Subgroups — C₂×C₃×#65529 #14411922

Order 1920.

1576 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×#41	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4072	C₂	1	2	yes	maximal, complemented
3	C₃×#65529	C₂	1	8	yes	maximal, direct product factor
4	C₂×C₃×#3966	C₂	1	4	yes	maximal, complemented
5	C₂×#65529	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×#41	—	2	2	no	—
7	C₂×C₃×C₅×#41	—	2	2	no	—
8	C₂×C₃×C₅×#41	—	2	4	no	—
9	C₂×C₃×C₅×#41	C₄	1	4	yes	complemented
10	C₂×C₃×C₅×#41	C₂²	1	4	yes	—
11	C₂²×C₃×C₅×Q₈	C₄	1	1	yes	characteristic, complemented
12	C₂²×C₃×C₅×D₄	C₄	1	1	yes	characteristic, complemented
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₄	1	2	yes	complemented
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₂²⋊Dic₅	C₂²	1	4	yes	—
17	C₃×#4072	—	2	4	no	—
18	C₃×#4072	C₂²	1	8	yes	complemented
19	C₂×C₃×C₄⋊Dic₅	—	2	2	no	—
20	C₂×C₃×C₄×Dic₅	—	2	2	no	—
21	C₃×#3966	C₂²	1	16	yes	complemented
22	C₂×C₃×#410	—	5	1	no	maximal, Hall
23	C₂²×C₅×#41	C₂×C₃	1	1	yes	characteristic
24	C₂×#4072	C₂×C₃	1	2	yes	complemented
25	#65529	C₂×C₃	1	8	yes	direct product factor
26	C₂×#3966	C₂×C₃	1	4	yes	complemented
27	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
28	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
29	C₃×C₅×#41	—	2	8	no	—
30	C₃×C₅×#41	—	2	8	no	—
31	C₃×C₅×#41	—	2	8	no	—
32	C₃×C₅×#41	—	2	8	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	—	2	2	no	—
35	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
36	C₂×C₃×C₅×D₄	—	2	4	no	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	2	2	no	—
39	C₂×C₃×C₅×D₄	—	2	2	no	—
40	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
41	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
42	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	—	2	4	no	—
44	C₂²×C₃×C₄×C₅	—	2	2	no	—
45	C₂²×C₃×C₄×C₅	—	2	2	no	—
46	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
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	C₂×C₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂×C₄	1	8	yes	complemented
51	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
52	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
53	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
55	C₂²×C₃×Dic₅	—	2	4	no	—
56	C₃×C₂²⋊Dic₅	—	2	4	no	—
57	C₃×C₂²⋊Dic₅	C₂³	1	8	yes	—
58	C₃×C₄⋊Dic₅	—	2	8	no	—
59	C₃×C₄×Dic₅	—	2	8	no	—
60	C₂²×C₃×#41	D₅	1	1	yes	characteristic
61	C₂×C₃×#117	—	5	2	no	—
62	C₃×#410	—	5	8	no	—
63	C₂×C₃×#99	—	5	4	no	—
64	C₂×C₅×#41	—	2	2	no	—
65	C₂×C₅×#41	—	2	2	no	—
66	C₂×C₅×#41	—	2	4	no	—
67	C₂×C₅×#41	C₃×C₄	1	4	yes	complemented
68	C₂×C₅×#41	C₂²×C₃	1	4	yes	—
69	C₂²×C₅×Q₈	C₃×C₄	1	1	yes	characteristic, complemented
70	C₂²×C₅×D₄	C₃×C₄	1	1	yes	characteristic, complemented
71	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
72	C₂³×C₄×C₅	C₃×C₄	1	2	yes	complemented
73	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₂²⋊Dic₅	C₂²×C₃	1	4	yes	—
75	#4072	—	2	4	no	—
76	#4072	C₂²×C₃	1	8	yes	complemented
77	C₂×C₄⋊Dic₅	—	2	2	no	—
78	C₂×C₄×Dic₅	—	2	2	no	—
79	#3966	C₂²×C₃	1	16	yes	complemented
80	C₂×#410	—	5	1	no	Sylow
81	C₂³×C₃×C₅	—	2	2	no	—
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂³×C₃×C₅	—	4	2	no	—
84	C₂³×C₃×C₅	—	4	4	no	—
85	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
87	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
88	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
89	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
90	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
91	C₃×C₅×Q₈	—	2	8	no	—
92	C₃×C₅×D₄	—	2	8	no	—
93	C₃×C₅×D₄	—	2	8	no	—
94	C₃×C₅×D₄	—	2	8	no	—
