Subgroups — C₂×C₃×#65434 #14417923

Order 1920.

928 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×#4047	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3969	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65434	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3957	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3954	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65434	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
11	C₂×C₃×#709	C₂²	1	1	yes	characteristic
12	C₃×C₅×#131	—	2	2	no	—
13	C₃×C₅×#131	C₂²	1	4	yes	complemented
14	C₂×C₃×C₅×M₁₆	—	2	1	no	—
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	—	2	1	no	—
17	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
18	C₃×#4096	C₄	1	4	yes	complemented
19	C₃×#4096	C₂²	1	4	yes	—
20	C₂×C₃×#689	C₄	1	1	yes	characteristic, complemented
21	C₂×C₃×#688	C₄	1	1	yes	characteristic, complemented
22	C₂×C₃×#687	C₄	1	1	yes	characteristic, complemented
23	C₂×C₃×#686	C₄	1	1	yes	characteristic, complemented
24	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×#681	C₂²	1	1	yes	characteristic
26	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
27	C₃×#4047	—	2	2	no	—
28	C₃×#4047	C₂²	1	4	yes	complemented
29	C₂×C₃×#676	—	2	1	no	—
30	C₂×C₃×C₈×D₅	—	2	1	no	—
31	C₃×#3969	C₂²	1	4	yes	complemented
32	C₃×#3957	C₂²	1	4	yes	complemented
33	C₃×#3954	C₂²	1	4	yes	complemented
34	C₃×#3947	C₂²	1	4	yes	complemented
35	C₂×C₃×#444	—	5	1	no	maximal, Hall
36	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
37	C₂×#4096	C₂×C₃	1	1	yes	characteristic
38	C₂×#4047	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#3969	C₂×C₃	1	1	yes	characteristic, complemented
40	#65434	C₂×C₃	1	8	yes	direct product factor
41	C₂×#3957	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂×#3954	C₂×C₃	1	1	yes	characteristic, complemented
43	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
44	C₃×C₅×#41	—	2	1	no	—
45	C₃×C₅×#41	—	2	1	no	—
46	C₃×C₅×#41	C₂×C₄	1	2	yes	—
47	C₃×C₅×#41	C₂³	1	2	yes	—
48	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic
49	C₂×C₃×C₅×D₄	—	2	1	no	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	—	2	1	no	—
52	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
53	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
54	C₂²×C₃×Dic₅	—	2	1	no	—
55	C₃×#709	—	2	1	no	—
56	C₃×#709	—	2	1	no	—
57	C₃×#709	C₂×C₄	1	2	yes	—
58	C₃×#709	C₂³	1	2	yes	—
59	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
60	C₂×C₃×C₄×D₅	—	2	1	no	—
61	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
62	C₃×C₅×M₁₆	—	2	1	no	—
63	C₃×C₅×M₁₆	—	2	4	no	—
64	C₃×C₅×M₁₆	C₂³	1	2	yes	—
65	C₂×C₃×C₅×C₈	—	2	1	no	—
66	C₂×C₃×C₅×C₈	—	2	4	no	—
67	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₃×#689	C₂×C₄	1	4	yes	complemented
72	C₃×#688	C₂×C₄	1	4	yes	complemented
73	C₃×#687	C₂×C₄	1	4	yes	complemented
74	C₃×#686	C₂×C₄	1	4	yes	complemented
75	C₃×C₄×Dic₅	—	2	1	no	—
76	C₃×C₄×Dic₅	C₂³	1	2	yes	—
77	C₃×#681	—	2	1	no	—
78	C₃×#681	C₂³	1	2	yes	—
79	C₂×C₃×#168	—	2	1	no	—
80	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
81	C₂×C₃×#168	C₂×C₄	1	1	yes	characteristic
82	C₂×C₃×#168	C₂×C₄	1	2	yes	—
83	C₂×C₃×#168	C₂³	1	2	yes	—
