Subgroups — C₃×#10611013 #14413901

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₄²×D₅	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65214	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65126	C₂	1	2	yes	maximal, complemented
5	C₃×#65124	C₂	1	2	yes	maximal, complemented
6	C₃×#65015	C₂	1	2	yes	maximal
7	C₃×#65008	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#676	C₂	1	2	yes	maximal, complemented
9	C₃×#64974	C₂	1	2	yes	maximal, complemented
10	#10611013	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₄	1	1	yes	characteristic
13	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
16	C₂×C₃×C₄×Dic₅	C₄	1	1	yes	characteristic
17	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#676	C₂²	1	4	yes	—
19	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
20	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
21	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
22	C₃×C₄²×D₅	C₄	1	1	yes	characteristic
23	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
24	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
25	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
26	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
27	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	complemented
28	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
29	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
30	C₃×C₂²⋊#168	C₂²	1	2	yes	—
31	C₃×#3952	C₂²	1	4	yes	—
32	C₃×#3947	C₂²	1	4	yes	complemented
33	C₃×#3946	C₂²	1	4	yes	complemented
34	C₃×C₄⋊#168	C₂²	1	2	yes	complemented
35	C₃×C₄×#168	C₂²	1	2	yes	complemented
36	C₃×#2920	—	5	1	no	maximal, Hall
37	C₂×C₄²×D₅	C₂×C₃	1	1	yes	characteristic
38	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
39	#65214	C₂×C₃	1	1	yes	characteristic, complemented
40	#65126	C₂×C₃	1	2	yes	complemented
41	#65124	C₂×C₃	1	2	yes	complemented
42	#65015	C₂×C₃	1	2	yes	—
43	#65008	C₂×C₃	1	2	yes	complemented
44	C₄×#676	C₂×C₃	1	2	yes	complemented
45	#64974	C₂×C₃	1	2	yes	complemented
46	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
48	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
52	C₂²×C₃×Dic₅	C₂×C₄	1	1	yes	characteristic
53	C₂×C₃×C₄×D₅	—	2	4	no	—
54	C₂×C₃×C₄×D₅	—	2	4	no	—
55	C₂×C₃×C₄×D₅	—	2	4	no	—
56	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
57	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
58	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
59	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
64	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	C₂×C₄	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
69	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
70	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
74	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
75	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
76	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
77	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
78	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
79	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
80	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
81	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
82	C₃×C₄×Dic₅	C₂×C₄	1	1	yes	characteristic
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×#168	C₂³	1	4	yes	—
86	C₃×#676	—	2	8	no	—
87	C₂²×C₃×C₄²	—	5	1	no	—
88	C₃×#432	—	5	2	no	—
89	C₃×#432	—	5	2	no	—