95	C₂×C₃×C₄×C₅	—	2	2	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	8	no	—
98	C₂×C₃×C₄×C₅	—	2	8	no	—
99	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
100	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
102	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
104	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
105	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
106	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
107	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
109	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
111	C₂×C₃×Dic₅	—	2	8	no	—
112	C₂×C₃×Dic₅	—	4	8	no	—
113	C₂×C₃×#41	—	2	2	no	—
114	C₂×C₃×#41	—	2	4	no	—
115	C₂×C₃×#41	—	2	2	no	—
116	C₂×C₃×#41	Dic₅	1	4	yes	complemented
117	C₂×C₃×#41	C₂×D₅	1	4	yes	—
118	C₂²×C₃×Q₈	Dic₅	1	1	yes	characteristic, complemented
119	C₂²×C₃×D₄	Dic₅	1	1	yes	characteristic, complemented
120	C₂²×C₃×D₄	C₂×D₅	1	2	yes	—
121	C₂³×C₃×C₄	Dic₅	1	2	yes	complemented
122	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
123	C₃×#117	—	5	8	no	—
124	C₃×#117	—	10	4	no	—
125	C₂×C₃×C₄⋊C₄	—	10	2	no	—
126	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
127	C₂×C₃×C₄²	—	10	2	no	—
128	C₃×#99	—	5	16	no	—
129	C₂⁴×C₅	C₂×C₃×C₄	1	2	yes	—
130	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₅×#41	—	2	8	no	—
132	C₅×#41	—	2	8	no	—
133	C₅×#41	—	2	8	no	—
134	C₅×#41	—	2	8	no	—
135	C₂×C₅×Q₈	—	2	2	no	—
136	C₂×C₅×Q₈	—	2	2	no	—
137	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
138	C₂×C₅×D₄	—	2	4	no	—
139	C₂×C₅×D₄	—	2	4	no	—
140	C₂×C₅×D₄	—	2	2	no	—
141	C₂×C₅×D₄	—	2	2	no	—
142	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
143	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
144	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
145	C₂²×C₄×C₅	—	2	4	no	—
146	C₂²×C₄×C₅	—	2	2	no	—
147	C₂²×C₄×C₅	—	2	2	no	—
148	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
149	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
150	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
151	C₂²×C₄×C₅	C₂×C₃×C₄	1	2	yes	—
152	C₂²×C₄×C₅	C₂×C₃×C₄	1	8	yes	complemented
153	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
154	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
155	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₂²×Dic₅	—	2	4	no	—
158	C₂²⋊Dic₅	—	2	4	no	—
159	C₂²⋊Dic₅	C₂³×C₃	1	8	yes	—
160	C₄⋊Dic₅	—	2	8	no	—
161	C₄×Dic₅	—	2	8	no	—
162	C₂²×#41	C₃×D₅	1	1	yes	characteristic
163	C₂×#117	—	5	2	no	—
164	#410	—	5	8	no	—
165	C₂×#99	—	5	4	no	—
166	C₂²×C₃×C₅	—	2	4	no	—
167	C₂²×C₃×C₅	—	2	2	no	—
168	C₂²×C₃×C₅	—	2	4	no	—
169	C₂²×C₃×C₅	—	4	1	no	—
170	C₂²×C₃×C₅	—	4	2	no	—
171	C₂²×C₃×C₅	—	4	1	no	—
172	C₂²×C₃×C₅	—	4	4	no	—
173	C₂²×C₃×C₅	—	4	4	no	—
174	C₂²×C₃×C₅	—	4	4	no	—
175	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
176	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
177	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
178	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
180	C₃×C₄×C₅	—	2	4	no	—
181	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
182	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
183	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
184	C₃×Dic₅	—	4	8	no	—
185	C₂⁴×C₃	C₂×Dic₅	1	2	yes	—
186	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
187	C₃×#41	—	2	8	no	—
188	C₃×#41	—	2	8	no	—
189	C₃×#41	—	2	8	no	—
190	C₃×#41	—	2	8	no	—
191	C₂×C₃×Q₈	—	2	2	no	—
192	C₂×C₃×Q₈	—	2	2	no	—
193	C₂×C₃×Q₈	C₂×Dic₅	1	4	yes	complemented
194	C₂×C₃×D₄	—	2	4	no	—
195	C₂×C₃×D₄	—	2	4	no	—
196	C₂×C₃×D₄	—	2	2	no	—
197	C₂×C₃×D₄	—	2	2	no	—
198	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	—
