Subgroups — C₂×C₃×#66025 #14479791

Order 1920.

2464 conjugacy classes of subgroups.

The subgroup lattice has 600 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×#66025	C₂	1	16	yes	maximal, direct product factor
3	C₂×C₃×#4044	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#4043	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4041	C₂	1	1	yes	maximal, characteristic
6	C₂×C₃×#4040	C₂	1	2	yes	maximal, complemented
7	C₂×C₃×#4039	C₂	1	2	yes	maximal, complemented
8	C₂×C₃×#4039	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×C₃×#4038	C₂	1	2	yes	maximal, complemented
10	C₂×C₃×#4033	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×#4021	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#66025	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
14	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
15	C₂²×C₃×D₂₀	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
17	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
19	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
20	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
21	C₃×C₅×#125	C₂²	1	8	yes	complemented
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×#685	C₂²	1	2	yes	—
28	C₂×C₃×#685	C₂²	1	2	yes	—
29	C₂×C₃×#685	C₂²	1	2	yes	—
30	C₂×C₃×#685	C₂²	1	2	yes	—
31	C₂×C₃×#685	C₂²	1	2	yes	—
32	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	—
33	C₂×C₃×#683	C₂²	1	2	yes	—
34	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
35	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
37	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	—
38	C₃×#4044	C₂²	1	16	yes	complemented
39	C₃×#4043	C₂²	1	8	yes	complemented
40	C₃×#4041	C₂²	1	8	yes	—
41	C₃×#4040	C₂²	1	16	yes	complemented
42	C₃×#4039	C₂²	1	8	yes	complemented
43	C₃×#4039	C₂²	1	16	yes	complemented
44	C₃×#4038	C₂²	1	16	yes	complemented
45	C₃×#4033	C₂²	1	8	yes	complemented
46	C₃×#4021	C₂²	1	8	yes	complemented
47	C₃×C₄²×D₅	C₂²	1	8	yes	complemented
48	C₂×C₃×#529	—	5	1	no	maximal, Hall
49	C₂×C₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
50	#66025	C₂×C₃	1	16	yes	direct product factor
51	C₂×#4044	C₂×C₃	1	2	yes	complemented
52	C₂×#4043	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×#4041	C₂×C₃	1	1	yes	characteristic
54	C₂×#4040	C₂×C₃	1	2	yes	complemented
55	C₂×#4039	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×#4039	C₂×C₃	1	2	yes	complemented
57	C₂×#4038	C₂×C₃	1	2	yes	complemented
58	C₂×#4033	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×#4021	C₂×C₃	1	1	yes	characteristic, complemented
60	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic, complemented
61	C₂³×C₃×D₅	C₂³	1	2	yes	—
62	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
69	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