84	C₃×#676	—	2	4	no	—
85	C₃×C₈×D₅	—	2	4	no	—
86	C₂×C₃×#135	—	5	1	no	—
87	C₂×C₃×#131	—	5	1	no	—
88	C₂×C₃×#131	D₅	1	1	yes	characteristic, complemented
89	C₃×#444	—	5	8	no	—
90	C₂×C₃×#108	—	5	1	no	—
91	C₂×C₃×#104	—	5	1	no	—
92	C₂×C₃×#104	—	5	1	no	—
93	C₂×C₃×#97	—	5	1	no	—
94	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
95	C₂×#709	C₂²×C₃	1	1	yes	characteristic
96	C₅×#131	—	2	2	no	—
97	C₅×#131	C₂²×C₃	1	4	yes	complemented
98	C₂×C₅×M₁₆	—	2	1	no	—
99	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₅×C₈	—	2	1	no	—
101	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
102	#4096	C₃×C₄	1	4	yes	complemented
103	#4096	C₂²×C₃	1	4	yes	—
104	C₂×#689	C₃×C₄	1	1	yes	characteristic, complemented
105	C₂×#688	C₃×C₄	1	1	yes	characteristic, complemented
106	C₂×#687	C₃×C₄	1	1	yes	characteristic, complemented
107	C₂×#686	C₃×C₄	1	1	yes	characteristic, complemented
108	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
109	C₂×#681	C₂²×C₃	1	1	yes	characteristic
110	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
111	#4047	—	2	2	no	—
112	#4047	C₂²×C₃	1	4	yes	complemented
113	C₂×#676	—	2	1	no	—
114	C₂×C₈×D₅	—	2	1	no	—
115	#3969	C₂²×C₃	1	4	yes	complemented
116	#3957	C₂²×C₃	1	4	yes	complemented
117	#3954	C₂²×C₃	1	4	yes	complemented
118	#3947	C₂²×C₃	1	4	yes	complemented
119	C₂×#444	—	5	1	no	Sylow
120	C₂³×C₃×C₅	—	2	1	no	—
121	C₂³×C₃×C₅	#41	1	1	yes	characteristic
122	C₂²×C₃×D₅	—	2	1	no	—
123	C₃×C₅×Q₈	—	2	1	no	—
124	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
125	C₃×C₅×D₄	—	2	2	no	—
126	C₃×C₅×D₄	—	2	2	no	—
127	C₃×C₅×D₄	—	2	1	no	—
128	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
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	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
138	C₃×C₂²⋊D₅	—	2	2	no	—
139	C₃×C₂²⋊D₅	—	2	2	no	—
140	C₂×C₃×Dic₅	—	2	1	no	—
141	C₂×C₃×Dic₅	—	2	2	no	—
142	C₂×C₃×Dic₅	—	4	2	no	—
143	C₃×D₂₀	—	2	1	no	—
144	C₃×D₂₀	C₂²×C₄	1	2	yes	—
145	C₃×C₄×D₅	—	2	2	no	—
146	C₃×C₄×D₅	—	2	2	no	—
147	C₃×Dic₁₀	—	2	1	no	—
148	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
151	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
152	C₃×#168	—	2	2	no	—
153	C₃×#168	C₂²×C₄	1	2	yes	—
154	C₃×#168	C₂²×C₄	1	2	yes	—
155	C₂×C₃×#41	—	5	1	no	—
156	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
157	C₃×#135	—	5	4	no	—
158	C₃×#135	—	5	4	no	—
159	C₂×C₃×Q₁₆	—	5	1	no	—
160	C₂×C₃×SD₁₆	—	5	1	no	—
161	C₂×C₃×SD₁₆	—	5	1	no	—
162	C₂×C₃×D₈	—	5	1	no	—
163	C₃×#131	—	2	2	no	—
164	C₃×#131	—	5	4	no	—
165	C₃×#131	—	10	2	no	—
166	C₃×#131	C₂×D₅	1	4	yes	complemented
167	C₂×C₃×M₁₆	—	2	1	no	—
168	C₂×C₃×M₁₆	—	5	1	no	—
169	C₂×C₃×M₁₆	—	10	1	no	—
170	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
171	C₂²×C₃×C₈	—	2	1	no	—
172	C₂²×C₃×C₈	—	5	1	no	—
173	C₂²×C₃×C₈	—	10	1	no	—
174	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
175	C₂×C₃×C₄²	—	5	1	no	—
176	C₃×#108	—	5	4	no	—
177	C₃×#104	—	5	4	no	—
178	C₃×#104	—	5	4	no	—
179	C₃×#97	—	5	4	no	—
180	C₅×#41	—	2	1	no	—
181	C₅×#41	—	2	1	no	—
182	C₅×#41	C₂×C₃×C₄	1	2	yes	—
183	C₅×#41	C₂³×C₃	1	2	yes	—
184	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic
185	C₂×C₅×D₄	—	2	1	no	—
186	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
