—
351	C₂×C₃×C₄	—	5	4	no	—
352	C₂×C₃×C₄	—	5	4	no	—
353	C₂×C₃×C₄	—	10	4	no	—
354	C₂×C₃×C₄	—	10	4	no	—
355	C₂×C₃×C₄	—	10	4	no	—
356	C₂×C₃×C₄	—	20	8	no	—
357	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
358	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
359	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
360	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
361	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
362	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
363	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
364	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
365	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
366	C₂×D₅	—	2	4	no	—
367	C₂×D₅	—	2	4	no	—
368	C₂×D₅	—	2	4	no	—
369	C₂×D₅	—	4	8	no	—
370	C₄×C₅	—	2	4	no	—
371	C₄×C₅	—	2	2	no	—
372	C₄×C₅	—	2	2	no	—
373	C₄×C₅	—	2	4	no	—
374	C₄×C₅	—	2	2	no	—
375	Dic₅	—	2	4	no	—
376	Dic₅	—	2	4	no	—
377	Dic₅	—	2	4	no	—
378	C₂⁴	—	5	2	no	—
379	C₂×Q₈	—	5	8	no	—
380	C₂×Q₈	—	5	4	no	—
381	C₂×Q₈	—	20	4	no	—
382	C₂×Q₈	—	20	2	no	—
383	C₂×D₄	—	5	4	no	—
384	C₂×D₄	—	20	2	no	—
385	C₂²×C₄	—	5	2	no	—
386	C₂²×C₄	—	5	2	no	—
387	C₂²×C₄	—	5	2	no	—
388	C₂²×C₄	—	5	8	no	—
389	C₂²×C₄	—	20	4	no	—
390	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
391	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
392	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
393	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
394	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
395	C₄⋊C₄	—	5	4	no	—
396	C₄⋊C₄	—	5	8	no	—
397	C₄⋊C₄	—	5	8	no	—
398	C₄⋊C₄	—	5	8	no	—
399	C₄⋊C₄	—	5	8	no	—
400	C₄⋊C₄	—	5	4	no	—
401	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
402	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
403	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
404	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
405	C₂²⋊C₄	—	5	8	no	—
406	C₂²⋊C₄	—	5	8	no	—
407	C₂²⋊C₄	—	5	8	no	—
408	C₂²⋊C₄	—	5	8	no	—
409	C₂²⋊C₄	—	5	8	no	—
410	C₄²	—	5	8	no	—
411	C₄²	C₂²×C₃×D₅	1	4	yes	—
412	C₃×C₅	C₂×#563	1	1	yes	characteristic, complemented, Hall
413	C₂²×C₃	—	10	4	no	—
414	C₂²×C₃	—	10	4	no	—
415	C₂²×C₃	—	10	4	no	—
416	C₂²×C₃	—	20	8	no	—
417	C₂²×C₃	#4147	1	2	yes	—
418	C₂²×C₃	#4149	1	2	yes	—
419	C₂²×C₃	#4150	1	2	yes	—
420	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
421	C₃×C₄	—	2	2	no	—
422	C₃×C₄	—	2	4	no	—
423	C₃×C₄	—	2	2	no	—
424	C₃×C₄	—	2	4	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	10	4	no	—
427	C₃×C₄	—	10	4	no	—
428	C₃×C₄	—	10	4	no	—
429	C₂×C₅	C₃×#563	1	4	yes	complemented
430	C₂×C₅	C₂×C₃×H(5,𝔽₂)	1	1	yes	characteristic
431	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
432	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
433	D₅	—	4	4	no	—
434	C₂³	—	5	4	no	—
435	C₂³	—	10	4	no	—
436	C₂³	—	10	4	no	—
437	C₂³	—	10	4	no	—
438	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
439	Q₈	—	20	8	no	—
440	Q₈	—	20	4	no	—
441	D₄	—	20	4	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	4	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	2	4	no	—
446	C₂×C₄	—	2	2	no	—
447	C₂×C₄	—	5	4	no	—
448	C₂×C₄	—	5	4	no	—
449	C₂×C₄	—	5	4	no	—
450	C₂×C₄	—	10	4	no	—
451	C₂×C₄	—	10	4	no	—
452	C₂×C₄	—	10	4	no	—
453	C₂×C₄	—	20	8	no	—
454	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
455	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
456	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
457	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
458	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
459	C₂×C₃	—	20	4	no	—
460	C₂×C₃	#66033	1	4	yes	direct product factor
461	C₂×C₃	C₂×#4147	1	1	yes	characteristic
462	C₂×C₃	C₂×#4149	1	1	yes	characteristic
463	C₂×C₃	C₂×#4150	1	1	yes	characteristic
464	C₅	C₂×C₃×#563	1	1	yes	characteristic, complemented, Sylow
465	C₂²	—	10	4	no	—
466	C₂²	—	10	4	no	—
467	C₂²	—	10	4	no	—
468	C₂²	—	20	8	no	—
469	C₂²	C₃×#4147	1	2	yes	—
470	C₂²	C₃×#4149	1	2	yes	—
471	C₂²	C₃×#4150	1	2	yes	—
472	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
473	C₄	—	2	2	no	—
474	C₄	—	2	4	no	—
475	C₄	—	2	2	no	—
476	C₄	—	2	4	no	—
477	C₄	—	2	2	no	—
478	C₄	—	10	4	no	—
479	C₄	—	10	4	no	—
480	C₄	—	10	4	no	—
481	C₃	C₂×#66033	1	1	yes	characteristic, direct product factor, Sylow
482	C₂	—	20	4	no	—
483	C₂	C₃×#66033	1	4	yes	direct product factor
484	C₂	C₂×C₃×#4147	1	1	yes	characteristic
485	C₂	C₂×C₃×#4149	1	1	yes	characteristic
486	C₂	C₂×C₃×#4150	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×C₅×#125	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂²×C₃×D₂₀	C₂²
hypercenter	C₂×C₃×#125	D₅
hypocenter	C₅	C₂×C₃×#563
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₂×C₃×#125