71	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
72	C₂×C₃×D₂₀	—	2	8	no	—
73	C₂×C₃×D₂₀	—	2	4	no	—
74	C₂×C₃×D₂₀	C₂³	1	4	yes	—
75	C₂×C₃×D₂₀	C₂³	1	8	yes	—
76	C₂×C₃×C₄×D₅	—	2	4	no	—
77	C₂×C₃×C₄×D₅	—	2	4	no	—
78	C₂×C₃×C₄×D₅	—	2	4	no	—
79	C₂×C₃×C₄×D₅	—	2	8	no	—
80	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
81	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
82	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
83	C₂×C₃×C₄×D₅	C₂³	1	8	yes	—
84	C₂×C₃×Dic₁₀	—	2	4	no	—
85	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
86	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
87	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
88	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
89	C₃×C₅×C₄⋊C₄	C₂³	1	8	yes	—
90	C₃×C₄²×C₅	C₂³	1	4	yes	—
91	C₃×#685	C₂³	1	8	yes	—
92	C₃×#685	C₂³	1	8	yes	—
93	C₃×#685	C₂³	1	8	yes	—
94	C₃×#685	C₂³	1	8	yes	—
95	C₃×#685	C₂³	1	8	yes	—
96	C₃×C₄⋊Dic₅	C₂³	1	8	yes	—
97	C₃×#683	C₂³	1	8	yes	—
98	C₃×C₄×Dic₅	C₂³	1	4	yes	—
99	C₃×C₄×Dic₅	C₂³	1	4	yes	—
100	C₃×C₄×Dic₅	C₂³	1	4	yes	—
101	C₃×C₄×Dic₅	C₂³	1	8	yes	—
102	C₃×#529	—	5	16	no	—
103	C₂×C₃×#126	—	5	2	no	—
104	C₂×C₃×#125	D₅	1	1	yes	characteristic, complemented
105	C₂×C₃×#124	—	5	1	no	—
106	C₂×C₃×#123	—	5	2	no	—
107	C₂×C₃×C₂²⋊Q₈	—	5	1	no	—
108	C₂×C₃×#121	—	5	1	no	—
109	C₂×C₃×C₄×Q₈	—	5	1	no	—
110	C₂×C₃×C₄×D₄	—	5	1	no	—
111	C₂×C₃×C₄×D₄	—	5	2	no	—
112	C₂×C₃×#117	—	5	2	no	—
113	C₂²×C₃×C₄²	—	5	1	no	—
114	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
115	C₂²×D₂₀	C₂²×C₃	1	2	yes	—
116	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
117	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
118	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
119	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
120	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
121	C₅×#125	C₂²×C₃	1	8	yes	complemented
122	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
123	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
124	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
125	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
126	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
127	C₂×#685	C₂²×C₃	1	2	yes	—
128	C₂×#685	C₂²×C₃	1	2	yes	—
129	C₂×#685	C₂²×C₃	1	2	yes	—
130	C₂×#685	C₂²×C₃	1	2	yes	—
131	C₂×#685	C₂²×C₃	1	2	yes	—
132	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	—
133	C₂×#683	C₂²×C₃	1	2	yes	—
134	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
135	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
137	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	—
138	#4044	C₂²×C₃	1	16	yes	complemented
139	#4043	C₂²×C₃	1	8	yes	complemented
140	#4041	C₂²×C₃	1	8	yes	—
141	#4040	C₂²×C₃	1	16	yes	complemented
142	#4039	C₂²×C₃	1	8	yes	complemented
143	#4039	C₂²×C₃	1	16	yes	complemented
