Subgroups — C₃×#10611088 #14435425

Order 1920.

772 conjugacy classes of subgroups.

The subgroup lattice has 528 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#65813	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×Dic₁₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65134	C₂	1	2	yes	maximal, complemented
5	C₃×#65118	C₂	1	2	yes	maximal, complemented
6	C₃×#65028	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65027	C₂	1	1	yes	maximal, characteristic
8	C₃×#65024	C₂	1	1	yes	maximal, characteristic
9	C₃×#65011	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65005	C₂	1	2	yes	maximal, complemented
11	C₃×#64999	C₂	1	2	yes	maximal, complemented
12	#10611088	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
15	C₃×#4076	C₂²	1	1	yes	characteristic
16	C₃×#4075	—	2	1	no	—
17	C₃×C₄×C₂²⋊D₅	—	2	1	no	—
18	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
19	C₃×#4070	C₂²	1	1	yes	characteristic
20	C₂×C₃×#683	—	2	1	no	—
21	C₂×C₃×C₄×Dic₅	—	2	1	no	—
22	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
23	C₂×C₃×#677	C₂²	1	2	yes	—
24	C₃×#4022	—	2	1	no	—
25	C₃×#4021	C₂²	1	1	yes	characteristic
26	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
27	C₃×#4018	—	2	1	no	—
28	C₃×#4016	C₂²	1	1	yes	characteristic
29	C₃×C₄×Dic₁₀	—	2	1	no	—
30	C₃×C₄×Dic₁₀	—	2	1	no	—
31	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
32	C₃×C₄×Dic₁₀	C₂²	1	2	yes	—
33	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
34	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
35	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×#97	C₂²	1	2	yes	—
38	C₃×#3953	C₂²	1	2	yes	—
39	C₃×#3950	C₂²	1	2	yes	—
40	C₃×#3949	C₂²	1	2	yes	—
41	C₃×#3948	C₂²	1	2	yes	—
42	C₃×#3948	C₂²	1	2	yes	—
43	C₃×#3948	C₂²	1	2	yes	—
44	C₃×#3117	—	5	1	no	maximal, Hall
45	#65813	C₂×C₃	1	1	yes	characteristic
46	C₂×C₄×Dic₁₀	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#432	C₂×C₃	1	1	yes	characteristic, complemented
48	#65134	C₂×C₃	1	2	yes	complemented
49	#65118	C₂×C₃	1	2	yes	complemented
50	#65028	C₂×C₃	1	1	yes	characteristic, complemented
51	#65027	C₂×C₃	1	1	yes	characteristic
52	#65024	C₂×C₃	1	1	yes	characteristic
53	#65011	C₂×C₃	1	1	yes	characteristic, complemented
54	#65005	C₂×C₃	1	2	yes	complemented
55	#64999	C₂×C₃	1	2	yes	complemented
56	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₂²×C₃×Dic₅	—	2	1	no	—
61	C₂²×C₃×Dic₅	—	2	1	no	—
62	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₄×D₅	—	2	1	no	—
64	C₂×C₃×Dic₁₀	—	2	1	no	—
65	C₂×C₃×Dic₁₀	—	2	4	no	—
66	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
67	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
71	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×C₂²⋊Dic₅	—	2	1	no	—
75	C₃×#685	—	2	1	no	—
76	C₃×#685	—	2	1	no	—
77	C₃×#685	—	2	1	no	—
78	C₃×#685	—	2	1	no	—
79	C₃×C₄⋊Dic₅	—	2	1	no	—
