Subgroups — C₂×C₃×#65416 #14414682

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₄×C₂²⋊D₅	C₂	1	1	yes	maximal, characteristic
3	C₂²×C₃×C₈×D₅	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×C₂²⋊#168	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65416	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3952	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3947	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×C₃×#3946	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#65416	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₂²⋊D₅	C₄	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	—	2	4	no	—
14	C₂×C₃×C₅×M₁₆	C₂²	1	4	yes	complemented
15	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₂²⋊Dic₅	C₄	1	1	yes	characteristic
18	C₃×C₄×C₂²⋊D₅	C₄	1	4	yes	—
19	C₃×C₄×C₂²⋊D₅	C₂²	1	4	yes	—
20	C₂×C₃×#685	C₄	1	1	yes	characteristic
21	C₂×C₃×#683	C₄	1	1	yes	characteristic
22	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
23	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
24	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₈×D₅	—	2	4	no	—
26	C₂×C₃×C₈×D₅	C₂²	1	4	yes	complemented
27	C₃×C₂²⋊#168	C₂²	1	4	yes	complemented
28	C₃×#3952	C₂²	1	4	yes	complemented
29	C₃×#3947	C₂²	1	4	yes	complemented
30	C₃×#3946	C₂²	1	4	yes	complemented
31	C₂×C₃×#435	—	5	1	no	maximal, Hall
32	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₄×C₂²⋊D₅	C₂×C₃	1	1	yes	characteristic
34	C₂²×C₈×D₅	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂×C₂²⋊#168	C₂×C₃	1	1	yes	characteristic, complemented
36	#65416	C₂×C₃	1	8	yes	direct product factor
37	C₂×#3952	C₂×C₃	1	1	yes	characteristic, complemented
38	C₂×#3947	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂×#3946	C₂×C₃	1	1	yes	characteristic, complemented
40	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
41	C₂³×C₃×D₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	—	2	2	no	—
43	C₂²×C₃×C₄×C₅	—	2	2	no	—
44	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
49	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	4	yes	—
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	2	no	—
54	C₂×C₃×C₄×D₅	—	2	2	no	—
55	C₂×C₃×C₄×D₅	C₂×C₄	1	2	yes	—
56	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
57	C₃×C₅×M₁₆	—	2	8	no	—
58	C₂×C₃×C₅×C₈	—	2	2	no	—
59	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
60	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₃×C₂²⋊Dic₅	C₂×C₄	1	4	yes	—
63	C₃×#685	C₂×C₄	1	4	yes	—
64	C₃×#683	C₂×C₄	1	4	yes	—
65	C₃×C₄×Dic₅	C₂×C₄	1	2	yes	—
66	C₃×C₄×Dic₅	C₂³	1	2	yes	—
67	C₂×C₃×#168	—	2	2	no	—
68	C₂×C₃×#168	—	2	2	no	—
69	C₂×C₃×#168	C₂³	1	2	yes	—
70	C₂×C₃×#168	C₂³	1	2	yes	—
71	C₃×C₈×D₅	—	2	8	no	—
72	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
73	C₂³×C₃×C₈	—	5	1	no	—
74	C₂×C₃×C₄×D₄	—	5	1	no	—
75	C₃×#435	—	5	8	no	—
76	C₂×C₃×C₄⋊C₈	—	5	1	no	—
77	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
78	C₂×C₃×C₂²⋊C₈	—	5	1	no	—
79	C₂×C₃×#97	—	5	1	no	—