144	#4038	C₂²×C₃	1	16	yes	complemented
145	#4033	C₂²×C₃	1	8	yes	complemented
146	#4021	C₂²×C₃	1	8	yes	complemented
147	C₄²×D₅	C₂²×C₃	1	8	yes	complemented
148	C₂×#529	—	5	1	no	Sylow
149	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
150	C₂²×C₃×D₅	—	2	2	no	—
151	C₂²×C₃×D₅	—	2	2	no	—
152	C₂²×C₃×D₅	—	2	4	no	—
153	C₂²×C₃×D₅	—	2	4	no	—
154	C₂²×C₃×D₅	—	2	4	no	—
155	C₂²×C₃×D₅	#41	1	4	yes	—
156	C₂²×C₃×D₅	C₂⁴	1	4	yes	—
157	C₂²×C₃×D₅	C₂⁴	1	2	yes	—
158	C₂×C₃×C₄×C₅	—	2	2	no	—
159	C₂×C₃×C₄×C₅	—	2	2	no	—
160	C₂×C₃×C₄×C₅	—	2	4	no	—
161	C₂×C₃×C₄×C₅	—	2	4	no	—
162	C₂×C₃×C₄×C₅	#41	1	4	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
164	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
165	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
166	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
167	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
168	C₂×C₃×Dic₅	—	2	4	no	—
169	C₂×C₃×Dic₅	—	2	2	no	—
170	C₂×C₃×Dic₅	—	2	2	no	—
171	C₂×C₃×Dic₅	#41	1	4	yes	—
172	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
173	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
174	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
175	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
176	C₃×D₂₀	—	2	16	no	—
177	C₃×D₂₀	—	2	8	no	—
178	C₃×C₄×D₅	—	2	8	no	—
179	C₃×C₄×D₅	—	2	8	no	—
180	C₃×C₄×D₅	—	2	8	no	—
181	C₃×C₄×D₅	—	2	16	no	—
182	C₃×Dic₁₀	—	2	8	no	—
183	C₂²×C₃×Q₈	—	5	1	no	—
184	C₂²×C₃×D₄	—	5	2	no	—
185	C₂²×C₃×D₄	—	5	1	no	—
186	C₂³×C₃×C₄	—	5	1	no	—
187	C₂³×C₃×C₄	—	5	1	no	—
188	C₂³×C₃×C₄	—	5	1	no	—
189	C₂³×C₃×C₄	—	5	2	no	—
190	C₃×#126	—	5	16	no	—
191	C₃×#125	C₂×D₅	1	8	yes	complemented
192	C₃×#124	—	5	8	no	—
193	C₃×#123	—	5	16	no	—
194	C₃×C₂²⋊Q₈	—	5	8	no	—
195	C₃×#121	—	5	8	no	—
196	C₃×C₄×Q₈	—	5	8	no	—
197	C₃×C₄×D₄	—	5	8	no	—
198	C₃×C₄×D₄	—	5	16	no	—
199	C₃×#117	—	5	16	no	—
200	C₂×C₃×C₄⋊C₄	—	5	2	no	—
201	C₂×C₃×C₄⋊C₄	—	5	2	no	—
202	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
203	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
204	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	—
205	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
206	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
207	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
208	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
209	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
210	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
211	C₂×C₃×C₄²	—	5	1	no	—
212	C₂×C₃×C₄²	—	5	1	no	—
213	C₂×C₃×C₄²	—	5	1	no	—
214	C₂×C₃×C₄²	—	5	2	no	—
215	C₂×C₃×C₄²	—	5	8	no	—
216	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
217	C₂³×D₅	C₂³×C₃	1	2	yes	—
218	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
220	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
221	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