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#125	C₂	semidirect
2. C₃×#66033	C₂	direct (N × H)
3. C₂×C₃×#4044	C₂	semidirect
4. C₂×C₃×#4044	C₂	semidirect
5. C₂×C₃×#4043	C₂	semidirect
6. C₂×C₃×#4042	C₂	semidirect
8. C₂×C₃×#4034	C₂	semidirect
10. C₂×C₃×#4016	C₂	semidirect
11. C₂×#66033	C₃	direct (N × H)
16. C₃×C₅×#125	C₂²	semidirect
34. C₃×#4044	C₂²	semidirect
35. C₃×#4044	C₂²	semidirect
36. C₃×#4043	C₂²	semidirect
37. C₃×#4042	C₂²	semidirect
39. C₃×#4034	C₂²	semidirect
41. C₃×#4016	C₂²	semidirect
43. C₂×C₅×#125	C₂×C₃	semidirect
44. #66033	C₂×C₃	direct (N × H)
45. C₂×#4044	C₂×C₃	semidirect
46. C₂×#4044	C₂×C₃	semidirect
47. C₂×#4043	C₂×C₃	semidirect
48. C₂×#4042	C₂×C₃	semidirect
50. C₂×#4034	C₂×C₃	semidirect
52. C₂×#4016	C₂×C₃	semidirect
92. C₂×C₃×#125	D₅	semidirect
101. C₅×#125	C₂²×C₃	semidirect
119. #4044	C₂²×C₃	semidirect
120. #4044	C₂²×C₃	semidirect
121. #4043	C₂²×C₃	semidirect
122. #4042	C₂²×C₃	semidirect
124. #4034	C₂²×C₃	semidirect
126. #4016	C₂²×C₃	semidirect
161. C₃×#125	C₂×D₅	semidirect
222. C₂×#125	C₃×D₅	semidirect
310. #125	C₂×C₃×D₅	semidirect
332. C₂×C₃×C₅	#563	semidirect
412. C₃×C₅	C₂×#563	semidirect
429. C₂×C₅	C₃×#563	semidirect
460. C₂×C₃	#66033	direct (N × H)
464. C₅	C₂×C₃×#563	semidirect
481. C₃	C₂×#66033	direct (N × H)
483. C₂	C₃×#66033	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×C₅×#125	2
C₃×#66033	2
C₂×C₃×#4044	2
C₂×C₃×#4043	2
C₂×C₃×#4042	2
C₂×C₃×#4040	2
C₂×C₃×#4034	2
C₂×C₃×#4021	2
C₂×C₃×#4016	2
C₂×#66033	3
C₂×C₃×#563	5

Subgroups — C2×C3×#66033 #14495378

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66033 #14495378