Subgroups — C₃×#10602795 #14302144

Order 1920.

780 conjugacy classes of subgroups.

The subgroup lattice has 456 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×#4076	C₂	1	1	yes	maximal, characteristic
3	C₃×#65496	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3955	C₂	1	2	yes	maximal, complemented
5	C₃×#64774	C₂	1	2	yes	maximal, complemented
6	#10602795	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₂²⋊D₅	C₄	1	2	yes	—
9	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
10	C₂×C₃×C₅×M₁₆	—	2	1	no	—
11	C₂×C₃×C₅×M₁₆	—	2	4	no	—
12	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×C₈	—	2	1	no	—
14	C₃×#4076	—	2	1	no	—
15	C₃×#4076	—	2	1	no	—
16	C₃×#4076	—	2	1	no	—
17	C₃×#4076	—	2	1	no	—
18	C₂×C₃×#685	C₄	1	2	yes	—
19	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×#681	C₂²	1	2	yes	—
21	C₃×C₂²⋊#168	—	2	1	no	—
22	C₃×C₂²⋊#168	—	2	1	no	—
23	C₃×#3955	—	2	4	no	—
24	C₃×#1900	—	5	1	no	maximal, Hall
25	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×#4076	C₂×C₃	1	1	yes	characteristic
27	#65496	C₂×C₃	1	1	yes	characteristic, complemented
28	C₂×#3955	C₂×C₃	1	2	yes	complemented
29	#64774	C₂×C₃	1	2	yes	complemented
30	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	—	2	2	no	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
35	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
38	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
39	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
41	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
42	C₂×C₃×C₂²⋊D₅	—	4	4	no	—
43	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
44	C₂×C₃×D₂₀	—	2	2	no	—
45	C₂×C₃×D₂₀	—	2	1	no	—
46	C₂×C₃×D₂₀	—	2	1	no	—
47	C₂×C₃×D₂₀	—	2	2	no	—
48	C₃×C₅×M₁₆	—	2	4	no	—
49	C₃×C₅×M₁₆	—	2	2	no	—
50	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
51	C₂×C₃×C₅×C₈	—	2	4	no	—
52	C₂×C₃×C₅×C₈	—	2	2	no	—
53	C₃×#685	—	2	2	no	—
54	C₃×#685	—	2	2	no	—
55	C₃×C₄⋊Dic₅	—	2	1	no	—
56	C₃×C₄⋊Dic₅	—	2	1	no	—
57	C₃×#681	—	2	2	no	—
58	C₃×#681	—	2	2	no	—
59	C₂×C₃×#168	—	2	2	no	—
60	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
61	C₂×C₃×#121	—	5	1	no	—
62	C₂×C₃×#100	—	5	2	no	—
63	C₃×#407	—	5	1	no	—
64	C₃×#343	—	5	2	no	—
65	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₂²⋊D₅	C₃×C₄	1	2	yes	—
67	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×M₁₆	—	2	1	no	—
69	C₂×C₅×M₁₆	—	2	4	no	—
70	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
71	C₂²×C₅×C₈	—	2	1	no	—
72	#4076	—	2	1	no	—
73	#4076	—	2	1	no	—
74	#4076	—	2	1	no	—
75	#4076	—	2	1	no	—
76	C₂×#685	C₃×C₄	1	2	yes	—
77	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
78	C₂×#681	C₂²×C₃	1	2	yes	—
79	C₂²⋊#168	—	2	1	no	—
80	C₂²⋊#168	—	2	1	no	—
81	#3955	—	2	4	no	—
82	#1900	—	5	1	no	Sylow
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	—	2	2	no	—
85	C₂³×C₃×C₅	—	4	1	no	—
86	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