80	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
81	C₂²×C₂²⋊D₅	C₃×C₄	1	1	yes	characteristic
82	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
83	C₂×C₅×M₁₆	—	2	4	no	—
84	C₂×C₅×M₁₆	C₂²×C₃	1	4	yes	complemented
85	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
86	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₂²⋊Dic₅	C₃×C₄	1	1	yes	characteristic
88	C₄×C₂²⋊D₅	C₃×C₄	1	4	yes	—
89	C₄×C₂²⋊D₅	C₂²×C₃	1	4	yes	—
90	C₂×#685	C₃×C₄	1	1	yes	characteristic
91	C₂×#683	C₃×C₄	1	1	yes	characteristic
92	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
93	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
94	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₈×D₅	—	2	4	no	—
96	C₂×C₈×D₅	C₂²×C₃	1	4	yes	complemented
97	C₂²⋊#168	C₂²×C₃	1	4	yes	complemented
98	#3952	C₂²×C₃	1	4	yes	complemented
99	#3947	C₂²×C₃	1	4	yes	complemented
100	#3946	C₂²×C₃	1	4	yes	complemented
101	C₂×#435	—	5	1	no	Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
106	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
107	C₂²×C₃×D₅	—	2	2	no	—
108	C₂²×C₃×D₅	—	2	2	no	—
109	C₂²×C₃×D₅	M₁₆	1	4	yes	complemented
110	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	4	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
118	C₂×C₃×C₄×C₅	#41	1	2	yes	—
119	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
120	C₃×C₂²⋊D₅	—	2	8	no	—
121	C₂×C₃×Dic₅	—	2	2	no	—
122	C₂×C₃×Dic₅	—	2	2	no	—
123	C₂×C₃×Dic₅	—	2	2	no	—
124	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
125	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
126	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
127	C₃×C₄×D₅	—	2	4	no	—
128	C₃×C₄×D₅	—	2	2	no	—
129	C₃×C₄×D₅	—	2	2	no	—
130	C₃×C₅×C₈	—	2	2	no	—
131	C₃×C₅×C₈	C₂×D₄	1	4	yes	complemented
132	C₃×#168	—	2	2	no	—
133	C₃×#168	—	2	2	no	—
134	C₂²×C₃×D₄	—	5	1	no	—
135	C₂³×C₃×C₄	—	5	1	no	—
136	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
137	C₂×C₃×M₁₆	—	2	4	no	—
138	C₂×C₃×M₁₆	C₂×D₅	1	4	yes	complemented
139	C₂²×C₃×C₈	—	5	1	no	—
140	C₂²×C₃×C₈	—	5	1	no	—
141	C₂²×C₃×C₈	—	5	4	no	—
142	C₂²×C₃×C₈	—	10	4	no	—
143	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
144	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
145	C₃×C₄×D₄	—	5	4	no	—
146	C₃×C₄×D₄	—	5	4	no	—
147	C₂×C₃×C₄⋊C₄	—	5	1	no	—
148	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
149	C₂×C₃×C₂²⋊C₄	—	5	1	no	—
150	C₂×C₃×C₄²	—	5	1	no	—
151	C₃×C₄⋊C₈	—	5	4	no	—
152	C₃×C₂²⋊C₈	—	5	4	no	—
153	C₃×C₂²⋊C₈	—	5	4	no	—
154	C₃×#97	—	5	4	no	—
155	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
156	C₂³×D₅	C₂×C₃×C₄	1	1	yes	characteristic
157	C₂²×C₄×C₅	—	2	2	no	—
158	C₂²×C₄×C₅	—	2	2	no	—
159	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
160	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₂²⋊D₅	—	2	4	no	—
164	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	4	yes	—
165	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
166	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
167	C₂²×Dic₅	C₂×C₃×C₄	1	1	yes	characteristic
