Subgroups — C₃×#10613600 #14439076

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4062	C₂	1	2	yes	maximal, complemented
3	C₃×#66059	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66002	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65479	C₂	1	2	yes	maximal, complemented
7	C₃×#65465	C₂	1	2	yes	maximal, complemented
8	C₃×#65375	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65347	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65001	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613600	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	1	yes	characteristic
14	C₂×C₃×#713	C₂²	1	2	yes	—
15	C₂×C₃×#711	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic
20	C₃×#4093	C₂²	1	2	yes	—
21	C₃×#4090	C₂²	1	1	yes	characteristic
22	C₂×C₃×#689	C₂²	1	2	yes	—
23	C₂×C₃×#688	C₂²	1	2	yes	—
24	C₂×C₃×#688	C₂²	1	2	yes	—
25	C₃×#4086	C₂²	1	1	yes	characteristic
26	C₂×C₃×#686	C₂²	1	2	yes	—
27	C₃×#4065	—	2	8	no	—
28	C₃×#4062	—	2	8	no	—
29	C₂×C₃×D₄₀	C₂²	1	2	yes	—
30	C₂×C₃×#677	C₂²	1	2	yes	—
31	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
32	C₃×#4041	—	2	2	no	—
33	C₃×#4039	—	2	2	no	—
34	C₃×#4030	—	2	2	no	—
35	C₃×#4027	—	2	2	no	—
36	C₃×#4021	C₂²	1	1	yes	characteristic
37	C₃×#4020	C₂²	1	1	yes	characteristic
38	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic
40	C₃×#3947	C₂²	1	2	yes	—
41	C₃×#3935	C₂²	1	1	yes	characteristic
42	C₃×#3150	—	5	1	no	maximal, Hall
43	C₂×#4065	C₂×C₃	1	2	yes	complemented
44	C₂×#4062	C₂×C₃	1	2	yes	complemented
45	#66059	C₂×C₃	1	1	yes	characteristic, complemented
46	#66002	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
48	#65479	C₂×C₃	1	2	yes	complemented
49	#65465	C₂×C₃	1	2	yes	complemented
50	#65375	C₂×C₃	1	1	yes	characteristic, complemented
51	#65347	C₂×C₃	1	1	yes	characteristic, complemented
52	#65001	C₂×C₃	1	1	yes	characteristic, complemented
53	D₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₂²×C₃×Dic₅	—	2	1	no	—
60	C₃×#713	—	2	4	no	—
61	C₃×#713	—	2	4	no	—
62	C₃×#713	—	2	4	no	—
63	C₃×#711	—	2	4	no	—
64	C₂×C₃×D₂₀	—	2	1	no	—
65	C₂×C₃×D₂₀	—	2	2	no	—
66	C₂×C₃×D₂₀	—	2	2	no	—
67	C₂×C₃×D₂₀	C₂³	1	2	yes	—
68	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	—	2	1	no	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
72	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
73	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
74	C₃×C₅×Q₁₆	—	2	4	no	—
75	C₃×C₅×SD₁₆	—	2	4	no	—
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
80	C₃×#689	—	2	4	no	—
81	C₃×#688	—	2	4	no	—
82	C₃×#688	—	2	4	no	—
83	C₃×#686	—	2	4	no	—
84	C₃×#685	—	2	2	no	—
85	C₃×#685	—	2	4	no	—
86	C₃×#683	—	2	2	no	—
87	C₃×C₄×Dic₅	D₄	1	2	yes	—
88	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×#168	C₂³	1	2	yes	—