199	C₂×C₃×D₄	C₂×Dic₅	1	4	yes	complemented
200	C₂×C₃×D₄	C₂²×D₅	1	4	yes	—
201	C₂²×C₃×C₄	—	2	4	no	—
202	C₂²×C₃×C₄	—	2	2	no	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	—	10	4	no	—
205	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
207	C₂²×C₃×C₄	C₂×Dic₅	1	2	yes	—
208	C₂²×C₃×C₄	C₂×Dic₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂×Dic₅	1	8	yes	complemented
210	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
212	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
213	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
214	C₃×C₄⋊C₄	—	10	8	no	—
215	C₃×C₂²⋊C₄	—	5	8	no	—
216	C₃×C₂²⋊C₄	—	10	4	no	—
217	C₃×C₄²	—	10	8	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	4	2	no	—
221	C₂³×C₅	—	4	4	no	—
222	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
223	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
224	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
225	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
226	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
227	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
228	C₅×Q₈	—	2	8	no	—
229	C₅×D₄	—	2	8	no	—
230	C₅×D₄	—	2	8	no	—
231	C₅×D₄	—	2	8	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	8	no	—
235	C₂×C₄×C₅	—	2	8	no	—
236	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
237	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
239	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
240	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	2	yes	—
241	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
242	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
243	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
244	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
245	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
248	C₂×Dic₅	—	2	8	no	—
249	C₂×Dic₅	—	4	8	no	—
250	C₂×#41	—	2	2	no	—
251	C₂×#41	—	2	2	no	—
252	C₂×#41	—	2	4	no	—
253	C₂×#41	C₃×Dic₅	1	4	yes	complemented
254	C₂×#41	C₂×C₃×D₅	1	4	yes	—
255	C₂²×Q₈	C₃×Dic₅	1	1	yes	characteristic, complemented
256	C₂²×D₄	C₃×Dic₅	1	1	yes	characteristic, complemented
257	C₂²×D₄	C₂×C₃×D₅	1	2	yes	—
258	C₂³×C₄	C₃×Dic₅	1	2	yes	complemented
259	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
260	#117	—	5	8	no	—
261	#117	—	10	4	no	—
262	C₂×C₄⋊C₄	—	10	2	no	—
263	C₂×C₂²⋊C₄	—	5	4	no	—
264	C₂×C₄²	—	10	2	no	—
265	#99	—	5	16	no	—
266	C₂×C₃×C₅	—	2	2	no	—
267	C₂×C₃×C₅	—	2	1	no	—
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	2	no	—
270	C₂×C₃×C₅	—	4	4	no	—
271	C₂×C₃×C₅	#410	1	2	yes	complemented
272	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
273	C₂³×C₃	—	2	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	4	2	no	—
276	C₂³×C₃	—	4	4	no	—
277	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
278	C₂³×C₃	C₂²×Dic₅	1	4	yes	—
279	C₂³×C₃	C₂²×Dic₅	1	1	yes	characteristic
280	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
281	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
282	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
283	C₃×Q₈	—	2	8	no	—
284	C₃×D₄	—	2	8	no	—
285	C₃×D₄	—	2	8	no	—
286	C₃×D₄	—	2	8	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	8	no	—
290	C₂×C₃×C₄	—	2	8	no	—
291	C₂×C₃×C₄	—	10	8	no	—
292	C₂×C₃×C₄	—	20	8	no	—
293	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
295	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
296	C₂×C₃×C₄	C₂²⋊Dic₅	1	2	yes	—
297	C₂×C₃×C₄	C₂²⋊Dic₅	1	4	yes	—
298	C₂×C₃×C₄	C₂²⋊Dic₅	1	4	yes	—
299	C₂×C₃×C₄	C₂²⋊Dic₅	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂²×Dic₅	1	4	yes	—
301	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