168	C₂×C₄×D₅	—	2	2	no	—
169	C₂×C₄×D₅	—	2	2	no	—
170	C₂×C₄×D₅	C₂×C₃×C₄	1	2	yes	—
171	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
172	C₅×M₁₆	—	2	8	no	—
173	C₂×C₅×C₈	—	2	2	no	—
174	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
175	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
176	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
177	C₂²⋊Dic₅	C₂×C₃×C₄	1	4	yes	—
178	#685	C₂×C₃×C₄	1	4	yes	—
179	#683	C₂×C₃×C₄	1	4	yes	—
180	C₄×Dic₅	C₂×C₃×C₄	1	2	yes	—
181	C₄×Dic₅	C₂³×C₃	1	2	yes	—
182	C₂×#168	—	2	2	no	—
183	C₂×#168	—	2	2	no	—
184	C₂×#168	C₂³×C₃	1	2	yes	—
185	C₂×#168	C₂³×C₃	1	2	yes	—
186	C₈×D₅	—	2	8	no	—
187	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
188	C₂³×C₈	—	5	1	no	—
189	C₂×C₄×D₄	—	5	1	no	—
190	#435	—	5	8	no	—
191	C₂×C₄⋊C₈	—	5	1	no	—
192	C₂×C₂²⋊C₈	—	5	1	no	—
193	C₂×C₂²⋊C₈	—	5	1	no	—
194	C₂×#97	—	5	1	no	—
195	C₂²×C₃×C₅	—	2	2	no	—
196	C₂²×C₃×C₅	—	2	2	no	—
197	C₂²×C₃×C₅	—	2	2	no	—
198	C₂²×C₃×C₅	—	4	4	no	—
199	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
200	C₂²×C₃×C₅	C₂×M₁₆	1	2	yes	—
201	C₂²×C₃×C₅	#131	1	2	yes	—
202	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
203	C₂×C₃×D₅	—	2	2	no	—
204	C₂×C₃×D₅	—	2	2	no	—
205	C₂×C₃×D₅	—	2	8	no	—
206	C₂×C₃×D₅	C₂×M₁₆	1	4	yes	complemented
207	C₃×C₄×C₅	—	2	2	no	—
208	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
209	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
210	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
211	C₃×Dic₅	—	2	2	no	—
212	C₃×Dic₅	—	2	2	no	—
213	C₃×Dic₅	—	2	2	no	—
214	C₂⁴×C₃	—	5	1	no	—
215	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
216	C₂×C₃×D₄	—	5	4	no	—
217	C₂×C₃×D₄	—	10	4	no	—
218	C₂²×C₃×C₄	—	2	2	no	—
219	C₂²×C₃×C₄	—	2	2	no	—
220	C₂²×C₃×C₄	—	5	1	no	—
221	C₂²×C₃×C₄	—	5	1	no	—
222	C₂²×C₃×C₄	—	5	1	no	—
223	C₂²×C₃×C₄	—	5	2	no	—
224	C₂²×C₃×C₄	—	5	2	no	—
225	C₂²×C₃×C₄	—	10	2	no	—
226	C₂²×C₃×C₄	—	10	2	no	—
227	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
228	C₂²×C₃×C₄	C₄×D₅	1	2	yes	—
229	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
230	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
231	C₃×M₁₆	—	2	8	no	—
232	C₂×C₃×C₈	—	2	2	no	—
233	C₂×C₃×C₈	—	5	2	no	—
234	C₂×C₃×C₈	—	5	2	no	—
235	C₂×C₃×C₈	—	10	2	no	—
236	C₂×C₃×C₈	—	10	2	no	—
237	C₂×C₃×C₈	—	10	8	no	—
238	C₂×C₃×C₈	C₂²⋊D₅	1	4	yes	complemented
239	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
240	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
241	C₃×C₄⋊C₄	—	5	4	no	—
242	C₃×C₂²⋊C₄	—	5	4	no	—
243	C₃×C₂²⋊C₄	—	5	4	no	—
244	C₃×C₄²	—	5	2	no	—
245	C₃×C₄²	—	5	2	no	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	2	2	no	—
248	C₂³×C₅	—	2	2	no	—
249	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
250	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
251	C₂²×D₅	—	2	2	no	—
252	C₂²×D₅	—	2	2	no	—
253	C₂²×D₅	C₃×M₁₆	1	4	yes	complemented
254	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	4	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