90	C₃×#431	—	5	1	no	—
91	C₃×#431	—	5	2	no	—
92	C₃×#431	D₅	1	1	yes	characteristic, complemented
93	C₃×#423	—	5	2	no	—
94	C₃×#407	—	5	2	no	—
95	C₃×C₄×M₁₆	—	5	2	no	—
96	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
97	C₂²×C₄×D₅	C₃×C₄	1	1	yes	characteristic
98	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
101	C₂×C₄×Dic₅	C₃×C₄	1	1	yes	characteristic
102	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
103	C₂×#676	C₂²×C₃	1	4	yes	—
104	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
105	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
106	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
107	C₄²×D₅	C₃×C₄	1	1	yes	characteristic
108	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
109	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
110	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
111	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
112	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	complemented
113	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
114	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
115	C₂²⋊#168	C₂²×C₃	1	2	yes	—
116	#3952	C₂²×C₃	1	4	yes	—
117	#3947	C₂²×C₃	1	4	yes	complemented
118	#3946	C₂²×C₃	1	4	yes	complemented
119	C₄⋊#168	C₂²×C₃	1	2	yes	complemented
120	C₄×#168	C₂²×C₃	1	2	yes	complemented
121	#2920	—	5	1	no	Sylow
122	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
123	C₂²×C₃×D₅	—	2	2	no	—
124	C₂²×C₃×D₅	—	2	2	no	—
125	C₂²×C₃×D₅	—	2	2	no	—
126	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
127	C₂²×C₃×D₅	C₂²×C₄	1	1	yes	characteristic
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	M₁₆	1	4	yes	complemented
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
137	C₂×C₃×Dic₅	—	2	2	no	—
138	C₂×C₃×Dic₅	—	2	2	no	—
139	C₂×C₃×Dic₅	—	2	2	no	—
140	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
143	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
144	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
145	C₂×C₃×Dic₅	C₂²×C₄	1	1	yes	characteristic
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×C₄×D₅	—	2	2	no	—
148	C₃×C₄×D₅	—	2	2	no	—
149	C₃×C₄×D₅	—	2	2	no	—
150	C₃×C₄×D₅	—	2	2	no	—
151	C₃×C₄×D₅	—	2	2	no	—
152	C₃×C₄×D₅	—	2	2	no	—
153	C₃×C₄×D₅	—	2	2	no	—
154	C₃×C₄×D₅	—	2	2	no	—
155	C₃×C₄×D₅	—	2	2	no	—
156	C₃×C₄×D₅	M₁₆	1	4	yes	complemented
157	C₃×C₄×D₅	#41	1	4	yes	—
158	C₃×C₅×C₈	—	2	4	no	—
159	C₃×#168	—	2	4	no	—
160	C₂³×C₃×C₄	—	5	1	no	—
161	C₂³×C₃×C₄	—	5	1	no	—
162	C₂³×C₃×C₄	—	5	1	no	—
163	C₂×C₃×M₁₆	—	5	4	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×C₃×C₄²	—	5	1	no	—
166	C₂×C₃×C₄²	—	5	1	no	—
167	C₂×C₃×C₄²	—	5	1	no	—
168	C₂×C₃×C₄²	—	5	1	no	—
169	C₂×C₃×C₄²	—	5	1	no	—
170	C₂×C₃×C₄²	—	5	1	no	—
171	C₂×C₃×C₄²	—	5	1	no	—
172	C₂×C₃×C₄²	—	5	1	no	—
173	C₂×C₃×C₄²	—	5	1	no	—
174	C₂×C₃×C₄²	—	5	1	no	—
175	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
176	C₃×C₄⋊C₈	—	5	4	no	—
177	C₃×C₄⋊C₈	—	5	2	no	—
178	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	complemented
179	C₃×C₂²⋊C₈	—	5	2	no	—
180	C₃×C₂²⋊C₈	—	5	4	no	—
181	C₃×C₂²⋊C₈	C₂×D₅	1	2	yes	—
182	C₃×#97	—	5	4	no	—
183	C₃×C₄×C₈	—	5	2	no	—
184	C₃×C₄×C₈	C₂×D₅	1	2	yes	complemented
185	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
190	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
191	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
192	C₂×C₄×D₅	—	2	4	no	—
193	C₂×C₄×D₅	—	2	4	no	—
194	C₂×C₄×D₅	—	2	4	no	—