80	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
81	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
82	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
83	C₃×#683	—	2	2	no	—
84	C₃×#683	—	2	2	no	—
85	C₃×#683	—	2	1	no	—
86	C₃×#683	—	2	1	no	—
87	C₃×#683	—	2	1	no	—
88	C₃×#683	—	2	1	no	—
89	C₃×C₄×Dic₅	—	2	2	no	—
90	C₃×C₄×Dic₅	—	2	2	no	—
91	C₃×C₄×Dic₅	—	2	1	no	—
92	C₃×Dic₂₀	—	2	4	no	—
93	C₃×#677	—	2	4	no	—
94	C₃×#529	—	5	1	no	—
95	C₂×C₃×C₄×Q₈	—	5	1	no	—
96	C₃×#484	—	5	1	no	—
97	C₃×#481	—	5	1	no	—
98	C₃×#479	—	5	2	no	—
99	C₃×#464	—	5	2	no	—
100	C₃×#451	—	5	1	no	—
101	C₃×#448	—	5	1	no	—
102	C₃×#441	—	5	2	no	—
103	C₃×#440	—	5	2	no	—
104	C₃×#432	D₅	1	1	yes	characteristic, complemented
105	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
107	#4076	C₂²×C₃	1	1	yes	characteristic
108	#4075	—	2	1	no	—
109	C₄×C₂²⋊D₅	—	2	1	no	—
110	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
111	#4070	C₂²×C₃	1	1	yes	characteristic
112	C₂×#683	—	2	1	no	—
113	C₂×C₄×Dic₅	—	2	1	no	—
114	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
115	C₂×#677	C₂²×C₃	1	2	yes	—
116	#4022	—	2	1	no	—
117	#4021	C₂²×C₃	1	1	yes	characteristic
118	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
119	#4018	—	2	1	no	—
120	#4016	C₂²×C₃	1	1	yes	characteristic
121	C₄×Dic₁₀	—	2	1	no	—
122	C₄×Dic₁₀	—	2	1	no	—
123	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
124	C₄×Dic₁₀	C₂²×C₃	1	2	yes	—
125	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
126	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
127	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
128	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
129	C₅×#97	C₂²×C₃	1	2	yes	—
130	#3953	C₂²×C₃	1	2	yes	—
131	#3950	C₂²×C₃	1	2	yes	—
132	#3949	C₂²×C₃	1	2	yes	—
133	#3948	C₂²×C₃	1	2	yes	—
134	#3948	C₂²×C₃	1	2	yes	—
135	#3948	C₂²×C₃	1	2	yes	—
136	#3117	—	5	1	no	Sylow
137	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂²×C₃×D₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	4	1	no	—
142	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
145	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₂²⋊D₅	—	4	2	no	—
149	C₂×C₃×Dic₅	—	2	4	no	—
150	C₂×C₃×Dic₅	—	2	2	no	—
151	C₂×C₃×Dic₅	—	2	2	no	—
152	C₂×C₃×Dic₅	—	2	1	no	—
153	C₂×C₃×Dic₅	—	2	1	no	—
154	C₂×C₃×Dic₅	—	2	1	no	—
155	C₂×C₃×Dic₅	—	4	2	no	—
156	C₃×D₂₀	—	2	2	no	—
157	C₃×C₄×D₅	—	4	2	no	—
158	C₃×Dic₁₀	—	2	4	no	—
159	C₃×Dic₁₀	—	2	2	no	—
160	C₃×Dic₁₀	—	2	2	no	—
161	C₃×Dic₁₀	#41	1	4	yes	—
162	C₃×C₅×C₈	—	2	2	no	—
163	C₃×C₅×C₈	—	2	2	no	—
164	C₂²×C₃×Q₈	—	5	1	no	—
165	C₂×C₃×Q₁₆	—	5	2	no	—
166	C₂×C₃×SD₁₆	—	5	2	no	—
167	C₃×#126	—	10	1	no	—
168	C₃×#125	—	5	1	no	—
169	C₃×#124	—	5	1	no	—
170	C₃×#123	—	10	1	no	—
171	C₃×C₂²⋊Q₈	—	5	1	no	—
172	C₃×#121	—	5	1	no	—
173	C₃×C₄×Q₈	—	5	2	no	—
174	C₃×C₄×Q₈	—	5	1	no	—
175	C₃×C₄×Q₈	—	5	2	no	—
176	C₃×C₄×Q₈	—	10	1	no	—