260	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
261	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
262	C₂×C₄×C₅	C₃×#41	1	2	yes	—
263	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
264	C₂²⋊D₅	—	2	8	no	—
265	C₂×Dic₅	—	2	2	no	—
266	C₂×Dic₅	—	2	2	no	—
267	C₂×Dic₅	—	2	2	no	—
268	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
269	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
270	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
271	C₄×D₅	—	2	4	no	—
272	C₄×D₅	—	2	2	no	—
273	C₄×D₅	—	2	2	no	—
274	C₅×C₈	—	2	2	no	—
275	C₅×C₈	C₂×C₃×D₄	1	4	yes	complemented
276	#168	—	2	2	no	—
277	#168	—	2	2	no	—
278	C₂²×D₄	—	5	1	no	—
279	C₂³×C₄	—	5	1	no	—
280	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
281	C₂×M₁₆	—	2	4	no	—
282	C₂×M₁₆	C₂×C₃×D₅	1	4	yes	complemented
283	C₂²×C₈	—	5	1	no	—
284	C₂²×C₈	—	5	1	no	—
285	C₂²×C₈	—	5	4	no	—
286	C₂²×C₈	—	10	4	no	—
287	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
288	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
289	C₄×D₄	—	5	4	no	—
290	C₄×D₄	—	5	4	no	—
291	C₂×C₄⋊C₄	—	5	1	no	—
292	C₂×C₂²⋊C₄	—	5	1	no	—
293	C₂×C₂²⋊C₄	—	5	1	no	—
294	C₂×C₄²	—	5	1	no	—
295	C₄⋊C₈	—	5	4	no	—
296	C₂²⋊C₈	—	5	4	no	—
297	C₂²⋊C₈	—	5	4	no	—
298	#97	—	5	4	no	—
299	C₂×C₃×C₅	—	4	2	no	—
300	C₂×C₃×C₅	#435	1	4	yes	complemented
301	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
302	C₂×C₃×C₅	C₂²×M₁₆	1	1	yes	characteristic
303	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
304	C₃×D₅	—	2	4	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	—	2	2	no	—
308	C₂³×C₃	—	5	2	no	—
309	C₂³×C₃	—	5	4	no	—
310	C₂³×C₃	—	10	2	no	—
311	C₂³×C₃	—	10	2	no	—
312	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
313	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
314	C₃×D₄	—	10	8	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	4	no	—
319	C₂×C₃×C₄	—	5	2	no	—
320	C₂×C₃×C₄	—	5	2	no	—
321	C₂×C₃×C₄	—	5	2	no	—
322	C₂×C₃×C₄	—	10	2	no	—
323	C₂×C₃×C₄	—	10	2	no	—
324	C₂×C₃×C₄	—	10	2	no	—
325	C₂×C₃×C₄	—	10	2	no	—
326	C₂×C₃×C₄	—	10	2	no	—
327	C₂×C₃×C₄	—	10	4	no	—
328	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
329	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
330	C₂×C₃×C₄	#709	1	2	yes	—
331	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
332	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
333	C₃×C₈	—	2	2	no	—
334	C₃×C₈	—	10	2	no	—
335	C₃×C₈	—	10	2	no	—
336	C₃×C₈	C₂×C₂²⋊D₅	1	4	yes	complemented
337	C₂²×C₅	—	2	2	no	—
338	C₂²×C₅	—	2	2	no	—
339	C₂²×C₅	—	2	2	no	—
340	C₂²×C₅	—	4	4	no	—
341	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
342	C₂²×C₅	C₂×C₃×M₁₆	1	2	yes	—
343	C₂²×C₅	C₃×#131	1	2	yes	—
344	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
345	C₂×D₅	—	2	2	no	—
346	C₂×D₅	—	2	8	no	—
347	C₂×D₅	—	2	2	no	—
348	C₂×D₅	C₂×C₃×M₁₆	1	4	yes	complemented
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
351	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
352	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