222	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
223	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
224	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
225	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
226	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
227	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
228	C₂×D₂₀	—	2	8	no	—
229	C₂×D₂₀	—	2	4	no	—
230	C₂×D₂₀	C₂³×C₃	1	4	yes	—
231	C₂×D₂₀	C₂³×C₃	1	8	yes	—
232	C₂×C₄×D₅	—	2	4	no	—
233	C₂×C₄×D₅	—	2	4	no	—
234	C₂×C₄×D₅	—	2	4	no	—
235	C₂×C₄×D₅	—	2	8	no	—
236	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
237	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
238	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
239	C₂×C₄×D₅	C₂³×C₃	1	8	yes	—
240	C₂×Dic₁₀	—	2	4	no	—
241	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
242	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
243	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
244	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
245	C₅×C₄⋊C₄	C₂³×C₃	1	8	yes	—
246	C₄²×C₅	C₂³×C₃	1	4	yes	—
247	#685	C₂³×C₃	1	8	yes	—
248	#685	C₂³×C₃	1	8	yes	—
249	#685	C₂³×C₃	1	8	yes	—
250	#685	C₂³×C₃	1	8	yes	—
251	#685	C₂³×C₃	1	8	yes	—
252	C₄⋊Dic₅	C₂³×C₃	1	8	yes	—
253	#683	C₂³×C₃	1	8	yes	—
254	C₄×Dic₅	C₂³×C₃	1	4	yes	—
255	C₄×Dic₅	C₂³×C₃	1	4	yes	—
256	C₄×Dic₅	C₂³×C₃	1	4	yes	—
257	C₄×Dic₅	C₂³×C₃	1	8	yes	—
258	#529	—	5	16	no	—
259	C₂×#126	—	5	2	no	—
260	C₂×#125	C₃×D₅	1	1	yes	characteristic, complemented
261	C₂×#124	—	5	1	no	—
262	C₂×#123	—	5	2	no	—
263	C₂×C₂²⋊Q₈	—	5	1	no	—
264	C₂×#121	—	5	1	no	—
265	C₂×C₄×Q₈	—	5	1	no	—
266	C₂×C₄×D₄	—	5	2	no	—
267	C₂×C₄×D₄	—	5	1	no	—
268	C₂×#117	—	5	2	no	—
269	C₂²×C₄²	—	5	1	no	—
270	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
271	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
272	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
273	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
274	C₂×C₃×D₅	—	2	8	no	—
275	C₂×C₃×D₅	—	2	2	no	—
276	C₂×C₃×D₅	—	2	2	no	—
277	C₂×C₃×D₅	—	2	4	no	—
278	C₂×C₃×D₅	—	2	4	no	—
279	C₂×C₃×D₅	—	2	4	no	—
280	C₂×C₃×D₅	—	4	8	no	—
281	C₂×C₃×D₅	C₂×#41	1	4	yes	—
282	C₃×C₄×C₅	—	2	2	no	—
283	C₃×C₄×C₅	—	2	2	no	—
284	C₃×C₄×C₅	—	2	4	no	—
285	C₃×C₄×C₅	—	2	4	no	—
286	C₃×C₄×C₅	C₂×#41	1	4	yes	—
287	C₃×Dic₅	—	2	4	no	—
288	C₃×Dic₅	—	2	2	no	—
289	C₃×Dic₅	—	2	2	no	—
290	C₃×Dic₅	C₂×#41	1	4	yes	—
291	C₂⁴×C₃	—	5	1	no	—
292	C₂⁴×C₃	—	5	2	no	—
293	C₂×C₃×Q₈	—	5	4	no	—
294	C₂×C₃×Q₈	—	10	4	no	—
295	C₂×C₃×D₄	—	5	8	no	—
296	C₂×C₃×D₄	—	5	4	no	—
297	C₂×C₃×D₄	—	10	8	no	—
298	C₂×C₃×D₄	—	10	4	no	—
299	C₂²×C₃×C₄	—	5	1	no	—
300	C₂²×C₃×C₄	—	5	1	no	—
301	C₂²×C₃×C₄	—	5	1	no	—
302	C₂²×C₃×C₄	—	5	2	no	—
303	C₂²×C₃×C₄	—	5	4	no	—
304	C₂²×C₃×C₄	—	5	4	no	—
305	C₂²×C₃×C₄	—	5	4	no	—
306	C₂²×C₃×C₄	—	5	8	no	—