90	C₃×D₄₀	—	2	4	no	—
91	C₃×#677	—	2	4	no	—
92	C₃×C₈×D₅	D₄	1	8	yes	complemented
93	C₂×C₃×#135	—	5	2	no	—
94	C₂×C₃×#135	—	5	2	no	—
95	C₃×#532	—	5	1	no	—
96	C₃×#532	—	5	1	no	—
97	C₃×#497	—	5	2	no	—
98	C₃×#497	—	5	1	no	—
99	C₃×#497	D₅	1	1	yes	characteristic, complemented
100	C₃×#496	—	5	2	no	—
101	C₃×#496	—	5	1	no	—
102	C₃×#496	—	5	1	no	—
103	C₂×C₃×#97	—	5	1	no	—
104	C₂×#713	C₂²×C₃	1	2	yes	—
105	C₂×#713	C₂²×C₃	1	1	yes	characteristic
106	C₂×#711	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
108	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
109	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₅×#124	C₂²×C₃	1	1	yes	characteristic
111	#4093	C₂²×C₃	1	2	yes	—
112	#4090	C₂²×C₃	1	1	yes	characteristic
113	C₂×#689	C₂²×C₃	1	2	yes	—
114	C₂×#688	C₂²×C₃	1	2	yes	—
115	C₂×#688	C₂²×C₃	1	2	yes	—
116	#4086	C₂²×C₃	1	1	yes	characteristic
117	C₂×#686	C₂²×C₃	1	2	yes	—
118	#4065	—	2	8	no	—
119	#4062	—	2	8	no	—
120	C₂×D₄₀	C₂²×C₃	1	2	yes	—
121	C₂×#677	C₂²×C₃	1	2	yes	—
122	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
123	#4041	—	2	2	no	—
124	#4039	—	2	2	no	—
125	#4030	—	2	2	no	—
126	#4027	—	2	2	no	—
127	#4021	C₂²×C₃	1	1	yes	characteristic
128	#4020	C₂²×C₃	1	1	yes	characteristic
129	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
130	C₅×#97	C₂²×C₃	1	1	yes	characteristic
131	#3947	C₂²×C₃	1	2	yes	—
132	#3935	C₂²×C₃	1	1	yes	characteristic
133	#3150	—	5	1	no	Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×D₅	—	2	2	no	—
136	C₂²×C₃×D₅	—	2	1	no	—
137	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₃×C₂²⋊D₅	—	4	4	no	—
147	C₃×C₂²⋊D₅	—	4	2	no	—
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₂×C₃×Dic₅	—	4	2	no	—
150	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
151	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
152	C₃×D₂₀	—	2	2	no	—
153	C₃×D₂₀	—	2	2	no	—
154	C₃×D₂₀	—	2	2	no	—
155	C₃×D₂₀	—	4	4	no	—
156	C₃×D₂₀	—	4	2	no	—
157	C₃×D₂₀	—	4	4	no	—
158	C₃×C₄×D₅	—	4	2	no	—
159	C₃×C₄×D₅	—	4	2	no	—
160	C₃×C₄×D₅	—	4	4	no	—
161	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
162	C₃×Dic₁₀	—	2	2	no	—
163	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
164	C₃×#168	C₂×D₄	1	4	yes	—
165	C₂×C₃×#41	—	5	2	no	—
166	C₂×C₃×#41	—	5	1	no	—
167	C₂×C₃×#41	—	5	1	no	—
168	C₃×#135	—	10	8	no	—
169	C₃×#135	—	10	8	no	—
170	C₂×C₃×Q₁₆	—	5	2	no	—
171	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	—
172	C₂×C₃×SD₁₆	—	5	2	no	—
173	C₂×C₃×SD₁₆	—	5	2	no	—
174	C₂×C₃×SD₁₆	—	5	2	no	—
175	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
176	C₂×C₃×D₈	—	5	2	no	—
177	C₂×C₃×D₈	—	5	2	no	—
178	C₂²×C₃×C₈	—	5	2	no	—
179	C₃×C₄⋊Q₈	—	5	1	no	—
180	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
181	C₃×#127	—	5	1	no	—
182	C₃×#127	—	5	1	no	—