177	C₃×C₄×Q₈	—	10	1	no	—
178	C₃×C₄×D₄	—	5	1	no	—
179	C₃×C₄×D₄	—	10	1	no	—
180	C₃×#117	—	10	1	no	—
181	C₂×C₃×C₄⋊C₄	—	5	1	no	—
182	C₂×C₃×C₄⋊C₄	—	10	1	no	—
183	C₂×C₃×C₄²	—	10	1	no	—
184	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
185	C₃×#107	—	5	2	no	—
186	C₃×#106	—	5	2	no	—
187	C₃×C₄⋊C₈	C₂×D₅	1	2	yes	—
188	C₃×#103	—	5	2	no	—
189	C₃×#103	—	5	2	no	—
190	C₃×#103	—	5	2	no	—
191	C₃×#102	—	5	2	no	—
192	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
193	C₃×C₂²⋊C₈	C₂×D₅	1	1	yes	characteristic
194	C₃×#97	C₂×D₅	1	2	yes	—
195	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
196	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
198	C₂×C₂²⋊D₅	—	2	1	no	—
199	C₂²×Dic₅	—	2	1	no	—
200	C₂²×Dic₅	—	2	1	no	—
201	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₄×D₅	—	2	1	no	—
203	C₂×Dic₁₀	—	2	1	no	—
204	C₂×Dic₁₀	—	2	4	no	—
205	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
206	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
207	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
208	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
209	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
210	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
211	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
213	C₂²⋊Dic₅	—	2	1	no	—
214	#685	—	2	1	no	—
215	#685	—	2	1	no	—
216	#685	—	2	1	no	—
217	#685	—	2	1	no	—
218	C₄⋊Dic₅	—	2	1	no	—
219	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
220	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
221	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
222	#683	—	2	2	no	—
223	#683	—	2	2	no	—
224	#683	—	2	1	no	—
225	#683	—	2	1	no	—
226	#683	—	2	1	no	—
227	#683	—	2	1	no	—
228	C₄×Dic₅	—	2	2	no	—
229	C₄×Dic₅	—	2	2	no	—
230	C₄×Dic₅	—	2	1	no	—
231	Dic₂₀	—	2	4	no	—
232	#677	—	2	4	no	—
233	#529	—	5	1	no	—
234	C₂×C₄×Q₈	—	5	1	no	—
235	#484	—	5	1	no	—
236	#481	—	5	1	no	—
237	#479	—	5	2	no	—
238	#464	—	5	2	no	—
239	#451	—	5	1	no	—
240	#448	—	5	1	no	—
241	#441	—	5	2	no	—
242	#440	—	5	2	no	—
243	#432	C₃×D₅	1	1	yes	characteristic, complemented
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	2	1	no	—
246	C₂²×C₃×C₅	#137	1	2	yes	—
247	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
248	C₂×C₃×D₅	—	4	1	no	—
249	C₂×C₃×D₅	—	4	1	no	—
250	C₂×C₃×D₅	—	4	1	no	—
251	C₃×C₄×C₅	—	2	1	no	—
252	C₃×C₄×C₅	—	2	1	no	—
253	C₃×C₄×C₅	—	2	1	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	C₂×#41	1	2	yes	—
257	C₃×Dic₅	—	2	4	no	—
258	C₃×Dic₅	—	4	1	no	—
259	C₃×Dic₅	—	4	1	no	—
260	C₃×Dic₅	—	4	1	no	—
261	C₃×Dic₅	—	4	2	no	—
262	C₂×C₃×Q₈	—	5	2	no	—
263	C₂×C₃×Q₈	—	5	1	no	—
264	C₂×C₃×Q₈	—	10	4	no	—
265	C₂×C₃×Q₈	—	10	1	no	—
266	C₂×C₃×D₄	—	5	1	no	—
267	C₂×C₃×D₄	—	10	1	no	—
268	C₂²×C₃×C₄	—	10	1	no	—
269	C₂²×C₃×C₄	—	10	1	no	—
270	C₂²×C₃×C₄	—	10	1	no	—
271	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