307	C₂²×C₃×C₄	—	10	4	no	—
308	C₂²×C₃×C₄	—	10	8	no	—
309	C₂²×C₃×C₄	—	10	4	no	—
310	C₂²×C₃×C₄	—	10	4	no	—
311	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
312	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
313	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
314	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
315	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
316	C₃×C₄⋊C₄	—	5	8	no	—
317	C₃×C₄⋊C₄	—	5	8	no	—
318	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
319	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
320	C₃×C₄⋊C₄	C₂²×D₅	1	8	yes	—
321	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
322	C₃×C₂²⋊C₄	—	5	8	no	—
323	C₃×C₂²⋊C₄	—	5	8	no	—
324	C₃×C₂²⋊C₄	—	5	8	no	—
325	C₃×C₂²⋊C₄	—	5	8	no	—
326	C₃×C₂²⋊C₄	—	5	8	no	—
327	C₃×C₄²	—	5	4	no	—
328	C₃×C₄²	—	5	4	no	—
329	C₃×C₄²	—	5	4	no	—
330	C₃×C₄²	—	5	8	no	—
331	C₃×C₄²	C₂²×D₅	1	4	yes	—
332	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
333	C₂²×D₅	—	2	2	no	—
334	C₂²×D₅	—	2	2	no	—
335	C₂²×D₅	—	2	4	no	—
336	C₂²×D₅	—	2	4	no	—
337	C₂²×D₅	—	2	4	no	—
338	C₂²×D₅	C₃×#41	1	4	yes	—
339	C₂²×D₅	C₂⁴×C₃	1	4	yes	—
340	C₂²×D₅	C₂⁴×C₃	1	2	yes	—
341	C₂×C₄×C₅	—	2	2	no	—
342	C₂×C₄×C₅	—	2	2	no	—
343	C₂×C₄×C₅	—	2	4	no	—
344	C₂×C₄×C₅	—	2	4	no	—
345	C₂×C₄×C₅	C₃×#41	1	4	yes	—
346	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
347	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
348	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
349	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
350	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
351	C₂×Dic₅	—	2	4	no	—
352	C₂×Dic₅	—	2	2	no	—
353	C₂×Dic₅	—	2	2	no	—
354	C₂×Dic₅	C₃×#41	1	4	yes	—
355	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
356	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
357	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
358	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
359	D₂₀	—	2	16	no	—
360	D₂₀	—	2	8	no	—
361	C₄×D₅	—	2	8	no	—
362	C₄×D₅	—	2	8	no	—
363	C₄×D₅	—	2	8	no	—
364	C₄×D₅	—	2	16	no	—
365	Dic₁₀	—	2	8	no	—
366	C₂²×Q₈	—	5	1	no	—
367	C₂²×D₄	—	5	2	no	—
368	C₂²×D₄	—	5	1	no	—
369	C₂³×C₄	—	5	2	no	—
370	C₂³×C₄	—	5	1	no	—
371	C₂³×C₄	—	5	1	no	—
372	C₂³×C₄	—	5	1	no	—
373	#126	—	5	16	no	—
374	#125	C₂×C₃×D₅	1	8	yes	complemented
375	#124	—	5	8	no	—
376	#123	—	5	16	no	—
377	C₂²⋊Q₈	—	5	8	no	—
378	#121	—	5	8	no	—
379	C₄×Q₈	—	5	8	no	—
380	C₄×D₄	—	5	8	no	—
381	C₄×D₄	—	5	16	no	—
382	#117	—	5	16	no	—
383	C₂×C₄⋊C₄	—	5	2	no	—
384	C₂×C₄⋊C₄	—	5	2	no	—
385	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
386	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
387	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	—
388	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
389	C₂×C₂²⋊C₄	—	5	2	no	—
390	C₂×C₂²⋊C₄	—	5	2	no	—