183	C₃×#124	—	5	2	no	—
184	C₃×#124	—	5	1	no	—
185	C₃×#124	C₂×D₅	1	1	yes	characteristic
186	C₃×#121	—	10	2	no	—
187	C₃×#121	—	10	2	no	—
188	C₃×C₄×D₄	—	10	2	no	—
189	C₃×C₄×D₄	—	10	2	no	—
190	C₂×C₃×C₄²	—	5	1	no	—
191	C₃×#97	—	5	2	no	—
192	C₃×#97	—	5	1	no	—
193	C₃×#97	C₂×D₅	1	1	yes	characteristic
194	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
196	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₂²⋊D₅	—	2	1	no	—
198	C₂×C₂²⋊D₅	—	2	2	no	—
199	C₂²×Dic₅	—	2	1	no	—
200	#713	—	2	4	no	—
201	#713	—	2	4	no	—
202	#713	—	2	4	no	—
203	#711	—	2	4	no	—
204	C₂×D₂₀	—	2	1	no	—
205	C₂×D₂₀	—	2	2	no	—
206	C₂×D₂₀	—	2	2	no	—
207	C₂×D₂₀	C₂³×C₃	1	2	yes	—
208	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
209	C₂×C₄×D₅	—	2	1	no	—
210	C₂×C₄×D₅	—	2	2	no	—
211	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
212	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
213	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
214	C₅×Q₁₆	—	2	4	no	—
215	C₅×SD₁₆	—	2	4	no	—
216	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
217	C₅×C₄⋊C₄	—	2	2	no	—
218	C₅×C₂²⋊C₄	—	2	2	no	—
219	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
220	#689	—	2	4	no	—
221	#688	—	2	4	no	—
222	#688	—	2	4	no	—
223	#686	—	2	4	no	—
224	#685	—	2	2	no	—
225	#685	—	2	4	no	—
226	#683	—	2	2	no	—
227	C₄×Dic₅	C₃×D₄	1	2	yes	—
228	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
229	C₂×#168	C₂³×C₃	1	2	yes	—
230	D₄₀	—	2	4	no	—
231	#677	—	2	4	no	—
232	C₈×D₅	C₃×D₄	1	8	yes	complemented
233	C₂×#135	—	5	2	no	—
234	C₂×#135	—	5	2	no	—
235	#532	—	5	1	no	—
236	#532	—	5	1	no	—
237	#497	—	5	2	no	—
238	#497	—	5	1	no	—
239	#497	C₃×D₅	1	1	yes	characteristic, complemented
240	#496	—	5	2	no	—
241	#496	—	5	1	no	—
242	#496	—	5	1	no	—
243	C₂×#97	—	5	1	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	4	2	no	—
246	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
247	C₂×C₃×D₅	—	2	2	no	—
248	C₂×C₃×D₅	—	4	2	no	—
249	C₂×C₃×D₅	—	4	1	no	—
250	C₂×C₃×D₅	—	4	4	no	—
251	C₂×C₃×D₅	—	4	2	no	—
252	C₂×C₃×D₅	#127	1	2	yes	—
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	4	1	no	—
255	C₃×C₄×C₅	—	4	2	no	—
256	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
257	C₃×Dic₅	—	2	2	no	—
258	C₃×Dic₅	—	4	1	no	—
259	C₃×Dic₅	#127	1	2	yes	—
260	C₃×#41	—	10	4	no	—
261	C₃×#41	—	10	4	no	—
262	C₃×#41	—	10	4	no	—
263	C₃×#41	—	10	4	no	—
264	C₂×C₃×Q₈	—	5	1	no	—
265	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
266	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
267	C₂×C₃×D₄	—	5	2	no	—
268	C₂×C₃×D₄	—	5	1	no	—
269	C₂×C₃×D₄	—	10	1	no	—
270	C₂×C₃×D₄	—	10	2	no	—
271	C₂×C₃×D₄	—	10	2	no	—
272	C₂×C₃×D₄	—	10	1	no	—
273	C₂×C₃×D₄	—	10	2	no	—
274	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	—	5	1	no	—