187	C₂²×C₄×C₅	—	2	1	no	—
188	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₂²⋊D₅	—	2	1	no	—
190	C₂²×Dic₅	—	2	1	no	—
191	#709	—	2	1	no	—
192	#709	—	2	1	no	—
193	#709	C₂×C₃×C₄	1	2	yes	—
194	#709	C₂³×C₃	1	2	yes	—
195	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
196	C₂×C₄×D₅	—	2	1	no	—
197	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
198	C₅×M₁₆	—	2	1	no	—
199	C₅×M₁₆	—	2	4	no	—
200	C₅×M₁₆	C₂³×C₃	1	2	yes	—
201	C₂×C₅×C₈	—	2	1	no	—
202	C₂×C₅×C₈	—	2	4	no	—
203	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
204	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
205	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
206	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
207	#689	C₂×C₃×C₄	1	4	yes	complemented
208	#688	C₂×C₃×C₄	1	4	yes	complemented
209	#687	C₂×C₃×C₄	1	4	yes	complemented
210	#686	C₂×C₃×C₄	1	4	yes	complemented
211	C₄×Dic₅	—	2	1	no	—
212	C₄×Dic₅	C₂³×C₃	1	2	yes	—
213	#681	—	2	1	no	—
214	#681	C₂³×C₃	1	2	yes	—
215	C₂×#168	—	2	1	no	—
216	C₂×#168	C₂×C₃×C₄	1	2	yes	—
217	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
218	C₂×#168	C₂×C₃×C₄	1	1	yes	characteristic
219	C₂×#168	C₂³×C₃	1	2	yes	—
220	#676	—	2	4	no	—
221	C₈×D₅	—	2	4	no	—
222	C₂×#135	—	5	1	no	—
223	C₂×#131	—	5	1	no	—
224	C₂×#131	C₃×D₅	1	1	yes	characteristic, complemented
225	#444	—	5	8	no	—
226	C₂×#108	—	5	1	no	—
227	C₂×#104	—	5	1	no	—
228	C₂×#104	—	5	1	no	—
229	C₂×#97	—	5	1	no	—
230	C₂²×C₃×C₅	—	2	2	no	—
231	C₂²×C₃×C₅	—	2	2	no	—
232	C₂²×C₃×C₅	—	4	2	no	—
233	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
234	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
235	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
236	C₂×C₃×D₅	—	2	2	no	—
237	C₂×C₃×D₅	—	4	2	no	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
240	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
242	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
243	C₃×Dic₅	—	2	2	no	—
244	C₃×Dic₅	—	4	2	no	—
245	C₃×#41	—	2	1	no	—
246	C₃×#41	—	2	1	no	—
247	C₃×#41	—	5	2	no	—
248	C₃×#41	—	5	2	no	—
249	C₃×#41	—	10	1	no	—
250	C₃×#41	—	10	1	no	—
251	C₃×#41	C₄×D₅	1	2	yes	—
252	C₃×#41	C₂²×D₅	1	2	yes	—
253	C₂×C₃×Q₈	—	5	1	no	—
254	C₂×C₃×Q₈	C₄×D₅	1	1	yes	characteristic
255	C₂×C₃×D₄	—	2	1	no	—
256	C₂×C₃×D₄	—	5	1	no	—
257	C₂×C₃×D₄	—	10	1	no	—
258	C₂×C₃×D₄	C₄×D₅	1	1	yes	characteristic
259	C₂²×C₃×C₄	—	2	1	no	—
260	C₂²×C₃×C₄	—	10	1	no	—
261	C₂²×C₃×C₄	—	10	1	no	—
262	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
263	C₃×Q₁₆	—	5	4	no	—
264	C₃×SD₁₆	—	5	4	no	—
265	C₃×SD₁₆	—	5	4	no	—
266	C₃×D₈	—	5	4	no	—
267	C₃×M₁₆	—	2	1	no	—
268	C₃×M₁₆	—	2	4	no	—
269	C₃×M₁₆	—	5	2	no	—
270	C₃×M₁₆	—	10	1	no	—
271	C₃×M₁₆	—	10	4	no	—
272	C₃×M₁₆	C₂²×D₅	1	2	yes	—
273	C₂×C₃×C₈	—	2	1	no	—
274	C₂×C₃×C₈	—	2	4	no	—
275	C₂×C₃×C₈	—	5	1	no	—
276	C₂×C₃×C₈	—	5	1	no	—
277	C₂×C₃×C₈	—	5	2	no	—
278	C₂×C₃×C₈	—	5	2	no	—
279	C₂×C₃×C₈	—	10	1	no	—
280	C₂×C₃×C₈	—	10	4	no	—
281	C₂×C₃×C₈	C₂²⋊D₅	1	2	yes	—
282	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
283	C₂×C₃×C₈	C₂²⋊D₅	1	1	yes	characteristic
284	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
285	C₃×C₄²	—	5	2	no	—
286	C₃×C₄²	—	10	1	no	—