353	Dic₅	—	2	2	no	—
354	Dic₅	—	2	2	no	—
355	Dic₅	—	2	2	no	—
356	C₂⁴	—	5	1	no	—
357	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
358	C₂×D₄	—	5	4	no	—
359	C₂×D₄	—	10	4	no	—
360	C₂²×C₄	—	2	2	no	—
361	C₂²×C₄	—	2	2	no	—
362	C₂²×C₄	—	5	1	no	—
363	C₂²×C₄	—	5	1	no	—
364	C₂²×C₄	—	5	1	no	—
365	C₂²×C₄	—	5	2	no	—
366	C₂²×C₄	—	5	2	no	—
367	C₂²×C₄	—	10	2	no	—
368	C₂²×C₄	—	10	2	no	—
369	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
370	C₂²×C₄	C₃×C₄×D₅	1	2	yes	—
371	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
372	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
373	M₁₆	—	2	8	no	—
374	C₂×C₈	—	2	2	no	—
375	C₂×C₈	—	5	2	no	—
376	C₂×C₈	—	5	2	no	—
377	C₂×C₈	—	10	2	no	—
378	C₂×C₈	—	10	2	no	—
379	C₂×C₈	—	10	8	no	—
380	C₂×C₈	C₃×C₂²⋊D₅	1	4	yes	complemented
381	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
382	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
383	C₄⋊C₄	—	5	4	no	—
384	C₂²⋊C₄	—	5	4	no	—
385	C₂²⋊C₄	—	5	4	no	—
386	C₄²	—	5	2	no	—
387	C₄²	—	5	2	no	—
388	C₃×C₅	C₂×#435	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	2	2	no	—
391	C₂²×C₃	—	2	2	no	—
392	C₂²×C₃	—	4	4	no	—
393	C₂²×C₃	—	5	4	no	—
394	C₂²×C₃	—	10	2	no	—
395	C₂²×C₃	—	10	2	no	—
396	C₂²×C₃	—	10	8	no	—
397	C₂²×C₃	D₅×M₁₆	1	2	yes	—
398	C₂²×C₃	#4053	1	2	yes	—
399	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
400	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
401	C₃×C₄	—	2	2	no	—
402	C₃×C₄	—	10	2	no	—
403	C₃×C₄	—	10	2	no	—
404	C₃×C₄	—	10	2	no	—
405	C₃×C₄	C₄×C₂²⋊D₅	1	2	yes	—
406	C₃×C₄	C₂×#709	1	1	yes	characteristic
407	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
408	C₂×C₅	—	4	2	no	—
409	C₂×C₅	C₃×#435	1	4	yes	complemented
410	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
411	C₂×C₅	C₂²×C₃×M₁₆	1	1	yes	characteristic
412	C₂×C₅	C₂×C₃×#131	1	1	yes	characteristic
413	D₅	—	2	4	no	—
414	C₂³	—	2	2	no	—
415	C₂³	—	2	2	no	—
416	C₂³	—	2	2	no	—
417	C₂³	—	5	2	no	—
418	C₂³	—	5	4	no	—
419	C₂³	—	10	2	no	—
420	C₂³	—	10	2	no	—
421	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
422	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
423	D₄	—	10	8	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	2	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	4	no	—
428	C₂×C₄	—	5	2	no	—
429	C₂×C₄	—	5	2	no	—
430	C₂×C₄	—	5	2	no	—
431	C₂×C₄	—	10	2	no	—
432	C₂×C₄	—	10	2	no	—
433	C₂×C₄	—	10	2	no	—
434	C₂×C₄	—	10	2	no	—
435	C₂×C₄	—	10	2	no	—
436	C₂×C₄	—	10	4	no	—
437	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
438	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
439	C₂×C₄	C₃×#709	1	2	yes	—
440	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
441	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
442	C₈	—	2	2	no	—
443	C₈	—	10	2	no	—
444	C₈	—	10	2	no	—
445	C₈	C₂×C₃×C₂²⋊D₅	1	4	yes	complemented
446	C₂×C₃	—	4	2	no	—
447	C₂×C₃	—	10	4	no	—
448	C₂×C₃	#65416	1	4	yes	direct product factor
449	C₂×C₃	C₂×D₅×M₁₆	1	1	yes	characteristic
450	C₂×C₃	C₂×#4053	1	1	yes	characteristic