276	C₂²×C₃×C₄	—	5	2	no	—
277	C₂²×C₃×C₄	—	10	1	no	—
278	C₂²×C₃×C₄	—	10	2	no	—
279	C₂²×C₃×C₄	—	10	1	no	—
280	C₃×Q₁₆	—	2	4	no	—
281	C₃×Q₁₆	—	10	4	no	—
282	C₃×SD₁₆	—	2	4	no	—
283	C₃×SD₁₆	—	10	4	no	—
284	C₃×SD₁₆	—	10	4	no	—
285	C₃×SD₁₆	—	10	4	no	—
286	C₃×D₈	—	10	4	no	—
287	C₃×D₈	—	10	4	no	—
288	C₂×C₃×C₈	—	5	2	no	—
289	C₂×C₃×C₈	—	5	8	no	—
290	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
291	C₃×C₄⋊C₄	—	2	2	no	—
292	C₃×C₄⋊C₄	—	10	2	no	—
293	C₃×C₂²⋊C₄	—	2	2	no	—
294	C₃×C₂²⋊C₄	—	10	4	no	—
295	C₃×C₂²⋊C₄	—	10	2	no	—
296	C₃×C₄²	—	5	2	no	—
297	C₃×C₄²	—	5	1	no	—
298	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
299	C₂³×C₅	—	2	1	no	—
300	C₂²×D₅	—	2	2	no	—
301	C₂²×D₅	—	2	1	no	—
302	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₅×Q₈	—	2	2	no	—
304	C₅×Q₈	—	2	2	no	—
305	C₅×Q₈	—	2	2	no	—
306	C₅×D₄	—	2	2	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
310	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
311	C₂²⋊D₅	—	4	4	no	—
312	C₂²⋊D₅	—	4	2	no	—
313	C₂×Dic₅	—	2	1	no	—
314	C₂×Dic₅	—	4	2	no	—
315	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
316	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
317	D₂₀	—	2	2	no	—
318	D₂₀	—	2	2	no	—
319	D₂₀	—	2	2	no	—
320	D₂₀	—	4	4	no	—
321	D₂₀	—	4	2	no	—
322	D₂₀	—	4	4	no	—
323	C₄×D₅	—	4	2	no	—
324	C₄×D₅	—	4	2	no	—
325	C₄×D₅	—	4	4	no	—
326	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
327	Dic₁₀	—	2	2	no	—
328	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
329	#168	C₂×C₃×D₄	1	4	yes	—
330	C₂×#41	—	5	2	no	—
331	C₂×#41	—	5	1	no	—
332	C₂×#41	—	5	1	no	—
333	#135	—	10	8	no	—
334	#135	—	10	8	no	—
335	C₂×Q₁₆	—	5	2	no	—
336	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	—
337	C₂×SD₁₆	—	5	2	no	—
338	C₂×SD₁₆	—	5	2	no	—
339	C₂×SD₁₆	—	5	2	no	—
340	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
341	C₂×D₈	—	5	2	no	—
342	C₂×D₈	—	5	2	no	—
343	C₂²×C₈	—	5	2	no	—
344	C₄⋊Q₈	—	5	1	no	—
345	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
346	#127	—	5	1	no	—
347	#127	—	5	1	no	—
348	#124	—	5	2	no	—
349	#124	—	5	1	no	—
350	#124	C₂×C₃×D₅	1	1	yes	characteristic
351	#121	—	10	2	no	—
352	#121	—	10	2	no	—
353	C₄×D₄	—	10	2	no	—
354	C₄×D₄	—	10	2	no	—
355	C₂×C₄²	—	5	1	no	—
356	#97	—	5	2	no	—
357	#97	—	5	1	no	—
358	#97	C₂×C₃×D₅	1	1	yes	characteristic
359	C₂×C₃×C₅	—	8	1	no	—
360	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
361	C₂×C₃×C₅	#575	1	2	yes	—
362	C₃×D₅	—	2	2	no	—
363	C₃×D₅	—	8	2	no	—
364	C₃×D₅	—	8	1	no	—
365	C₂³×C₃	—	2	1	no	—
366	C₂³×C₃	—	5	1	no	—
367	C₂³×C₃	—	10	2	no	—
368	C₂³×C₃	—	10	1	no	—
369	C₃×Q₈	—	2	2	no	—
370	C₃×Q₈	—	2	2	no	—
371	C₃×Q₈	—	2	2	no	—
372	C₃×Q₈	—	10	2	no	—
373	C₃×D₄	—	2	2	no	—
374	C₃×D₄	—	10	2	no	—
375	C₃×D₄	—	10	2	no	—
376	C₃×D₄	—	10	2	no	—