195	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
196	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
197	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
198	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
199	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
200	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
201	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
202	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
203	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
204	C₂×C₄×D₅	C₂×C₃×C₄	1	1	yes	characteristic
205	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
206	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
208	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
209	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic
210	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
213	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
214	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
215	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
216	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
217	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
218	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
219	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
220	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
221	C₄×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
222	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
223	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
224	C₂×#168	C₂³×C₃	1	4	yes	—
225	#676	—	2	8	no	—
226	C₂²×C₄²	—	5	1	no	—
227	#432	—	5	2	no	—
228	#432	—	5	2	no	—
229	#431	—	5	1	no	—
230	#431	—	5	2	no	—
231	#431	C₃×D₅	1	1	yes	characteristic, complemented
232	#423	—	5	2	no	—
233	#407	—	5	2	no	—
234	C₄×M₁₆	—	5	2	no	—
235	C₂²×C₃×C₅	—	2	1	no	—
236	C₂²×C₃×C₅	—	2	1	no	—
237	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
238	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₂×C₃×D₅	—	2	8	no	—
240	C₂×C₃×D₅	—	2	1	no	—
241	C₂×C₃×D₅	—	2	1	no	—
242	C₂×C₃×D₅	—	2	1	no	—
243	C₂×C₃×D₅	—	2	1	no	—
244	C₂×C₃×D₅	#117	1	2	yes	—
245	C₂×C₃×D₅	C₂×M₁₆	1	2	yes	—
246	C₃×C₄×C₅	—	2	1	no	—
247	C₃×C₄×C₅	—	2	1	no	—
248	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
249	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
250	C₃×C₄×C₅	C₂×M₁₆	1	2	yes	—
251	C₃×C₄×C₅	C₂×#41	1	2	yes	—
252	C₃×Dic₅	—	2	1	no	—
253	C₃×Dic₅	—	2	1	no	—
254	C₃×Dic₅	—	2	1	no	—
255	C₃×Dic₅	—	2	1	no	—
256	C₃×Dic₅	#117	1	2	yes	—
257	C₃×Dic₅	C₂×M₁₆	1	2	yes	—
258	C₂⁴×C₃	—	5	1	no	—
259	C₂²×C₃×C₄	—	5	1	no	—
260	C₂²×C₃×C₄	—	5	1	no	—
261	C₂²×C₃×C₄	—	5	1	no	—
262	C₂²×C₃×C₄	—	5	1	no	—
263	C₂²×C₃×C₄	—	5	1	no	—
264	C₂²×C₃×C₄	—	5	1	no	—
265	C₂²×C₃×C₄	—	5	1	no	—
266	C₂²×C₃×C₄	—	5	1	no	—
267	C₂²×C₃×C₄	—	5	1	no	—
268	C₂²×C₃×C₄	—	5	1	no	—
269	C₂²×C₃×C₄	—	5	1	no	—
270	C₂²×C₃×C₄	—	5	1	no	—
271	C₂²×C₃×C₄	—	5	1	no	—
272	C₂²×C₃×C₄	—	5	1	no	—
273	C₂²×C₃×C₄	—	5	1	no	—
274	C₂²×C₃×C₄	—	10	4	no	—
275	C₂²×C₃×C₄	—	10	4	no	—
276	C₂²×C₃×C₄	—	10	4	no	—
277	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
280	C₃×M₁₆	—	10	8	no	—
281	C₂×C₃×C₈	—	5	4	no	—
282	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
283	C₃×C₄²	—	5	1	no	—
284	C₃×C₄²	—	5	1	no	—
285	C₃×C₄²	—	5	1	no	—
286	C₃×C₄²	—	5	1	no	—
287	C₃×C₄²	—	5	1	no	—
288	C₃×C₄²	—	5	1	no	—
289	C₃×C₄²	—	5	1	no	—
290	C₃×C₄²	—	5	1	no	—
291	C₃×C₄²	—	5	1	no	—