391	C₂×C₂²⋊C₄	—	5	2	no	—
392	C₂×C₂²⋊C₄	—	5	2	no	—
393	C₂×C₂²⋊C₄	—	5	2	no	—
394	C₂×C₄²	—	5	1	no	—
395	C₂×C₄²	—	5	2	no	—
396	C₂×C₄²	—	5	1	no	—
397	C₂×C₄²	—	5	1	no	—
398	C₂×C₄²	—	5	8	no	—
399	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
400	C₂×C₃×C₅	#529	1	4	yes	complemented
401	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
402	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
403	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
404	C₃×D₅	—	2	4	no	—
405	C₃×D₅	—	4	4	no	—
406	C₂³×C₃	—	5	4	no	—
407	C₂³×C₃	—	5	2	no	—
408	C₂³×C₃	—	5	4	no	—
409	C₂³×C₃	—	10	2	no	—
410	C₂³×C₃	—	10	2	no	—
411	C₂³×C₃	—	10	4	no	—
412	C₂³×C₃	—	10	4	no	—
413	C₂³×C₃	—	10	4	no	—
414	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
415	C₃×Q₈	—	10	8	no	—
416	C₃×D₄	—	10	16	no	—
417	C₃×D₄	—	10	8	no	—
418	C₂×C₃×C₄	—	2	2	no	—
419	C₂×C₃×C₄	—	2	4	no	—
420	C₂×C₃×C₄	—	2	2	no	—
421	C₂×C₃×C₄	—	2	4	no	—
422	C₂×C₃×C₄	—	5	4	no	—
423	C₂×C₃×C₄	—	5	2	no	—
424	C₂×C₃×C₄	—	5	2	no	—
425	C₂×C₃×C₄	—	5	2	no	—
426	C₂×C₃×C₄	—	5	4	no	—
427	C₂×C₃×C₄	—	10	8	no	—
428	C₂×C₃×C₄	—	10	16	no	—
429	C₂×C₃×C₄	—	10	8	no	—
430	C₂×C₃×C₄	—	10	2	no	—
431	C₂×C₃×C₄	—	10	4	no	—
432	C₂×C₃×C₄	—	10	2	no	—
433	C₂×C₃×C₄	—	10	8	no	—
434	C₂×C₃×C₄	#713	1	4	yes	—
435	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
436	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
437	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
438	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
439	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
440	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
441	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
442	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
443	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
444	C₂×D₅	—	2	2	no	—
445	C₂×D₅	—	2	2	no	—
446	C₂×D₅	—	2	8	no	—
447	C₂×D₅	—	2	4	no	—
448	C₂×D₅	—	2	4	no	—
449	C₂×D₅	—	2	4	no	—
450	C₂×D₅	—	4	8	no	—
451	C₂×D₅	C₂×C₃×#41	1	4	yes	—
452	C₄×C₅	—	2	2	no	—
453	C₄×C₅	—	2	2	no	—
454	C₄×C₅	—	2	4	no	—
455	C₄×C₅	—	2	4	no	—
456	C₄×C₅	C₂×C₃×#41	1	4	yes	—
457	Dic₅	—	2	4	no	—
458	Dic₅	—	2	2	no	—
459	Dic₅	—	2	2	no	—
460	Dic₅	C₂×C₃×#41	1	4	yes	—
461	C₂⁴	—	5	1	no	—
462	C₂⁴	—	5	2	no	—
463	C₂×Q₈	—	5	4	no	—
464	C₂×Q₈	—	10	4	no	—
465	C₂×D₄	—	5	8	no	—
466	C₂×D₄	—	5	4	no	—
467	C₂×D₄	—	10	8	no	—
468	C₂×D₄	—	10	4	no	—
469	C₂²×C₄	—	5	1	no	—
470	C₂²×C₄	—	5	1	no	—
471	C₂²×C₄	—	5	1	no	—
472	C₂²×C₄	—	5	2	no	—
473	C₂²×C₄	—	5	4	no	—
474	C₂²×C₄	—	5	4	no	—
475	C₂²×C₄	—	5	4	no	—
476	C₂²×C₄	—	5	8	no	—
477	C₂²×C₄	—	10	4	no	—
478	C₂²×C₄	—	10	8	no	—
479	C₂²×C₄	—	10	4	no	—
480	C₂²×C₄	—	10	4	no	—
481	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
482	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
483	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