87	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
88	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₃×D₅	—	2	2	no	—
90	C₂²×C₃×D₅	—	2	4	no	—
91	C₂²×C₃×D₅	—	4	2	no	—
92	C₂²×C₃×D₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	2	2	no	—
94	C₂×C₃×C₄×C₅	—	2	1	no	—
95	C₂×C₃×C₄×C₅	—	2	1	no	—
96	C₂×C₃×C₄×C₅	—	2	2	no	—
97	C₂×C₃×C₄×C₅	—	2	2	no	—
98	C₂×C₃×C₄×C₅	—	2	1	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	2	yes	—
106	C₃×C₂²⋊D₅	—	4	4	no	—
107	C₃×C₂²⋊D₅	—	4	4	no	—
108	C₂×C₃×Dic₅	—	2	2	no	—
109	C₂×C₃×Dic₅	—	4	2	no	—
110	C₃×D₂₀	—	4	1	no	—
111	C₃×D₂₀	—	4	2	no	—
112	C₃×D₂₀	—	4	1	no	—
113	C₃×C₅×C₈	—	2	4	no	—
114	C₃×#168	—	4	2	no	—
115	C₂²×C₃×D₄	—	5	2	no	—
116	C₂²×C₃×D₄	—	5	1	no	—
117	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
118	C₂×C₃×M₁₆	—	2	1	no	—
119	C₂×C₃×M₁₆	—	2	4	no	—
120	C₂×C₃×M₁₆	—	5	2	no	—
121	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
122	C₂²×C₃×C₈	—	2	1	no	—
123	C₃×#121	—	10	1	no	—
124	C₃×#121	—	10	1	no	—
125	C₃×#121	—	10	1	no	—
126	C₃×#121	—	10	1	no	—
127	C₂×C₃×C₄⋊C₄	—	5	1	no	—
128	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
129	C₃×#100	—	10	4	no	—
130	C₃×C₂²⋊C₈	—	10	1	no	—
131	C₃×C₂²⋊C₈	—	10	1	no	—
132	C₂⁴×C₅	C₂×C₃×C₄	1	1	yes	characteristic
133	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
134	C₂²×C₄×C₅	—	2	2	no	—
135	C₂²×C₄×C₅	—	2	2	no	—
136	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
137	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
138	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
140	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
141	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂×C₂²⋊D₅	—	2	2	no	—
143	C₂×C₂²⋊D₅	—	2	2	no	—
144	C₂×C₂²⋊D₅	—	4	4	no	—
145	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
146	C₂×D₂₀	—	2	2	no	—
147	C₂×D₂₀	—	2	1	no	—
148	C₂×D₂₀	—	2	1	no	—
149	C₂×D₂₀	—	2	2	no	—
150	C₅×M₁₆	—	2	4	no	—
151	C₅×M₁₆	—	2	2	no	—
152	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
153	C₂×C₅×C₈	—	2	4	no	—
154	C₂×C₅×C₈	—	2	2	no	—
155	#685	—	2	2	no	—
156	#685	—	2	2	no	—
157	C₄⋊Dic₅	—	2	1	no	—
158	C₄⋊Dic₅	—	2	1	no	—
159	#681	—	2	2	no	—
160	#681	—	2	2	no	—
161	C₂×#168	—	2	2	no	—
162	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
163	C₂×#121	—	5	1	no	—
164	C₂×#100	—	5	2	no	—
165	#407	—	5	1	no	—
166	#343	—	5	2	no	—
167	C₂²×C₃×C₅	—	2	1	no	—
168	C₂²×C₃×C₅	—	2	1	no	—
169	C₂²×C₃×C₅	—	2	1	no	—
170	C₂²×C₃×C₅	—	2	1	no	—
171	C₂²×C₃×C₅	—	2	1	no	—
172	C₂²×C₃×C₅	—	2	1	no	—
173	C₂²×C₃×C₅	—	2	1	no	—
174	C₂²×C₃×C₅	—	4	4	no	—
175	C₂²×C₃×C₅	#100	1	2	yes	complemented
176	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
177	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
178	C₂×C₃×D₅	—	4	2	no	—
179	C₂×C₃×D₅	—	4	2	no	—
180	C₂×C₃×D₅	—	4	2	no	—
181	C₂×C₃×D₅	—	8	4	no	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	—	2	1	no	—
184	C₃×C₄×C₅	#120	1	1	yes	characteristic