377	C₃×D₄	—	20	4	no	—
378	C₃×D₄	—	20	2	no	—
379	C₃×D₄	—	20	4	no	—
380	C₃×D₄	—	20	4	no	—
381	C₃×D₄	—	20	2	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	5	1	no	—
385	C₂×C₃×C₄	—	5	4	no	—
386	C₂×C₃×C₄	—	5	2	no	—
387	C₂×C₃×C₄	—	10	1	no	—
388	C₂×C₃×C₄	—	20	2	no	—
389	C₂×C₃×C₄	—	20	2	no	—
390	C₂×C₃×C₄	—	20	4	no	—
391	C₂×C₃×C₄	—	20	2	no	—
392	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
393	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
394	C₃×C₈	—	5	4	no	—
395	C₃×C₈	D₄×D₅	1	4	yes	—
396	C₂²×C₅	—	4	2	no	—
397	C₂²×C₅	—	4	1	no	—
398	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
399	C₂×D₅	—	2	2	no	—
400	C₂×D₅	—	4	4	no	—
401	C₂×D₅	—	4	2	no	—
402	C₂×D₅	—	4	2	no	—
403	C₂×D₅	—	4	1	no	—
404	C₂×D₅	C₃×#127	1	2	yes	—
405	C₄×C₅	—	2	2	no	—
406	C₄×C₅	—	4	1	no	—
407	C₄×C₅	—	4	2	no	—
408	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
409	Dic₅	—	2	2	no	—
410	Dic₅	—	4	1	no	—
411	Dic₅	C₃×#127	1	2	yes	—
412	#41	—	10	4	no	—
413	#41	—	10	4	no	—
414	#41	—	10	4	no	—
415	#41	—	10	4	no	—
416	C₂×Q₈	—	5	1	no	—
417	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
418	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
419	C₂×D₄	—	5	2	no	—
420	C₂×D₄	—	5	1	no	—
421	C₂×D₄	—	10	1	no	—
422	C₂×D₄	—	10	2	no	—
423	C₂×D₄	—	10	2	no	—
424	C₂×D₄	—	10	1	no	—
425	C₂×D₄	—	10	2	no	—
426	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
427	C₂²×C₄	—	5	1	no	—
428	C₂²×C₄	—	5	2	no	—
429	C₂²×C₄	—	10	1	no	—
430	C₂²×C₄	—	10	2	no	—
431	C₂²×C₄	—	10	1	no	—
432	Q₁₆	—	2	4	no	—
433	Q₁₆	—	10	4	no	—
434	SD₁₆	—	2	4	no	—
435	SD₁₆	—	10	4	no	—
436	SD₁₆	—	10	4	no	—
437	SD₁₆	—	10	4	no	—
438	D₈	—	10	4	no	—
439	D₈	—	10	4	no	—
440	C₂×C₈	—	5	2	no	—
441	C₂×C₈	—	5	8	no	—
442	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
443	C₄⋊C₄	—	2	2	no	—
444	C₄⋊C₄	—	10	2	no	—
445	C₂²⋊C₄	—	2	2	no	—
446	C₂²⋊C₄	—	10	4	no	—
447	C₂²⋊C₄	—	10	2	no	—
448	C₄²	—	5	2	no	—
449	C₄²	—	5	1	no	—
450	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
451	C₃×C₅	#3150	1	1	yes	characteristic, complemented, Hall
452	C₂²×C₃	—	4	1	no	—
453	C₂²×C₃	—	4	2	no	—
454	C₂²×C₃	—	5	2	no	—
455	C₂²×C₃	—	10	2	no	—
456	C₂²×C₃	—	20	2	no	—
457	C₂²×C₃	—	20	1	no	—
458	C₂²×C₃	—	20	4	no	—
459	C₂²×C₃	—	20	2	no	—
460	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
461	C₃×C₄	—	2	2	no	—
462	C₃×C₄	—	4	1	no	—
463	C₃×C₄	—	4	2	no	—
464	C₃×C₄	—	5	2	no	—
465	C₃×C₄	—	10	2	no	—
466	C₃×C₄	—	20	1	no	—
467	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
468	C₂×C₅	—	8	1	no	—
469	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
470	C₂×C₅	C₃×#575	1	2	yes	—
471	D₅	—	2	2	no	—
472	D₅	—	8	2	no	—
473	D₅	—	8	1	no	—
474	C₂³	—	2	1	no	—
475	C₂³	—	5	1	no	—
476	C₂³	—	10	2	no	—
477	C₂³	—	10	1	no	—
478	Q₈	—	2	2	no	—
479	Q₈	—	2	2	no	—