292	C₃×C₄²	—	5	1	no	—
293	C₃×C₄²	—	5	1	no	—
294	C₃×C₄²	—	5	1	no	—
295	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
296	C₃×C₄²	C₄×D₅	1	1	yes	characteristic
297	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
298	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
299	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
300	C₂²×D₅	—	2	2	no	—
301	C₂²×D₅	—	2	2	no	—
302	C₂²×D₅	—	2	2	no	—
303	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
304	C₂²×D₅	C₂²×C₃×C₄	1	1	yes	characteristic
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	C₃×M₁₆	1	4	yes	complemented
308	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
314	C₂×Dic₅	—	2	2	no	—
315	C₂×Dic₅	—	2	2	no	—
316	C₂×Dic₅	—	2	2	no	—
317	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
318	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
319	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
320	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
321	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
322	C₂×Dic₅	C₂²×C₃×C₄	1	1	yes	characteristic
323	C₄×D₅	—	2	2	no	—
324	C₄×D₅	—	2	2	no	—
325	C₄×D₅	—	2	2	no	—
326	C₄×D₅	—	2	2	no	—
327	C₄×D₅	—	2	2	no	—
328	C₄×D₅	—	2	2	no	—
329	C₄×D₅	—	2	2	no	—
330	C₄×D₅	—	2	2	no	—
331	C₄×D₅	—	2	2	no	—
332	C₄×D₅	—	2	2	no	—
333	C₄×D₅	C₃×M₁₆	1	4	yes	complemented
334	C₄×D₅	C₃×#41	1	4	yes	—
335	C₅×C₈	—	2	4	no	—
336	#168	—	2	4	no	—
337	C₂³×C₄	—	5	1	no	—
338	C₂³×C₄	—	5	1	no	—
339	C₂³×C₄	—	5	1	no	—
340	C₂×M₁₆	—	5	4	no	—
341	C₂×C₄²	—	5	1	no	—
342	C₂×C₄²	—	5	1	no	—
343	C₂×C₄²	—	5	1	no	—
344	C₂×C₄²	—	5	1	no	—
345	C₂×C₄²	—	5	1	no	—
346	C₂×C₄²	—	5	1	no	—
347	C₂×C₄²	—	5	1	no	—
348	C₂×C₄²	—	5	1	no	—
349	C₂×C₄²	—	5	1	no	—
350	C₂×C₄²	—	5	1	no	—
351	C₂×C₄²	—	5	1	no	—
352	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
353	C₄⋊C₈	—	5	4	no	—
354	C₄⋊C₈	—	5	2	no	—
355	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	complemented
356	C₂²⋊C₈	—	5	2	no	—
357	C₂²⋊C₈	—	5	4	no	—
358	C₂²⋊C₈	C₂×C₃×D₅	1	2	yes	—
359	#97	—	5	4	no	—
360	C₄×C₈	—	5	2	no	—
361	C₄×C₈	C₂×C₃×D₅	1	2	yes	complemented
362	C₂×C₃×C₅	—	2	2	no	—
363	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
364	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
366	C₃×D₅	—	2	2	no	—
367	C₃×D₅	—	2	2	no	—
368	C₂³×C₃	—	5	1	no	—
369	C₂³×C₃	—	5	1	no	—
370	C₂³×C₃	—	10	2	no	—
371	C₂³×C₃	—	10	2	no	—
372	C₂³×C₃	—	10	2	no	—
373	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
374	C₂×C₃×C₄	—	2	2	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	5	1	no	—
377	C₂×C₃×C₄	—	5	1	no	—
378	C₂×C₃×C₄	—	5	4	no	—
379	C₂×C₃×C₄	—	5	4	no	—
380	C₂×C₃×C₄	—	5	1	no	—
381	C₂×C₃×C₄	—	5	1	no	—
382	C₂×C₃×C₄	—	5	1	no	—
383	C₂×C₃×C₄	—	5	1	no	—
384	C₂×C₃×C₄	—	10	2	no	—
385	C₂×C₃×C₄	—	10	2	no	—
386	C₂×C₃×C₄	—	10	2	no	—
387	C₂×C₃×C₄	—	10	2	no	—
388	C₂×C₃×C₄	—	10	2	no	—
389	C₂×C₃×C₄	—	10	2	no	—
390	C₂×C₃×C₄	—	10	2	no	—
391	C₂×C₃×C₄	—	10	2	no	—
392	C₂×C₃×C₄	—	10	2	no	—
393	C₂×C₃×C₄	—	10	2	no	—
394	C₂×C₃×C₄	—	10	2	no	—
395	C₂×C₃×C₄	—	10	2	no	—
396	C₂×C₃×C₄	—	10	2	no	—
397	C₂×C₃×C₄	#676	1	4	yes	complemented
398	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
399	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
400	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
401	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
402	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
403	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