272	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
274	C₃×Q₁₆	—	10	4	no	—
275	C₃×SD₁₆	—	10	4	no	—
276	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
277	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
278	C₃×C₄⋊C₄	—	5	2	no	—
279	C₃×C₄⋊C₄	—	5	1	no	—
280	C₃×C₄⋊C₄	—	5	1	no	—
281	C₃×C₄⋊C₄	—	10	2	no	—
282	C₃×C₄⋊C₄	—	10	2	no	—
283	C₃×C₄⋊C₄	—	10	1	no	—
284	C₃×C₄⋊C₄	—	10	1	no	—
285	C₃×C₄⋊C₄	—	10	1	no	—
286	C₃×C₄⋊C₄	—	10	1	no	—
287	C₃×C₄⋊C₄	—	10	1	no	—
288	C₃×C₂²⋊C₄	—	10	1	no	—
289	C₃×C₂²⋊C₄	—	10	1	no	—
290	C₃×C₂²⋊C₄	—	10	1	no	—
291	C₃×C₂²⋊C₄	—	10	1	no	—
292	C₃×C₂²⋊C₄	—	10	1	no	—
293	C₃×C₄²	—	10	2	no	—
294	C₃×C₄²	—	10	2	no	—
295	C₃×C₄²	—	10	1	no	—
296	C₃×C₄²	D₂₀	1	1	yes	characteristic
297	C₃×C₄²	D₂₀	1	1	yes	characteristic
298	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
299	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
300	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂²×D₅	—	2	1	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	4	1	no	—
305	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
306	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₂²⋊D₅	—	4	2	no	—
312	C₂×Dic₅	—	2	4	no	—
313	C₂×Dic₅	—	2	2	no	—
314	C₂×Dic₅	—	2	2	no	—
315	C₂×Dic₅	—	2	1	no	—
316	C₂×Dic₅	—	2	1	no	—
317	C₂×Dic₅	—	2	1	no	—
318	C₂×Dic₅	—	4	2	no	—
319	D₂₀	—	2	2	no	—
320	C₄×D₅	—	4	2	no	—
321	Dic₁₀	—	2	4	no	—
322	Dic₁₀	—	2	2	no	—
323	Dic₁₀	—	2	2	no	—
324	Dic₁₀	C₃×#41	1	4	yes	—
325	C₅×C₈	—	2	2	no	—
326	C₅×C₈	—	2	2	no	—
327	C₂²×Q₈	—	5	1	no	—
328	C₂×Q₁₆	—	5	2	no	—
329	C₂×SD₁₆	—	5	2	no	—
330	#126	—	10	1	no	—
331	#125	—	5	1	no	—
332	#124	—	5	1	no	—
333	#123	—	10	1	no	—
334	C₂²⋊Q₈	—	5	1	no	—
335	#121	—	5	1	no	—
336	C₄×Q₈	—	5	2	no	—
337	C₄×Q₈	—	5	2	no	—
338	C₄×Q₈	—	5	1	no	—
339	C₄×Q₈	—	10	1	no	—
340	C₄×Q₈	—	10	1	no	—
341	C₄×D₄	—	5	1	no	—
342	C₄×D₄	—	10	1	no	—
343	#117	—	10	1	no	—
344	C₂×C₄⋊C₄	—	5	1	no	—
345	C₂×C₄⋊C₄	—	10	1	no	—
346	C₂×C₄²	—	10	1	no	—
347	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
348	#107	—	5	2	no	—
349	#106	—	5	2	no	—
350	C₄⋊C₈	C₂×C₃×D₅	1	2	yes	—
351	#103	—	5	2	no	—
352	#103	—	5	2	no	—
353	#103	—	5	2	no	—
354	#102	—	5	2	no	—
355	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
356	C₂²⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
357	#97	C₂×C₃×D₅	1	2	yes	—
358	C₂×C₃×C₅	—	2	2	no	—
359	C₂×C₃×C₅	#525	1	1	yes	characteristic
360	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
361	C₂×C₃×C₅	#575	1	1	yes	characteristic
362	C₃×D₅	—	8	1	no	—
363	C₂³×C₃	—	10	1	no	—
364	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
365	C₃×Q₈	—	5	4	no	—
366	C₃×Q₈	—	10	4	no	—
367	C₃×Q₈	—	10	2	no	—
368	C₃×Q₈	—	10	2	no	—
369	C₃×D₄	—	10	2	no	—
370	C₃×D₄	—	20	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	4	1	no	—
374	C₂×C₃×C₄	—	10	4	no	—
375	C₂×C₃×C₄	—	10	2	no	—
376	C₂×C₃×C₄	—	10	2	no	—