451	C₂×C₃	C₂×C₄×C₂²⋊D₅	1	1	yes	characteristic
452	C₅	C₂×C₃×#435	1	1	yes	characteristic, complemented, Sylow
453	C₂²	—	2	2	no	—
454	C₂²	—	2	2	no	—
455	C₂²	—	2	2	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	5	4	no	—
458	C₂²	—	10	2	no	—
459	C₂²	—	10	8	no	—
460	C₂²	—	10	2	no	—
461	C₂²	C₃×D₅×M₁₆	1	2	yes	—
462	C₂²	C₃×#4053	1	2	yes	—
463	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
464	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
465	C₄	—	2	2	no	—
466	C₄	—	10	2	no	—
467	C₄	—	10	2	no	—
468	C₄	—	10	2	no	—
469	C₄	C₃×C₄×C₂²⋊D₅	1	2	yes	—
470	C₄	C₂×C₃×#709	1	1	yes	characteristic
471	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
472	C₃	C₂×#65416	1	1	yes	characteristic, direct product factor, Sylow
473	C₂	—	4	2	no	—
474	C₂	—	10	4	no	—
475	C₂	C₃×#65416	1	4	yes	direct product factor
476	C₂	C₂×C₃×D₅×M₁₆	1	1	yes	characteristic
477	C₂	C₂×C₃×#4053	1	1	yes	characteristic
478	C₂	C₂×C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂³×C₃×C₅	C₂²×C₄
prime radical	C₂²×C₃×C₂²⋊D₅	C₄
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₂×C₃×#435
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂²×C₃×C₈×D₅	C₂	semidirect
4. C₂×C₃×C₂²⋊#168	C₂	semidirect
5. C₃×#65416	C₂	direct (N × H)
6. C₂×C₃×#3952	C₂	semidirect
7. C₂×C₃×#3947	C₂	semidirect
8. C₂×C₃×#3946	C₂	semidirect
9. C₂×#65416	C₃	direct (N × H)
14. C₂×C₃×C₅×M₁₆	C₂²	semidirect
26. C₂×C₃×C₈×D₅	C₂²	semidirect
27. C₃×C₂²⋊#168	C₂²	semidirect
28. C₃×#3952	C₂²	semidirect
29. C₃×#3947	C₂²	semidirect
30. C₃×#3946	C₂²	semidirect
32. C₂²×C₅×M₁₆	C₂×C₃	semidirect
34. C₂²×C₈×D₅	C₂×C₃	semidirect
35. C₂×C₂²⋊#168	C₂×C₃	semidirect
36. #65416	C₂×C₃	direct (N × H)
37. C₂×#3952	C₂×C₃	semidirect
38. C₂×#3947	C₂×C₃	semidirect
39. C₂×#3946	C₂×C₃	semidirect
59. C₂×C₃×C₅×C₈	D₄	semidirect
72. C₂²×C₃×M₁₆	D₅	semidirect
84. C₂×C₅×M₁₆	C₂²×C₃	semidirect
96. C₂×C₈×D₅	C₂²×C₃	semidirect
97. C₂²⋊#168	C₂²×C₃	semidirect
98. #3952	C₂²×C₃	semidirect
99. #3947	C₂²×C₃	semidirect
100. #3946	C₂²×C₃	semidirect
109. C₂²×C₃×D₅	M₁₆	semidirect
131. C₃×C₅×C₈	C₂×D₄	semidirect
138. C₂×C₃×M₁₆	C₂×D₅	semidirect
174. C₂×C₅×C₈	C₃×D₄	semidirect
187. C₂²×M₁₆	C₃×D₅	semidirect
206. C₂×C₃×D₅	C₂×M₁₆	semidirect
238. C₂×C₃×C₈	C₂²⋊D₅	semidirect
253. C₂²×D₅	C₃×M₁₆	semidirect
275. C₅×C₈	C₂×C₃×D₄	semidirect
282. C₂×M₁₆	C₂×C₃×D₅	semidirect
300. C₂×C₃×C₅	#435	semidirect
336. C₃×C₈	C₂×C₂²⋊D₅	semidirect
348. C₂×D₅	C₂×C₃×M₁₆	semidirect
380. C₂×C₈	C₃×C₂²⋊D₅	semidirect
388. C₃×C₅	C₂×#435	semidirect
409. C₂×C₅	C₃×#435	semidirect
445. C₈	C₂×C₃×C₂²⋊D₅	semidirect
448. C₂×C₃	#65416	direct (N × H)
452. C₅	C₂×C₃×#435	semidirect
472. C₃	C₂×#65416	direct (N × H)
475. C₂	C₃×#65416	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×M₁₆	2
C₂×C₃×C₄×C₂²⋊D₅	2
C₂²×C₃×C₈×D₅	2
C₂×C₃×C₂²⋊#168	2
C₃×#65416	2
C₂×C₃×#3952	2
C₂×C₃×#3947	2
C₂×C₃×#3946	2
C₂×#65416	3
C₂×C₃×#435	5

Subgroups — C2×C3×#65416 #14414682

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65416 #14414682