404	C₃×C₈	—	2	4	no	—
405	C₃×C₈	—	10	4	no	—
406	C₂²×C₅	—	2	1	no	—
407	C₂²×C₅	—	2	1	no	—
408	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
409	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
410	C₂×D₅	—	2	8	no	—
411	C₂×D₅	—	2	1	no	—
412	C₂×D₅	—	2	1	no	—
413	C₂×D₅	—	2	1	no	—
414	C₂×D₅	—	2	1	no	—
415	C₂×D₅	C₃×#117	1	2	yes	—
416	C₂×D₅	C₂×C₃×M₁₆	1	2	yes	—
417	C₄×C₅	—	2	1	no	—
418	C₄×C₅	—	2	1	no	—
419	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
420	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
421	C₄×C₅	C₂×C₃×M₁₆	1	2	yes	—
422	C₄×C₅	C₂×C₃×#41	1	2	yes	—
423	Dic₅	—	2	1	no	—
424	Dic₅	—	2	1	no	—
425	Dic₅	—	2	1	no	—
426	Dic₅	—	2	1	no	—
427	Dic₅	C₃×#117	1	2	yes	—
428	Dic₅	C₂×C₃×M₁₆	1	2	yes	—
429	C₂⁴	—	5	1	no	—
430	C₂²×C₄	—	5	1	no	—
431	C₂²×C₄	—	5	1	no	—
432	C₂²×C₄	—	5	1	no	—
433	C₂²×C₄	—	5	1	no	—
434	C₂²×C₄	—	5	1	no	—
435	C₂²×C₄	—	5	1	no	—
436	C₂²×C₄	—	5	1	no	—
437	C₂²×C₄	—	5	1	no	—
438	C₂²×C₄	—	5	1	no	—
439	C₂²×C₄	—	5	1	no	—
440	C₂²×C₄	—	5	1	no	—
441	C₂²×C₄	—	5	1	no	—
442	C₂²×C₄	—	5	1	no	—
443	C₂²×C₄	—	5	1	no	—
444	C₂²×C₄	—	5	1	no	—
445	C₂²×C₄	—	10	4	no	—
446	C₂²×C₄	—	10	4	no	—
447	C₂²×C₄	—	10	4	no	—
448	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
449	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
450	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
451	M₁₆	—	10	8	no	—
452	C₂×C₈	—	5	4	no	—
453	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
454	C₄²	—	5	1	no	—
455	C₄²	—	5	1	no	—
456	C₄²	—	5	1	no	—
457	C₄²	—	5	1	no	—
458	C₄²	—	5	1	no	—
459	C₄²	—	5	1	no	—
460	C₄²	—	5	1	no	—
461	C₄²	—	5	1	no	—
462	C₄²	—	5	1	no	—
463	C₄²	—	5	1	no	—
464	C₄²	—	5	1	no	—
465	C₄²	—	5	1	no	—
466	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
467	C₄²	C₃×C₄×D₅	1	1	yes	characteristic
468	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
469	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
470	C₃×C₅	#2920	1	1	yes	characteristic, complemented, Hall
471	C₂²×C₃	—	2	1	no	—
472	C₂²×C₃	—	2	1	no	—
473	C₂²×C₃	—	5	2	no	—
474	C₂²×C₃	—	5	2	no	—
475	C₂²×C₃	—	10	8	no	—
476	C₂²×C₃	—	10	1	no	—
477	C₂²×C₃	—	10	1	no	—
478	C₂²×C₃	—	10	1	no	—
479	C₂²×C₃	—	10	1	no	—
480	C₂²×C₃	C₂×#676	1	2	yes	—
481	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
482	C₃×C₄	—	2	1	no	—
483	C₃×C₄	—	2	1	no	—
484	C₃×C₄	—	5	2	no	—
485	C₃×C₄	—	5	2	no	—
486	C₃×C₄	—	10	1	no	—
487	C₃×C₄	—	10	1	no	—
488	C₃×C₄	—	10	1	no	—
489	C₃×C₄	—	10	1	no	—
490	C₃×C₄	C₂×#676	1	2	yes	—
491	C₃×C₄	C₂×#676	1	2	yes	—
492	C₃×C₄	D₅×M₁₆	1	2	yes	—
493	C₃×C₄	D₅×#41	1	2	yes	—
494	C₂×C₅	—	2	2	no	—
495	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
496	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
497	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
498	D₅	—	2	2	no	—
499	D₅	—	2	2	no	—
500	C₂³	—	5	1	no	—
501	C₂³	—	5	1	no	—
502	C₂³	—	10	2	no	—
503	C₂³	—	10	2	no	—
504	C₂³	—	10	2	no	—
505	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	2	no	—
508	C₂×C₄	—	5	1	no	—
509	C₂×C₄	—	5	1	no	—
510	C₂×C₄	—	5	4	no	—
511	C₂×C₄	—	5	4	no	—
512	C₂×C₄	—	5	1	no	—
513	C₂×C₄	—	5	1	no	—
514	C₂×C₄	—	5	1	no	—
515	C₂×C₄	—	5	1	no	—
516	C₂×C₄	—	10	2	no	—
517	C₂×C₄	—	10	2	no	—
518	C₂×C₄	—	10	2	no	—
519	C₂×C₄	—	10	2	no	—
520	C₂×C₄	—	10	2	no	—
521	C₂×C₄	—	10	2	no	—
522	C₂×C₄	—	10	2	no	—
523	C₂×C₄	—	10	2	no	—
524	C₂×C₄	—	10	2	no	—
525	C₂×C₄	—	10	2	no	—
526	C₂×C₄	—	10	2	no	—
527	C₂×C₄	—	10	2	no	—
528	C₂×C₄	—	10	2	no	—