302	C₂×C₃×C₄	C₂²×Dic₅	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
304	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
305	C₂²×C₅	—	2	4	no	—
306	C₂²×C₅	—	2	2	no	—
307	C₂²×C₅	—	2	4	no	—
308	C₂²×C₅	—	4	1	no	—
309	C₂²×C₅	—	4	2	no	—
310	C₂²×C₅	—	4	1	no	—
311	C₂²×C₅	—	4	4	no	—
312	C₂²×C₅	—	4	4	no	—
313	C₂²×C₅	—	4	4	no	—
314	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
315	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
316	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
317	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
318	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
319	C₄×C₅	—	2	4	no	—
320	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
321	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
322	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
323	Dic₅	—	4	8	no	—
324	C₂⁴	C₂×C₃×Dic₅	1	2	yes	—
325	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
326	#41	—	2	8	no	—
327	#41	—	2	8	no	—
328	#41	—	2	8	no	—
329	#41	—	2	8	no	—
330	C₂×Q₈	—	2	2	no	—
331	C₂×Q₈	—	2	2	no	—
332	C₂×Q₈	C₂×C₃×Dic₅	1	4	yes	complemented
333	C₂×D₄	—	2	4	no	—
334	C₂×D₄	—	2	4	no	—
335	C₂×D₄	—	2	2	no	—
336	C₂×D₄	—	2	2	no	—
337	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	—
338	C₂×D₄	C₂×C₃×Dic₅	1	4	yes	complemented
339	C₂×D₄	C₂²×C₃×D₅	1	4	yes	—
340	C₂²×C₄	—	2	4	no	—
341	C₂²×C₄	—	2	2	no	—
342	C₂²×C₄	—	2	2	no	—
343	C₂²×C₄	—	10	4	no	—
344	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
345	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
346	C₂²×C₄	C₂×C₃×Dic₅	1	1	yes	characteristic
347	C₂²×C₄	C₂×C₃×Dic₅	1	2	yes	—
348	C₂²×C₄	C₂×C₃×Dic₅	1	8	yes	complemented
349	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
350	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
351	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
352	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
353	C₄⋊C₄	—	10	8	no	—
354	C₂²⋊C₄	—	5	8	no	—
355	C₂²⋊C₄	—	10	4	no	—
356	C₄²	—	10	8	no	—
357	C₃×C₅	C₂×#410	1	1	yes	characteristic, complemented, Hall
358	C₂²×C₃	—	2	4	no	—
359	C₂²×C₃	—	2	2	no	—
360	C₂²×C₃	—	2	4	no	—
361	C₂²×C₃	—	4	1	no	—
362	C₂²×C₃	—	4	2	no	—
363	C₂²×C₃	—	4	1	no	—
364	C₂²×C₃	—	4	4	no	—
365	C₂²×C₃	—	4	4	no	—
366	C₂²×C₃	—	4	4	no	—
367	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
368	C₂²×C₃	C₂×C₂²⋊Dic₅	1	2	yes	—
369	C₂²×C₃	C₂×C₂²⋊Dic₅	1	1	yes	characteristic
370	C₂²×C₃	C₂³×Dic₅	1	1	yes	characteristic
371	C₂²×C₃	C₂²×C₂²⋊D₅	1	2	yes	—
372	C₃×C₄	—	2	4	no	—
373	C₃×C₄	—	20	8	no	—
374	C₃×C₄	C₂×C₂²⋊Dic₅	1	2	yes	—
375	C₃×C₄	C₂×C₂²⋊Dic₅	1	2	yes	—
376	C₃×C₄	C₂×C₂²⋊Dic₅	1	4	yes	—
377	C₂×C₅	—	2	2	no	—
378	C₂×C₅	—	2	1	no	—
379	C₂×C₅	—	2	1	no	—
380	C₂×C₅	—	2	2	no	—
381	C₂×C₅	—	4	4	no	—
382	C₂×C₅	C₃×#410	1	2	yes	complemented
383	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
384	C₂³	—	2	2	no	—
385	C₂³	—	2	2	no	—
386	C₂³	—	4	2	no	—
387	C₂³	—	4	4	no	—
388	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
389	C₂³	C₂²×C₃×Dic₅	1	4	yes	—
390	C₂³	C₂²×C₃×Dic₅	1	1	yes	characteristic
391	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
392	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
393	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
394	Q₈	—	2	8	no	—
395	D₄	—	2	8	no	—
396	D₄	—	2	8	no	—
397	D₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	8	no	—
401	C₂×C₄	—	2	8	no	—
402	C₂×C₄	—	10	8	no	—
403	C₂×C₄	—	20	8	no	—
404	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
405	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
406	C₂×C₄	C₃×C₂²⋊Dic₅	1	1	yes	characteristic
407	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