480	Q₈	—	2	2	no	—
481	Q₈	—	10	2	no	—
482	D₄	—	2	2	no	—
483	D₄	—	10	2	no	—
484	D₄	—	10	2	no	—
485	D₄	—	10	2	no	—
486	D₄	—	20	4	no	—
487	D₄	—	20	2	no	—
488	D₄	—	20	4	no	—
489	D₄	—	20	4	no	—
490	D₄	—	20	2	no	—
491	C₂×C₄	—	2	1	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	5	1	no	—
494	C₂×C₄	—	5	4	no	—
495	C₂×C₄	—	5	2	no	—
496	C₂×C₄	—	10	1	no	—
497	C₂×C₄	—	20	2	no	—
498	C₂×C₄	—	20	2	no	—
499	C₂×C₄	—	20	4	no	—
500	C₂×C₄	—	20	2	no	—
501	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
502	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
503	C₈	—	5	4	no	—
504	C₈	C₃×D₄×D₅	1	4	yes	—
505	C₂×C₃	—	8	1	no	—
506	C₂×C₃	—	10	2	no	—
507	C₂×C₃	—	40	2	no	—
508	C₂×C₃	—	40	1	no	—
509	C₂×C₃	D₅×#127	1	1	yes	characteristic
510	C₂×C₃	#66111	1	2	yes	—
511	C₅	C₃×#3150	1	1	yes	characteristic, complemented, Sylow
512	C₂²	—	4	2	no	—
513	C₂²	—	4	1	no	—
514	C₂²	—	5	2	no	—
515	C₂²	—	10	2	no	—
516	C₂²	—	20	4	no	—
517	C₂²	—	20	2	no	—
518	C₂²	—	20	2	no	—
519	C₂²	—	20	1	no	—
520	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
521	C₄	—	2	2	no	—
522	C₄	—	4	1	no	—
523	C₄	—	4	2	no	—
524	C₄	—	5	2	no	—
525	C₄	—	10	2	no	—
526	C₄	—	20	1	no	—
527	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
528	C₃	#10613600	1	1	yes	characteristic, direct product factor, Sylow
529	C₂	—	8	1	no	—
530	C₂	—	10	2	no	—
531	C₂	—	40	2	no	—
532	C₂	—	40	1	no	—
533	C₂	C₃×D₅×#127	1	1	yes	characteristic
534	C₂	C₃×#66111	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₃×#497	D₅
hypocenter	C₅	C₃×#3150
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4065	C₂	semidirect
2. C₂×C₃×#4062	C₂	semidirect
3. C₃×#66059	C₂	semidirect
4. C₃×#66002	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×#65479	C₂	semidirect
7. C₃×#65465	C₂	semidirect
8. C₃×#65375	C₂	semidirect
9. C₃×#65347	C₂	semidirect
10. C₃×#65001	C₂	semidirect
11. C₃×D₅×#97	C₂	semidirect
12. #10613600	C₃	direct (N × H)
43. C₂×#4065	C₂×C₃	semidirect
44. C₂×#4062	C₂×C₃	semidirect
45. #66059	C₂×C₃	semidirect
46. #66002	C₂×C₃	semidirect
47. C₅×#497	C₂×C₃	semidirect
48. #65479	C₂×C₃	semidirect
49. #65465	C₂×C₃	semidirect
50. #65375	C₂×C₃	semidirect
51. #65347	C₂×C₃	semidirect
52. #65001	C₂×C₃	semidirect
53. D₅×#97	C₂×C₃	semidirect
92. C₃×C₈×D₅	D₄	semidirect
99. C₃×#497	D₅	semidirect
232. C₈×D₅	C₃×D₄	semidirect
239. #497	C₃×D₅	semidirect
451. C₃×C₅	#3150	semidirect
511. C₅	C₃×#3150	semidirect
528. C₃	#10613600	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×#4065	2
C₂×C₃×#4062	2
C₃×#66059	2
C₃×#66002	2
C₃×C₅×#497	2
C₃×#65479	2
C₃×#65465	2
C₃×#65375	2
C₃×#65347	2
C₃×#65001	2
C₃×D₅×#97	2
#10613600	3
C₃×#3150	5

Subgroups — C3×#10613600 #14439076

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613600 #14439076