377	C₂×C₃×C₄	—	10	1	no	—
378	C₂×C₃×C₄	—	10	1	no	—
379	C₂×C₃×C₄	—	10	1	no	—
380	C₂×C₃×C₄	—	20	2	no	—
381	C₂×C₃×C₄	—	20	2	no	—
382	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
383	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
384	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
385	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
386	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
387	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
388	C₃×C₈	—	2	2	no	—
389	C₃×C₈	—	2	2	no	—
390	C₂²×C₅	—	2	1	no	—
391	C₂²×C₅	—	2	1	no	—
392	C₂²×C₅	C₃×#137	1	2	yes	—
393	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
394	C₂×D₅	—	4	1	no	—
395	C₂×D₅	—	4	1	no	—
396	C₂×D₅	—	4	1	no	—
397	C₄×C₅	—	2	1	no	—
398	C₄×C₅	—	2	1	no	—
399	C₄×C₅	—	2	1	no	—
400	C₄×C₅	—	2	1	no	—
401	C₄×C₅	—	2	1	no	—
402	C₄×C₅	C₂×C₃×#41	1	2	yes	—
403	Dic₅	—	2	4	no	—
404	Dic₅	—	4	1	no	—
405	Dic₅	—	4	1	no	—
406	Dic₅	—	4	2	no	—
407	Dic₅	—	4	1	no	—
408	C₂×Q₈	—	5	2	no	—
409	C₂×Q₈	—	5	1	no	—
410	C₂×Q₈	—	10	4	no	—
411	C₂×Q₈	—	10	1	no	—
412	C₂×D₄	—	5	1	no	—
413	C₂×D₄	—	10	1	no	—
414	C₂²×C₄	—	10	1	no	—
415	C₂²×C₄	—	10	1	no	—
416	C₂²×C₄	—	10	1	no	—
417	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
418	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
419	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
420	Q₁₆	—	10	4	no	—
421	SD₁₆	—	10	4	no	—
422	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
423	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
424	C₄⋊C₄	—	5	2	no	—
425	C₄⋊C₄	—	5	1	no	—
426	C₄⋊C₄	—	5	1	no	—
427	C₄⋊C₄	—	10	1	no	—
428	C₄⋊C₄	—	10	2	no	—
429	C₄⋊C₄	—	10	2	no	—
430	C₄⋊C₄	—	10	1	no	—
431	C₄⋊C₄	—	10	1	no	—
432	C₄⋊C₄	—	10	1	no	—
433	C₄⋊C₄	—	10	1	no	—
434	C₂²⋊C₄	—	10	1	no	—
435	C₂²⋊C₄	—	10	1	no	—
436	C₂²⋊C₄	—	10	1	no	—
437	C₂²⋊C₄	—	10	1	no	—
438	C₂²⋊C₄	—	10	1	no	—
439	C₄²	—	10	2	no	—
440	C₄²	—	10	2	no	—
441	C₄²	—	10	1	no	—
442	C₄²	C₃×D₂₀	1	1	yes	characteristic
443	C₄²	C₃×D₂₀	1	1	yes	characteristic
444	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
445	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
446	C₃×C₅	#3117	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	1	no	—
448	C₂²×C₃	—	2	1	no	—
449	C₂²×C₃	—	20	1	no	—
450	C₂²×C₃	—	20	1	no	—
451	C₂²×C₃	—	20	1	no	—
452	C₂²×C₃	#4055	1	2	yes	—
453	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
454	C₃×C₄	—	2	1	no	—
455	C₃×C₄	—	2	1	no	—
456	C₃×C₄	—	2	1	no	—
457	C₃×C₄	—	2	1	no	—
458	C₃×C₄	—	2	1	no	—
459	C₃×C₄	—	10	4	no	—
460	C₃×C₄	—	20	1	no	—
461	C₃×C₄	—	20	1	no	—
462	C₃×C₄	—	20	2	no	—
463	C₃×C₄	—	20	1	no	—
464	C₃×C₄	D₅×#41	1	2	yes	—
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	C₃×#525	1	1	yes	characteristic
467	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
468	C₂×C₅	C₃×#575	1	1	yes	characteristic
469	D₅	—	8	1	no	—
470	C₂³	—	10	1	no	—