287	C₂³×C₅	—	2	1	no	—
288	C₂³×C₅	C₃×#41	1	1	yes	characteristic
289	C₂²×D₅	—	2	1	no	—
290	C₅×Q₈	—	2	1	no	—
291	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	—	2	1	no	—
295	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
302	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
304	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
305	C₂²⋊D₅	—	2	2	no	—
306	C₂²⋊D₅	—	2	2	no	—
307	C₂×Dic₅	—	2	1	no	—
308	C₂×Dic₅	—	2	2	no	—
309	C₂×Dic₅	—	4	2	no	—
310	D₂₀	—	2	1	no	—
311	D₂₀	C₂²×C₃×C₄	1	2	yes	—
312	C₄×D₅	—	2	2	no	—
313	C₄×D₅	—	2	2	no	—
314	Dic₁₀	—	2	1	no	—
315	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
316	C₅×C₈	—	2	2	no	—
317	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
318	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
319	#168	—	2	2	no	—
320	#168	C₂²×C₃×C₄	1	2	yes	—
321	#168	C₂²×C₃×C₄	1	2	yes	—
322	C₂×#41	—	5	1	no	—
323	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
324	#135	—	5	4	no	—
325	#135	—	5	4	no	—
326	C₂×Q₁₆	—	5	1	no	—
327	C₂×SD₁₆	—	5	1	no	—
328	C₂×SD₁₆	—	5	1	no	—
329	C₂×D₈	—	5	1	no	—
330	#131	—	2	2	no	—
331	#131	—	5	4	no	—
332	#131	—	10	2	no	—
333	#131	C₂×C₃×D₅	1	4	yes	complemented
334	C₂×M₁₆	—	2	1	no	—
335	C₂×M₁₆	—	5	1	no	—
336	C₂×M₁₆	—	10	1	no	—
337	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
338	C₂²×C₈	—	2	1	no	—
339	C₂²×C₈	—	5	1	no	—
340	C₂²×C₈	—	10	1	no	—
341	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
342	C₂×C₄²	—	5	1	no	—
343	#108	—	5	4	no	—
344	#104	—	5	4	no	—
345	#104	—	5	4	no	—
346	#97	—	5	4	no	—
347	C₂×C₃×C₅	—	2	1	no	—
348	C₂×C₃×C₅	—	2	1	no	—
349	C₂×C₃×C₅	—	4	2	no	—
350	C₂×C₃×C₅	#444	1	2	yes	complemented
351	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
352	C₃×D₅	—	4	2	no	—
353	C₂³×C₃	—	2	1	no	—
354	C₂³×C₃	—	10	1	no	—
355	C₂³×C₃	#709	1	1	yes	characteristic
356	C₃×Q₈	—	2	1	no	—
357	C₃×Q₈	—	5	2	no	—
358	C₃×Q₈	—	10	1	no	—
359	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
360	C₃×D₄	—	2	2	no	—
361	C₃×D₄	—	2	2	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	5	2	no	—
364	C₃×D₄	—	10	2	no	—
365	C₃×D₄	—	10	2	no	—
366	C₃×D₄	—	10	1	no	—
367	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	10	1	no	—
372	C₂×C₃×C₄	—	10	2	no	—
373	C₂×C₃×C₄	—	10	2	no	—
374	C₂×C₃×C₄	—	10	2	no	—
375	C₂×C₃×C₄	—	20	2	no	—
376	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
378	C₂×C₃×C₄	#709	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
382	C₃×C₈	—	2	2	no	—
383	C₃×C₈	—	5	2	no	—
384	C₃×C₈	—	5	2	no	—
385	C₃×C₈	—	10	2	no	—
386	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
387	C₃×C₈	C₂×C₂²⋊D₅	1	2	yes	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	2	2	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
392	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
393	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
394	C₂×D₅	—	2	2	no	—
395	C₂×D₅	—	4	2	no	—
396	C₄×C₅	—	2	2	no	—
397	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
398	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
399	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
400	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
401	Dic₅	—	2	2	no	—
402	Dic₅	—	4	2	no	—
403	#41	—	2	1	no	—
