Subgroups — C₅×#72002 #14302143

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×C₅×#930	C₂	1	1	yes	maximal, characteristic
3	C₅×#5207	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₅×#823	C₂	1	2	yes	maximal, complemented
5	C₅×#4554	C₂	1	2	yes	maximal, complemented
6	C₅×#1900	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₅×#67	C₄	1	2	yes	—
9	C₂²×C₅×D₁₂	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	C₅×#930	—	2	1	no	—
15	C₅×#930	—	2	1	no	—
16	C₅×#930	—	2	1	no	—
17	C₅×#930	—	2	1	no	—
18	C₂×C₅×(C₂×D₃)⋊C₄	C₄	1	2	yes	—
19	C₂×C₅×C₄⋊Dic₃	C₂²	1	1	yes	characteristic
20	C₂×C₅×#208	C₂²	1	2	yes	—
21	C₅×#830	—	2	1	no	—
22	C₅×#830	—	2	1	no	—
23	C₅×#823	—	2	4	no	—
24	#72002	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×M₁₆	D₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#121	—	3	1	no	—
27	C₂×C₅×#100	—	3	2	no	—
28	C₅×#407	—	3	1	no	—
29	C₅×#343	—	3	2	no	—
30	C₂⁴×C₃×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂³×C₅×D₃	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×C₅×#67	—	2	2	no	—
41	C₂×C₅×#67	—	2	2	no	—
42	C₂×C₅×#67	—	4	4	no	—
43	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
44	C₂×C₅×D₁₂	—	2	1	no	—
45	C₂×C₅×D₁₂	—	2	1	no	—
46	C₂×C₅×D₁₂	—	2	2	no	—
47	C₂×C₅×D₁₂	—	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	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
54	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
55	C₅×C₄⋊Dic₃	—	2	1	no	—
56	C₅×C₄⋊Dic₃	—	2	1	no	—
57	C₅×#208	—	2	2	no	—
58	C₅×#208	—	2	2	no	—
59	C₂×C₅×C₃⋊C₈	—	2	2	no	—
60	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic, complemented
61	C₂×#930	C₂×C₅	1	1	yes	characteristic
62	#5207	C₂×C₅	1	1	yes	characteristic, complemented
63	C₂×#823	C₂×C₅	1	2	yes	complemented
64	#4554	C₂×C₅	1	2	yes	complemented
65	C₂²×C₅×D₄	—	3	2	no	—
66	C₂²×C₅×D₄	—	3	1	no	—
67	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
68	C₂×C₅×M₁₆	—	2	1	no	—
69	C₂×C₅×M₁₆	—	2	4	no	—
70	C₂×C₅×M₁₆	—	3	2	no	—
71	C₂×C₅×M₁₆	C₂×D₃	1	2	yes	—
72	C₂²×C₅×C₈	—	2	1	no	—
73	C₅×#121	—	6	1	no	—
74	C₅×#121	—	6	1	no	—
75	C₅×#121	—	6	1	no	—
76	C₅×#121	—	6	1	no	—
77	C₂×C₅×C₄⋊C₄	—	3	1	no	—
78	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
79	C₅×#100	—	6	4	no	—
80	C₅×C₂²⋊C₈	—	6	1	no	—
81	C₅×C₂²⋊C₈	—	6	1	no	—
82	#1900	—	3	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×C₅×D₃	—	2	2	no	—
90	C₂²×C₅×D₃	—	2	4	no	—
91	C₂²×C₅×D₃	—	4	2	no	—
92	C₂²×C₅×D₃	—	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	C₅×#67	—	4	4	no	—
107	C₅×#67	—	4	4	no	—
108	C₂×C₅×Dic₃	—	2	2	no	—
109	C₂×C₅×Dic₃	—	4	2	no	—
110	C₅×D₁₂	—	4	1	no	—
111	C₅×D₁₂	—	4	2	no	—
112	C₅×D₁₂	—	4	1	no	—
113	C₃×C₅×C₈	—	2	4	no	—
114	C₅×C₃⋊C₈	—	4	2	no	—
115	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
116	C₂²×#67	C₄×C₅	1	2	yes	—
117	C₂²×D₁₂	C₂²×C₅	1	1	yes	characteristic
118	C₂×C₃×M₁₆	—	2	1	no	—
119	C₂×C₃×M₁₆	—	2	4	no	—
120	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
121	C₂²×C₃×C₈	—	2	1	no	—
122	#930	—	2	1	no	—
123	#930	—	2	1	no	—
124	#930	—	2	1	no	—
125	#930	—	2	1	no	—
126	C₂×(C₂×D₃)⋊C₄	C₄×C₅	1	2	yes	—
127	C₂×C₄⋊Dic₃	C₂²×C₅	1	1	yes	characteristic
128	C₂×#208	C₂²×C₅	1	2	yes	—
129	#830	—	2	1	no	—
130	#830	—	2	1	no	—