185	C₃×C₄×C₅	#121	1	2	yes	—
186	C₃×C₄×C₅	#123	1	1	yes	characteristic
187	C₃×Dic₅	—	4	2	no	—
188	C₂⁴×C₃	—	5	2	no	—
189	C₂⁴×C₃	C₄×D₅	1	1	yes	characteristic
190	C₂×C₃×D₄	—	10	2	no	—
191	C₂×C₃×D₄	—	10	2	no	—
192	C₂×C₃×D₄	—	10	1	no	—
193	C₂×C₃×D₄	—	10	2	no	—
194	C₂×C₃×D₄	—	10	2	no	—
195	C₂×C₃×D₄	—	10	1	no	—
196	C₂×C₃×D₄	—	20	4	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	—	5	2	no	—
200	C₂²×C₃×C₄	C₄×D₅	1	1	yes	characteristic
201	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
202	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₂²⋊D₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
206	C₃×M₁₆	—	2	4	no	—
207	C₃×M₁₆	—	2	2	no	—
208	C₃×M₁₆	—	10	2	no	—
209	C₃×M₁₆	—	10	2	no	—
210	C₃×M₁₆	C₂²⋊D₅	1	4	yes	complemented
211	C₂×C₃×C₈	—	2	4	no	—
212	C₂×C₃×C₈	—	2	2	no	—
213	C₂×C₃×C₈	—	10	2	no	—
214	C₃×C₄⋊C₄	—	10	1	no	—
215	C₃×C₄⋊C₄	—	10	1	no	—
216	C₃×C₂²⋊C₄	—	10	2	no	—
217	C₃×C₂²⋊C₄	—	10	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	4	1	no	—
221	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
222	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
223	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
224	C₂²×D₅	—	2	2	no	—
225	C₂²×D₅	—	2	4	no	—
226	C₂²×D₅	—	4	2	no	—
227	C₂²×D₅	—	4	2	no	—
228	C₂×C₄×C₅	—	2	2	no	—
229	C₂×C₄×C₅	—	2	1	no	—
230	C₂×C₄×C₅	—	2	1	no	—
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
236	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
237	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
238	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
239	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₃×#41	1	2	yes	—
241	C₂²⋊D₅	—	4	4	no	—
242	C₂²⋊D₅	—	4	4	no	—
243	C₂×Dic₅	—	2	2	no	—
244	C₂×Dic₅	—	4	2	no	—
245	D₂₀	—	4	1	no	—
246	D₂₀	—	4	2	no	—
247	D₂₀	—	4	1	no	—
248	C₅×C₈	—	2	4	no	—
249	#168	—	4	2	no	—
250	C₂²×D₄	—	5	2	no	—
251	C₂²×D₄	—	5	1	no	—
252	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	4	no	—
255	C₂×M₁₆	—	5	2	no	—
256	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
257	C₂²×C₈	—	2	1	no	—
258	#121	—	10	1	no	—
259	#121	—	10	1	no	—
260	#121	—	10	1	no	—
261	#121	—	10	1	no	—
262	C₂×C₄⋊C₄	—	5	1	no	—
263	C₂×C₂²⋊C₄	—	5	2	no	—
264	#100	—	10	4	no	—
265	C₂²⋊C₈	—	10	1	no	—
266	C₂²⋊C₈	—	10	1	no	—
267	C₂×C₃×C₅	—	2	2	no	—
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	—	4	1	no	—
270	C₂×C₃×C₅	#386	1	1	yes	characteristic
271	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
272	C₂×C₃×C₅	#413	1	1	yes	characteristic
273	C₃×D₅	—	8	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	4	1	no	—
277	C₂³×C₃	—	10	2	no	—
278	C₂³×C₃	—	10	4	no	—
279	C₂³×C₃	—	20	2	no	—
280	C₂³×C₃	—	20	2	no	—
281	C₂³×C₃	#685	1	1	yes	characteristic
282	C₂³×C₃	#685	1	1	yes	characteristic
283	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
284	C₃×D₄	—	20	4	no	—
285	C₃×D₄	—	20	4	no	—
286	C₃×D₄	—	20	1	no	—
287	C₃×D₄	—	20	1	no	—