404	#41	—	2	1	no	—
405	#41	—	5	2	no	—
406	#41	—	5	2	no	—
407	#41	—	10	1	no	—
408	#41	—	10	1	no	—
409	#41	C₃×C₄×D₅	1	2	yes	—
410	#41	C₂²×C₃×D₅	1	2	yes	—
411	C₂×Q₈	—	5	1	no	—
412	C₂×Q₈	C₃×C₄×D₅	1	1	yes	characteristic
413	C₂×D₄	—	2	1	no	—
414	C₂×D₄	—	5	1	no	—
415	C₂×D₄	—	10	1	no	—
416	C₂×D₄	C₃×C₄×D₅	1	1	yes	characteristic
417	C₂²×C₄	—	2	1	no	—
418	C₂²×C₄	—	10	1	no	—
419	C₂²×C₄	—	10	1	no	—
420	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
421	Q₁₆	—	5	4	no	—
422	SD₁₆	—	5	4	no	—
423	SD₁₆	—	5	4	no	—
424	D₈	—	5	4	no	—
425	M₁₆	—	2	1	no	—
426	M₁₆	—	2	4	no	—
427	M₁₆	—	5	2	no	—
428	M₁₆	—	10	1	no	—
429	M₁₆	—	10	4	no	—
430	M₁₆	C₂²×C₃×D₅	1	2	yes	—
431	C₂×C₈	—	2	1	no	—
432	C₂×C₈	—	2	4	no	—
433	C₂×C₈	—	5	1	no	—
434	C₂×C₈	—	5	1	no	—
435	C₂×C₈	—	5	2	no	—
436	C₂×C₈	—	5	2	no	—
437	C₂×C₈	—	10	1	no	—
438	C₂×C₈	—	10	4	no	—
439	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
440	C₂×C₈	C₃×C₂²⋊D₅	1	1	yes	characteristic
441	C₂×C₈	C₃×C₂²⋊D₅	1	2	yes	—
442	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
443	C₄²	—	5	2	no	—
444	C₄²	—	10	1	no	—
445	C₃×C₅	C₂×#444	1	1	yes	characteristic, complemented, Hall
446	C₂²×C₃	—	2	2	no	—
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	4	2	no	—
449	C₂²×C₃	—	10	2	no	—
450	C₂²×C₃	—	20	2	no	—
451	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
452	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
453	C₂²×C₃	C₂×#709	1	1	yes	characteristic
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	10	2	no	—
456	C₃×C₄	—	20	2	no	—
457	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
458	C₃×C₄	C₄×C₂²⋊D₅	1	1	yes	characteristic
459	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
460	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
461	C₂×C₅	—	2	1	no	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	4	2	no	—
464	C₂×C₅	C₃×#444	1	2	yes	complemented
465	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
466	D₅	—	4	2	no	—
467	C₂³	—	2	1	no	—
468	C₂³	—	10	1	no	—
469	C₂³	C₃×#709	1	1	yes	characteristic
470	Q₈	—	2	1	no	—
471	Q₈	—	5	2	no	—
472	Q₈	—	10	1	no	—
473	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	2	1	no	—
477	D₄	—	5	2	no	—
478	D₄	—	10	2	no	—
479	D₄	—	10	2	no	—
480	D₄	—	10	1	no	—
481	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	2	no	—
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	10	1	no	—
486	C₂×C₄	—	10	2	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	10	2	no	—
489	C₂×C₄	—	20	2	no	—
490	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
491	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
492	C₂×C₄	C₃×#709	1	1	yes	characteristic
493	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
494	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
495	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
496	C₈	—	2	2	no	—
497	C₈	—	5	2	no	—
498	C₈	—	5	2	no	—
499	C₈	—	10	2	no	—
500	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
501	C₈	C₂×C₃×C₂²⋊D₅	1	2	yes	—
502	C₂×C₃	—	2	1	no	—
503	C₂×C₃	—	2	1	no	—
504	C₂×C₃	—	4	2	no	—
505	C₂×C₃	—	20	2	no	—
506	C₂×C₃	#65434	1	2	yes	direct product factor
507	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