471	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
472	Q₈	—	5	4	no	—
473	Q₈	—	10	4	no	—
474	Q₈	—	10	2	no	—
475	Q₈	—	10	2	no	—
476	D₄	—	10	2	no	—
477	D₄	—	20	2	no	—
478	C₂×C₄	—	2	2	no	—
479	C₂×C₄	—	2	2	no	—
480	C₂×C₄	—	4	1	no	—
481	C₂×C₄	—	10	4	no	—
482	C₂×C₄	—	10	2	no	—
483	C₂×C₄	—	10	2	no	—
484	C₂×C₄	—	10	1	no	—
485	C₂×C₄	—	10	1	no	—
486	C₂×C₄	—	10	1	no	—
487	C₂×C₄	—	20	2	no	—
488	C₂×C₄	—	20	2	no	—
489	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
490	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
491	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
492	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
493	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
494	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	2	2	no	—
497	C₂×C₃	—	2	2	no	—
498	C₂×C₃	—	40	1	no	—
499	C₂×C₃	#65858	1	1	yes	characteristic
500	C₂×C₃	C₂×#4055	1	1	yes	characteristic
501	C₂×C₃	#66082	1	1	yes	characteristic
502	C₅	C₃×#3117	1	1	yes	characteristic, complemented, Sylow
503	C₂²	—	2	1	no	—
504	C₂²	—	2	1	no	—
505	C₂²	—	20	1	no	—
506	C₂²	—	20	1	no	—
507	C₂²	—	20	1	no	—
508	C₂²	C₃×#4055	1	2	yes	—
509	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
510	C₄	—	2	1	no	—
511	C₄	—	2	1	no	—
512	C₄	—	2	1	no	—
513	C₄	—	2	1	no	—
514	C₄	—	2	1	no	—
515	C₄	—	10	4	no	—
516	C₄	—	20	1	no	—
517	C₄	—	20	1	no	—
518	C₄	—	20	2	no	—
519	C₄	—	20	1	no	—
520	C₄	C₃×D₅×#41	1	2	yes	—
521	C₃	#10611088	1	1	yes	characteristic, direct product factor, Sylow
522	C₂	—	2	2	no	—
523	C₂	—	40	1	no	—
524	C₂	C₃×#65858	1	1	yes	characteristic
525	C₂	C₂×C₃×#4055	1	1	yes	characteristic
526	C₂	C₃×#66082	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#432	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#4076	C₂²
hypercenter	C₃×#432	D₅
hypocenter	C₅	C₃×#3117
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₃×#432

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×Dic₁₀	C₂	semidirect
3. C₃×C₅×#432	C₂	semidirect
4. C₃×#65134	C₂	semidirect
5. C₃×#65118	C₂	semidirect
6. C₃×#65028	C₂	semidirect
9. C₃×#65011	C₂	semidirect
10. C₃×#65005	C₂	semidirect
11. C₃×#64999	C₂	semidirect
12. #10611088	C₃	direct (N × H)
46. C₂×C₄×Dic₁₀	C₂×C₃	semidirect
47. C₅×#432	C₂×C₃	semidirect
48. #65134	C₂×C₃	semidirect
49. #65118	C₂×C₃	semidirect
50. #65028	C₂×C₃	semidirect
53. #65011	C₂×C₃	semidirect
54. #65005	C₂×C₃	semidirect
55. #64999	C₂×C₃	semidirect
104. C₃×#432	D₅	semidirect
243. #432	C₃×D₅	semidirect
446. C₃×C₅	#3117	semidirect
502. C₅	C₃×#3117	semidirect
521. C₃	#10611088	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#65813	2
C₂×C₃×C₄×Dic₁₀	2
C₃×C₅×#432	2
C₃×#65134	2
C₃×#65118	2
C₃×#65028	2
C₃×#65027	2
C₃×#65024	2
C₃×#65011	2
C₃×#65005	2
C₃×#64999	2
#10611088	3
C₃×#3117	5

Subgroups — C3×#10611088 #14435425

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611088 #14435425