288	C₃×D₄	—	20	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	—	2	1	no	—
292	C₂×C₃×C₄	—	2	1	no	—
293	C₂×C₃×C₄	—	2	1	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	10	2	no	—
297	C₂×C₃×C₄	—	20	2	no	—
298	C₂×C₃×C₄	#685	1	1	yes	characteristic
299	C₂×C₃×C₄	#685	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
301	C₂×C₃×C₄	#709	1	2	yes	—
302	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
304	C₃×C₈	—	2	4	no	—
305	C₃×C₈	—	20	2	no	—
306	C₂²×C₅	—	2	1	no	—
307	C₂²×C₅	—	2	1	no	—
308	C₂²×C₅	—	2	1	no	—
309	C₂²×C₅	—	2	1	no	—
310	C₂²×C₅	—	2	1	no	—
311	C₂²×C₅	—	2	1	no	—
312	C₂²×C₅	—	2	1	no	—
313	C₂²×C₅	—	4	4	no	—
314	C₂²×C₅	C₃×#100	1	2	yes	complemented
315	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
316	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
317	C₂×D₅	—	4	2	no	—
318	C₂×D₅	—	4	2	no	—
319	C₂×D₅	—	4	2	no	—
320	C₂×D₅	—	8	4	no	—
321	C₄×C₅	—	2	1	no	—
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	C₃×#120	1	1	yes	characteristic
324	C₄×C₅	C₃×#121	1	2	yes	—
325	C₄×C₅	C₃×#123	1	1	yes	characteristic
326	Dic₅	—	4	2	no	—
327	C₂⁴	—	5	2	no	—
328	C₂⁴	C₃×C₄×D₅	1	1	yes	characteristic
329	C₂×D₄	—	10	2	no	—
330	C₂×D₄	—	10	2	no	—
331	C₂×D₄	—	10	1	no	—
332	C₂×D₄	—	10	2	no	—
333	C₂×D₄	—	10	2	no	—
334	C₂×D₄	—	10	1	no	—
335	C₂×D₄	—	20	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	5	2	no	—
339	C₂²×C₄	C₃×C₄×D₅	1	1	yes	characteristic
340	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
341	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
342	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
343	C₂²×C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	10	2	no	—
348	M₁₆	—	10	2	no	—
349	M₁₆	C₃×C₂²⋊D₅	1	4	yes	complemented
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	10	2	no	—
353	C₄⋊C₄	—	10	1	no	—
354	C₄⋊C₄	—	10	1	no	—
355	C₂²⋊C₄	—	10	2	no	—
356	C₂²⋊C₄	—	10	2	no	—
357	C₃×C₅	#1900	1	1	yes	characteristic, complemented, Hall
358	C₂²×C₃	—	2	1	no	—
359	C₂²×C₃	—	2	1	no	—
360	C₂²×C₃	—	2	1	no	—
361	C₂²×C₃	—	2	1	no	—
362	C₂²×C₃	—	2	1	no	—
363	C₂²×C₃	—	2	1	no	—
364	C₂²×C₃	—	2	1	no	—
365	C₂²×C₃	—	4	4	no	—
366	C₂²×C₃	—	20	2	no	—
367	C₂²×C₃	—	20	2	no	—
368	C₂²×C₃	—	20	2	no	—
369	C₂²×C₃	—	40	4	no	—
370	C₂²×C₃	#3955	1	2	yes	complemented
371	C₂²×C₃	C₂×#685	1	1	yes	characteristic
372	C₂²×C₃	C₄×C₂²⋊D₅	1	2	yes	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	20	2	no	—
376	C₃×C₄	#4075	1	1	yes	characteristic
377	C₃×C₄	#4076	1	2	yes	—
378	C₃×C₄	#4099	1	1	yes	characteristic
379	C₂×C₅	—	2	2	no	—
380	C₂×C₅	—	2	2	no	—
381	C₂×C₅	—	4	1	no	—
382	C₂×C₅	C₃×#386	1	1	yes	characteristic
383	C₂×C₅	C₂×C₃×#100	1	1	yes	characteristic
384	C₂×C₅	C₃×#413	1	1	yes	characteristic
385	D₅	—	8	2	no	—
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	10	2	no	—
390	C₂³	—	10	4	no	—
391	C₂³	—	20	2	no	—
392	C₂³	—	20	2	no	—
393	C₂³	C₃×#685	1	1	yes	characteristic
394	C₂³	C₃×#685	1	1	yes	characteristic