484	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
485	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
486	C₄⋊C₄	—	5	8	no	—
487	C₄⋊C₄	—	5	8	no	—
488	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
489	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
490	C₄⋊C₄	C₂²×C₃×D₅	1	8	yes	—
491	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
492	C₂²⋊C₄	—	5	8	no	—
493	C₂²⋊C₄	—	5	8	no	—
494	C₂²⋊C₄	—	5	8	no	—
495	C₂²⋊C₄	—	5	8	no	—
496	C₂²⋊C₄	—	5	8	no	—
497	C₄²	—	5	4	no	—
498	C₄²	—	5	4	no	—
499	C₄²	—	5	4	no	—
500	C₄²	—	5	8	no	—
501	C₄²	C₂²×C₃×D₅	1	4	yes	—
502	C₃×C₅	C₂×#529	1	1	yes	characteristic, complemented, Hall
503	C₂²×C₃	—	5	4	no	—
504	C₂²×C₃	—	10	2	no	—
505	C₂²×C₃	—	10	2	no	—
506	C₂²×C₃	—	10	8	no	—
507	C₂²×C₃	—	10	4	no	—
508	C₂²×C₃	—	10	4	no	—
509	C₂²×C₃	—	10	4	no	—
510	C₂²×C₃	—	20	8	no	—
511	C₂²×C₃	C₂×#713	1	2	yes	—
512	C₂²×C₃	D₅×#41	1	2	yes	—
513	C₂²×C₃	D₅×#41	1	2	yes	—
514	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
515	C₃×C₄	—	2	2	no	—
516	C₃×C₄	—	2	4	no	—
517	C₃×C₄	—	2	2	no	—
518	C₃×C₄	—	2	4	no	—
519	C₃×C₄	—	5	4	no	—
520	C₃×C₄	—	10	2	no	—
521	C₃×C₄	—	10	4	no	—
522	C₃×C₄	—	10	2	no	—
523	C₃×C₄	C₂×#713	1	4	yes	—
524	C₂×C₅	C₃×#529	1	4	yes	complemented
525	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
526	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
527	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
528	D₅	—	2	4	no	—
529	D₅	—	4	4	no	—
530	C₂³	—	5	4	no	—
531	C₂³	—	5	2	no	—
532	C₂³	—	5	4	no	—
533	C₂³	—	10	2	no	—
534	C₂³	—	10	2	no	—
535	C₂³	—	10	4	no	—
536	C₂³	—	10	4	no	—
537	C₂³	—	10	4	no	—
538	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
539	Q₈	—	10	8	no	—
540	D₄	—	10	16	no	—
541	D₄	—	10	8	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	4	no	—
544	C₂×C₄	—	2	2	no	—
545	C₂×C₄	—	2	4	no	—
546	C₂×C₄	—	5	4	no	—
547	C₂×C₄	—	5	2	no	—
548	C₂×C₄	—	5	2	no	—
549	C₂×C₄	—	5	2	no	—
550	C₂×C₄	—	5	4	no	—
551	C₂×C₄	—	10	8	no	—
552	C₂×C₄	—	10	16	no	—
553	C₂×C₄	—	10	8	no	—
554	C₂×C₄	—	10	2	no	—
555	C₂×C₄	—	10	4	no	—
556	C₂×C₄	—	10	2	no	—
557	C₂×C₄	—	10	8	no	—
558	C₂×C₄	C₃×#713	1	4	yes	—
559	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
560	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
561	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
562	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
563	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
564	C₂×C₃	—	10	4	no	—
565	C₂×C₃	—	20	4	no	—
566	C₂×C₃	#66025	1	4	yes	direct product factor
567	C₂×C₃	C₂²×#713	1	1	yes	characteristic
568	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
569	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
570	C₅	C₂×C₃×#529	1	1	yes	characteristic, complemented, Sylow
571	C₂²	—	5	4	no	—
572	C₂²	—	10	2	no	—
573	C₂²	—	10	2	no	—