408	C₂×C₄	C₃×C₂²⋊Dic₅	1	2	yes	—
409	C₂×C₄	C₃×C₂²⋊Dic₅	1	4	yes	—
410	C₂×C₄	C₃×C₂²⋊Dic₅	1	4	yes	—
411	C₂×C₄	C₂²×C₃×Dic₅	1	4	yes	—
412	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
413	C₂×C₄	C₂²×C₃×Dic₅	1	2	yes	—
414	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
415	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
416	C₂×C₃	—	2	2	no	—
417	C₂×C₃	—	2	1	no	—
418	C₂×C₃	—	2	1	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	4	4	no	—
421	C₂×C₃	#65529	1	2	yes	direct product factor
422	C₂×C₃	C₂²×C₂²⋊Dic₅	1	1	yes	characteristic
423	C₅	C₂×C₃×#410	1	1	yes	characteristic, complemented, Sylow
424	C₂²	—	2	4	no	—
425	C₂²	—	2	2	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	4	1	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	1	no	—
430	C₂²	—	4	4	no	—
431	C₂²	—	4	4	no	—
432	C₂²	—	4	4	no	—
433	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
434	C₂²	C₂×C₃×C₂²⋊Dic₅	1	2	yes	—
435	C₂²	C₂×C₃×C₂²⋊Dic₅	1	1	yes	characteristic
436	C₂²	C₂³×C₃×Dic₅	1	1	yes	characteristic
437	C₂²	C₂²×C₃×C₂²⋊D₅	1	2	yes	—
438	C₄	—	2	4	no	—
439	C₄	—	20	8	no	—
440	C₄	C₂×C₃×C₂²⋊Dic₅	1	2	yes	—
441	C₄	C₂×C₃×C₂²⋊Dic₅	1	2	yes	—
442	C₄	C₂×C₃×C₂²⋊Dic₅	1	4	yes	—
443	C₃	C₂×#65529	1	1	yes	characteristic, direct product factor, Sylow
444	C₂	—	2	2	no	—
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	2	no	—
448	C₂	—	4	4	no	—
449	C₂	C₃×#65529	1	2	yes	direct product factor
450	C₂	C₂²×C₃×C₂²⋊Dic₅	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂²⋊Dic₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting, prime radical	C₂²×C₃×C₅×#41	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×#41	D₅
hypocenter	C₅	C₂×C₃×#410
LCS	G ▷ C₂²×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×#41

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4072	C₂	semidirect
3. C₃×#65529	C₂	direct (N × H)
4. C₂×C₃×#3966	C₂	semidirect
5. C₂×#65529	C₃	direct (N × H)
9. C₂×C₃×C₅×#41	C₄	semidirect
11. C₂²×C₃×C₅×Q₈	C₄	semidirect
12. C₂²×C₃×C₅×D₄	C₄	semidirect
14. C₂³×C₃×C₄×C₅	C₄	semidirect
18. C₃×#4072	C₂²	semidirect
21. C₃×#3966	C₂²	semidirect
24. C₂×#4072	C₂×C₃	semidirect
25. #65529	C₂×C₃	direct (N × H)
26. C₂×#3966	C₂×C₃	semidirect
35. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
41. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
50. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
67. C₂×C₅×#41	C₃×C₄	semidirect
69. C₂²×C₅×Q₈	C₃×C₄	semidirect
70. C₂²×C₅×D₄	C₃×C₄	semidirect
72. C₂³×C₄×C₅	C₃×C₄	semidirect
76. #4072	C₂²×C₃	semidirect
79. #3966	C₂²×C₃	semidirect
116. C₂×C₃×#41	Dic₅	semidirect
118. C₂²×C₃×Q₈	Dic₅	semidirect
119. C₂²×C₃×D₄	Dic₅	semidirect
121. C₂³×C₃×C₄	Dic₅	semidirect
137. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
143. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
152. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
193. C₂×C₃×Q₈	C₂×Dic₅	semidirect
199. C₂×C₃×D₄	C₂×Dic₅	semidirect
209. C₂²×C₃×C₄	C₂×Dic₅	semidirect
253. C₂×#41	C₃×Dic₅	semidirect
255. C₂²×Q₈	C₃×Dic₅	semidirect
256. C₂²×D₄	C₃×Dic₅	semidirect
258. C₂³×C₄	C₃×Dic₅	semidirect
271. C₂×C₃×C₅	#410	semidirect
332. C₂×Q₈	C₂×C₃×Dic₅	semidirect
338. C₂×D₄	C₂×C₃×Dic₅	semidirect
348. C₂²×C₄	C₂×C₃×Dic₅	semidirect
357. C₃×C₅	C₂×#410	semidirect
382. C₂×C₅	C₃×#410	semidirect
421. C₂×C₃	#65529	direct (N × H)
423. C₅	C₂×C₃×#410	semidirect
443. C₃	C₂×#65529	direct (N × H)
449. C₂	C₃×#65529	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×#41	2
C₂×C₃×#4072	2
C₃×#65529	2
C₂×C₃×#3966	2
C₂×#65529	3
C₂×C₃×#410	5

Subgroups — C2×C3×#65529 #14411922

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65529 #14411922