508	C₅	C₂×C₃×#444	1	1	yes	characteristic, complemented, Sylow
509	C₂²	—	2	2	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	4	2	no	—
512	C₂²	—	10	2	no	—
513	C₂²	—	20	2	no	—
514	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
515	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
516	C₂²	C₂×C₃×#709	1	1	yes	characteristic
517	C₄	—	2	2	no	—
518	C₄	—	10	2	no	—
519	C₄	—	20	2	no	—
520	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
521	C₄	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
522	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
523	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
524	C₃	C₂×#65434	1	1	yes	characteristic, direct product factor, Sylow
525	C₂	—	2	1	no	—
526	C₂	—	2	1	no	—
527	C₂	—	4	2	no	—
528	C₂	—	20	2	no	—
529	C₂	C₃×#65434	1	2	yes	direct product factor
530	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×C₂²⋊D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#131	C₂
socle	C₂²×C₃×C₅	C₄×D₄
prime radical	C₂×C₃×#4096	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#131	D₅
hypocenter	C₅	C₂×C₃×#444
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₈ ◁ C₂×C₃×#131

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#131	C₂	semidirect
3. C₂×C₃×#4047	C₂	semidirect
4. C₂×C₃×#3969	C₂	semidirect
5. C₃×#65434	C₂	direct (N × H)
6. C₂×C₃×#3957	C₂	semidirect
7. C₂×C₃×#3954	C₂	semidirect
8. C₂×C₃×#3947	C₂	semidirect
9. C₂×#65434	C₃	direct (N × H)
13. C₃×C₅×#131	C₂²	semidirect
18. C₃×#4096	C₄	semidirect
20. C₂×C₃×#689	C₄	semidirect
21. C₂×C₃×#688	C₄	semidirect
22. C₂×C₃×#687	C₄	semidirect
23. C₂×C₃×#686	C₄	semidirect
28. C₃×#4047	C₂²	semidirect
31. C₃×#3969	C₂²	semidirect
32. C₃×#3957	C₂²	semidirect
33. C₃×#3954	C₂²	semidirect
34. C₃×#3947	C₂²	semidirect
36. C₂×C₅×#131	C₂×C₃	semidirect
38. C₂×#4047	C₂×C₃	semidirect
39. C₂×#3969	C₂×C₃	semidirect
40. #65434	C₂×C₃	direct (N × H)
41. C₂×#3957	C₂×C₃	semidirect
42. C₂×#3954	C₂×C₃	semidirect
43. C₂×#3947	C₂×C₃	semidirect
71. C₃×#689	C₂×C₄	semidirect
72. C₃×#688	C₂×C₄	semidirect
73. C₃×#687	C₂×C₄	semidirect
74. C₃×#686	C₂×C₄	semidirect
88. C₂×C₃×#131	D₅	semidirect
97. C₅×#131	C₂²×C₃	semidirect
102. #4096	C₃×C₄	semidirect
104. C₂×#689	C₃×C₄	semidirect
105. C₂×#688	C₃×C₄	semidirect
106. C₂×#687	C₃×C₄	semidirect
107. C₂×#686	C₃×C₄	semidirect
112. #4047	C₂²×C₃	semidirect
115. #3969	C₂²×C₃	semidirect
116. #3957	C₂²×C₃	semidirect
117. #3954	C₂²×C₃	semidirect
118. #3947	C₂²×C₃	semidirect
166. C₃×#131	C₂×D₅	semidirect
207. #689	C₂×C₃×C₄	semidirect
208. #688	C₂×C₃×C₄	semidirect
209. #687	C₂×C₃×C₄	semidirect
210. #686	C₂×C₃×C₄	semidirect
224. C₂×#131	C₃×D₅	semidirect
333. #131	C₂×C₃×D₅	semidirect
350. C₂×C₃×C₅	#444	semidirect
445. C₃×C₅	C₂×#444	semidirect
464. C₂×C₅	C₃×#444	semidirect
506. C₂×C₃	#65434	direct (N × H)
508. C₅	C₂×C₃×#444	semidirect
524. C₃	C₂×#65434	direct (N × H)
529. C₂	C₃×#65434	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×#131	2
C₂×C₃×#4096	2
C₂×C₃×#4047	2
C₂×C₃×#3969	2
C₃×#65434	2
C₂×C₃×#3957	2
C₂×C₃×#3954	2
C₂×C₃×#3947	2
C₂×#65434	3
C₂×C₃×#444	5

Subgroups — C2×C3×#65434 #14417923

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65434 #14417923