529	C₂×C₄	C₃×#676	1	4	yes	complemented
530	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
531	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
532	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
533	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
534	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
535	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
536	C₈	—	2	4	no	—
537	C₈	—	10	4	no	—
538	C₂×C₃	—	2	2	no	—
539	C₂×C₃	—	10	2	no	—
540	C₂×C₃	—	10	2	no	—
541	C₂×C₃	D₅×#117	1	1	yes	characteristic
542	C₂×C₃	C₂²×#676	1	1	yes	characteristic
543	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
544	C₅	C₃×#2920	1	1	yes	characteristic, complemented, Sylow
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	5	2	no	—
548	C₂²	—	5	2	no	—
549	C₂²	—	10	8	no	—
550	C₂²	—	10	1	no	—
551	C₂²	—	10	1	no	—
552	C₂²	—	10	1	no	—
553	C₂²	—	10	1	no	—
554	C₂²	C₂×C₃×#676	1	2	yes	—
555	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
556	C₄	—	2	1	no	—
557	C₄	—	2	1	no	—
558	C₄	—	5	2	no	—
559	C₄	—	5	2	no	—
560	C₄	—	10	1	no	—
561	C₄	—	10	1	no	—
562	C₄	—	10	1	no	—
563	C₄	—	10	1	no	—
564	C₄	C₂×C₃×#676	1	2	yes	—
565	C₄	C₂×C₃×#676	1	2	yes	—
566	C₄	C₃×D₅×M₁₆	1	2	yes	—
567	C₄	C₃×D₅×#41	1	2	yes	—
568	C₃	#10611013	1	1	yes	characteristic, direct product factor, Sylow
569	C₂	—	2	2	no	—
570	C₂	—	10	2	no	—
571	C₂	—	10	2	no	—
572	C₂	C₃×D₅×#117	1	1	yes	characteristic
573	C₂	C₂²×C₃×#676	1	1	yes	characteristic
574	C₂	C₂×C₃×D₅×M₁₆	1	1	yes	characteristic

	subgroup	G/H
center	C₃×C₄²	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#431	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₂³×C₃×D₅	C₂×C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#431	D₅
hypocenter	C₅	C₃×#2920
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₃×C₄² ◁ C₃×#431

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#431	C₂	semidirect
3. C₃×#65214	C₂	semidirect
4. C₃×#65126	C₂	semidirect
5. C₃×#65124	C₂	semidirect
7. C₃×#65008	C₂	semidirect
8. C₃×C₄×#676	C₂	semidirect
9. C₃×#64974	C₂	semidirect
10. #10611013	C₃	direct (N × H)
27. C₃×C₅×C₄⋊C₈	C₂²	semidirect
29. C₃×C₄×C₅×C₈	C₂²	semidirect
32. C₃×#3947	C₂²	semidirect
33. C₃×#3946	C₂²	semidirect
34. C₃×C₄⋊#168	C₂²	semidirect
35. C₃×C₄×#168	C₂²	semidirect
38. C₅×#431	C₂×C₃	semidirect
39. #65214	C₂×C₃	semidirect
40. #65126	C₂×C₃	semidirect
41. #65124	C₂×C₃	semidirect
43. #65008	C₂×C₃	semidirect
44. C₄×#676	C₂×C₃	semidirect
45. #64974	C₂×C₃	semidirect
92. C₃×#431	D₅	semidirect
112. C₅×C₄⋊C₈	C₂²×C₃	semidirect
114. C₄×C₅×C₈	C₂²×C₃	semidirect
117. #3947	C₂²×C₃	semidirect
118. #3946	C₂²×C₃	semidirect
119. C₄⋊#168	C₂²×C₃	semidirect
120. C₄×#168	C₂²×C₃	semidirect
130. C₂×C₃×C₄×C₅	M₁₆	semidirect
156. C₃×C₄×D₅	M₁₆	semidirect
178. C₃×C₄⋊C₈	C₂×D₅	semidirect
184. C₃×C₄×C₈	C₂×D₅	semidirect
231. #431	C₃×D₅	semidirect
307. C₂×C₄×C₅	C₃×M₁₆	semidirect
333. C₄×D₅	C₃×M₁₆	semidirect
355. C₄⋊C₈	C₂×C₃×D₅	semidirect
361. C₄×C₈	C₂×C₃×D₅	semidirect
397. C₂×C₃×C₄	#676	semidirect
470. C₃×C₅	#2920	semidirect
529. C₂×C₄	C₃×#676	semidirect
544. C₅	C₃×#2920	semidirect
568. C₃	#10611013	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×C₄²×D₅	2
C₃×C₅×#431	2
C₃×#65214	2
C₃×#65126	2
C₃×#65124	2
C₃×#65015	2
C₃×#65008	2
C₃×C₄×#676	2
C₃×#64974	2
#10611013	3
C₃×#2920	5

Subgroups — C3×#10611013 #14413901

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611013 #14413901