395	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
396	D₄	—	20	4	no	—
397	D₄	—	20	4	no	—
398	D₄	—	20	1	no	—
399	D₄	—	20	1	no	—
400	D₄	—	20	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	1	no	—
405	C₂×C₄	—	2	1	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	2	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	20	2	no	—
410	C₂×C₄	C₃×#685	1	1	yes	characteristic
411	C₂×C₄	C₃×#685	1	1	yes	characteristic
412	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
413	C₂×C₄	C₃×#709	1	2	yes	—
414	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
415	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
416	C₈	—	2	4	no	—
417	C₈	—	20	2	no	—
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	4	1	no	—
421	C₂×C₃	—	40	2	no	—
422	C₂×C₃	C₂×#3955	1	1	yes	characteristic
423	C₂×C₃	#65421	1	1	yes	characteristic
424	C₂×C₃	#65502	1	1	yes	characteristic
425	C₅	C₃×#1900	1	1	yes	characteristic, complemented, Sylow
426	C₂²	—	2	1	no	—
427	C₂²	—	2	1	no	—
428	C₂²	—	2	1	no	—
429	C₂²	—	2	1	no	—
430	C₂²	—	2	1	no	—
431	C₂²	—	2	1	no	—
432	C₂²	—	2	1	no	—
433	C₂²	—	4	4	no	—
434	C₂²	—	20	2	no	—
435	C₂²	—	20	2	no	—
436	C₂²	—	20	2	no	—
437	C₂²	—	40	4	no	—
438	C₂²	C₃×#3955	1	2	yes	complemented
439	C₂²	C₂×C₃×#685	1	1	yes	characteristic
440	C₂²	C₃×C₄×C₂²⋊D₅	1	2	yes	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	20	2	no	—
444	C₄	C₃×#4075	1	1	yes	characteristic
445	C₄	C₃×#4076	1	2	yes	—
446	C₄	C₃×#4099	1	1	yes	characteristic
447	C₃	#10602795	1	1	yes	characteristic, direct product factor, Sylow
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	—	4	1	no	—
451	C₂	—	40	2	no	—
452	C₂	C₂×C₃×#3955	1	1	yes	characteristic
453	C₂	C₃×#65421	1	1	yes	characteristic
454	C₂	C₃×#65502	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×#685
commutator	C₂³×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#4076	C₂
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₃×#1900
LCS	G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂³×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. C₃×#65496	C₂	semidirect
4. C₂×C₃×#3955	C₂	semidirect
5. C₃×#64774	C₂	semidirect
6. #10602795	C₃	direct (N × H)
25. C₂²×C₅×M₁₆	C₂×C₃	semidirect
27. #65496	C₂×C₃	semidirect
28. C₂×#3955	C₂×C₃	semidirect
29. #64774	C₂×C₃	semidirect
50. C₃×C₅×M₁₆	D₄	semidirect
60. C₂²×C₃×M₁₆	D₅	semidirect
152. C₅×M₁₆	C₃×D₄	semidirect
162. C₂²×M₁₆	C₃×D₅	semidirect
175. C₂²×C₃×C₅	#100	semidirect
210. C₃×M₁₆	C₂²⋊D₅	semidirect
314. C₂²×C₅	C₃×#100	semidirect
349. M₁₆	C₃×C₂²⋊D₅	semidirect
357. C₃×C₅	#1900	semidirect
370. C₂²×C₃	#3955	semidirect
425. C₅	C₃×#1900	semidirect
438. C₂²	C₃×#3955	semidirect
447. C₃	#10602795	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×#4076	2
C₃×#65496	2
C₂×C₃×#3955	2
C₃×#64774	2
#10602795	3
C₃×#1900	5

Subgroups — C3×#10602795 #14302144

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10602795 #14302144