574	C₂²	—	10	8	no	—
575	C₂²	—	10	4	no	—
576	C₂²	—	10	4	no	—
577	C₂²	—	10	4	no	—
578	C₂²	—	20	8	no	—
579	C₂²	C₂×C₃×#713	1	2	yes	—
580	C₂²	C₃×D₅×#41	1	2	yes	—
581	C₂²	C₃×D₅×#41	1	2	yes	—
582	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
583	C₄	—	2	2	no	—
584	C₄	—	2	4	no	—
585	C₄	—	2	2	no	—
586	C₄	—	2	4	no	—
587	C₄	—	5	4	no	—
588	C₄	—	10	2	no	—
589	C₄	—	10	4	no	—
590	C₄	—	10	2	no	—
591	C₄	C₂×C₃×#713	1	4	yes	—
592	C₃	C₂×#66025	1	1	yes	characteristic, direct product factor, Sylow
593	C₂	—	10	4	no	—
594	C₂	—	20	4	no	—
595	C₂	C₃×#66025	1	4	yes	direct product factor
596	C₂	C₂²×C₃×#713	1	1	yes	characteristic
597	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
598	C₂	C₂×C₃×D₅×#41	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	C₂×C₃×#4041	C₂
hypercenter	C₂×C₃×#125	D₅
hypocenter	C₅	C₂×C₃×#529
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×#66025	C₂	direct (N × H)
3. C₂×C₃×#4044	C₂	semidirect
4. C₂×C₃×#4043	C₂	semidirect
6. C₂×C₃×#4040	C₂	semidirect
7. C₂×C₃×#4039	C₂	semidirect
8. C₂×C₃×#4039	C₂	semidirect
9. C₂×C₃×#4038	C₂	semidirect
10. C₂×C₃×#4033	C₂	semidirect
11. C₂×C₃×#4021	C₂	semidirect
12. C₂×C₃×C₄²×D₅	C₂	semidirect
13. C₂×#66025	C₃	direct (N × H)
21. C₃×C₅×#125	C₂²	semidirect
38. C₃×#4044	C₂²	semidirect
39. C₃×#4043	C₂²	semidirect
41. C₃×#4040	C₂²	semidirect
42. C₃×#4039	C₂²	semidirect
43. C₃×#4039	C₂²	semidirect
44. C₃×#4038	C₂²	semidirect
45. C₃×#4033	C₂²	semidirect
46. C₃×#4021	C₂²	semidirect
47. C₃×C₄²×D₅	C₂²	semidirect
49. C₂×C₅×#125	C₂×C₃	semidirect
50. #66025	C₂×C₃	direct (N × H)
51. C₂×#4044	C₂×C₃	semidirect
52. C₂×#4043	C₂×C₃	semidirect
54. C₂×#4040	C₂×C₃	semidirect
55. C₂×#4039	C₂×C₃	semidirect
56. C₂×#4039	C₂×C₃	semidirect
57. C₂×#4038	C₂×C₃	semidirect
58. C₂×#4033	C₂×C₃	semidirect
59. C₂×#4021	C₂×C₃	semidirect
60. C₂×C₄²×D₅	C₂×C₃	semidirect
104. C₂×C₃×#125	D₅	semidirect
121. C₅×#125	C₂²×C₃	semidirect
138. #4044	C₂²×C₃	semidirect
139. #4043	C₂²×C₃	semidirect
141. #4040	C₂²×C₃	semidirect
142. #4039	C₂²×C₃	semidirect
143. #4039	C₂²×C₃	semidirect
144. #4038	C₂²×C₃	semidirect
145. #4033	C₂²×C₃	semidirect
146. #4021	C₂²×C₃	semidirect
147. C₄²×D₅	C₂²×C₃	semidirect
191. C₃×#125	C₂×D₅	semidirect
260. C₂×#125	C₃×D₅	semidirect
374. #125	C₂×C₃×D₅	semidirect
400. C₂×C₃×C₅	#529	semidirect
502. C₃×C₅	C₂×#529	semidirect
524. C₂×C₅	C₃×#529	semidirect
566. C₂×C₃	#66025	direct (N × H)
570. C₅	C₂×C₃×#529	semidirect
592. C₃	C₂×#66025	direct (N × H)
595. C₂	C₃×#66025	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×#66025	2
C₂×C₃×#4044	2
C₂×C₃×#4043	2
C₂×C₃×#4041	2
C₂×C₃×#4040	2
C₂×C₃×#4039	2
C₂×C₃×#4038	2
C₂×C₃×#4033	2
C₂×C₃×#4021	2
C₂×C₃×C₄²×D₅	2
C₂×#66025	3
C₂×C₃×#529	5

Subgroups — C2×C3×#66025 #14479791

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#66025 #14479791