131	#823	—	2	4	no	—
132	C₂⁴×C₅	—	3	2	no	—
133	C₂⁴×C₅	C₄×D₃	1	1	yes	characteristic
134	C₂×C₅×D₄	—	6	2	no	—
135	C₂×C₅×D₄	—	6	2	no	—
136	C₂×C₅×D₄	—	6	1	no	—
137	C₂×C₅×D₄	—	6	2	no	—
138	C₂×C₅×D₄	—	6	1	no	—
139	C₂×C₅×D₄	—	6	2	no	—
140	C₂×C₅×D₄	—	12	4	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	—	3	2	no	—
144	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
145	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
146	C₂²×C₄×C₅	D₁₂	1	1	yes	characteristic
147	C₂²×C₄×C₅	#67	1	1	yes	characteristic
148	C₂²×C₄×C₅	#67	1	1	yes	characteristic
149	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
150	C₅×M₁₆	—	2	4	no	—
151	C₅×M₁₆	—	2	2	no	—
152	C₅×M₁₆	—	6	2	no	—
153	C₅×M₁₆	—	6	2	no	—
154	C₅×M₁₆	#67	1	4	yes	complemented
155	C₂×C₅×C₈	—	2	4	no	—
156	C₂×C₅×C₈	—	2	2	no	—
157	C₂×C₅×C₈	—	6	2	no	—
158	C₅×C₄⋊C₄	—	6	1	no	—
159	C₅×C₄⋊C₄	—	6	1	no	—
160	C₅×C₂²⋊C₄	—	6	2	no	—
161	C₅×C₂²⋊C₄	—	6	2	no	—
162	C₂²×M₁₆	C₅×D₃	1	1	yes	characteristic, complemented
163	C₂×#121	—	3	1	no	—
164	C₂×#100	—	3	2	no	—
165	#407	—	3	1	no	—
166	#343	—	3	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×C₅×D₃	—	4	2	no	—
179	C₂×C₅×D₃	—	4	2	no	—
180	C₂×C₅×D₃	—	4	2	no	—
181	C₂×C₅×D₃	—	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	C₅×Dic₃	—	4	2	no	—
188	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂³×D₃	C₂×C₄×C₅	1	2	yes	—
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
193	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
194	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
195	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
197	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
198	C₂×#67	—	2	2	no	—
199	C₂×#67	—	2	2	no	—
200	C₂×#67	—	4	4	no	—
201	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
202	C₂×D₁₂	—	2	2	no	—
203	C₂×D₁₂	—	2	1	no	—
204	C₂×D₁₂	—	2	1	no	—
205	C₂×D₁₂	—	2	2	no	—
206	C₃×M₁₆	—	2	4	no	—
207	C₃×M₁₆	—	2	2	no	—
208	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
209	C₂×C₃×C₈	—	2	4	no	—
210	C₂×C₃×C₈	—	2	2	no	—
211	(C₂×D₃)⋊C₄	—	2	2	no	—
212	(C₂×D₃)⋊C₄	—	2	2	no	—
213	C₄⋊Dic₃	—	2	1	no	—
214	C₄⋊Dic₃	—	2	1	no	—
215	#208	—	2	2	no	—
216	#208	—	2	2	no	—
217	C₂×C₃⋊C₈	—	2	2	no	—
218	C₂³×C₅	—	2	2	no	—
219	C₂³×C₅	—	2	2	no	—
220	C₂³×C₅	—	4	1	no	—
221	C₂³×C₅	—	6	2	no	—
222	C₂³×C₅	—	6	4	no	—
223	C₂³×C₅	—	12	2	no	—
224	C₂³×C₅	—	12	2	no	—
225	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
226	C₂³×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
227	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
228	C₅×D₄	—	12	4	no	—
229	C₅×D₄	—	12	4	no	—
230	C₅×D₄	—	12	1	no	—
231	C₅×D₄	—	12	2	no	—
232	C₅×D₄	—	12	1	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	1	no	—
235	C₂×C₄×C₅	—	2	1	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	1	no	—
239	C₂×C₄×C₅	—	2	1	no	—
240	C₂×C₄×C₅	—	6	2	no	—
241	C₂×C₄×C₅	—	12	2	no	—
242	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
243	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×D₁₂	1	1	yes	characteristic
245	C₂×C₄×C₅	#235	1	2	yes	—
246	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#67	1	2	yes	—
248	C₅×C₈	—	2	4	no	—
249	C₅×C₈	—	12	2	no	—
250	C₂²×D₄	—	3	2	no	—
251	C₂²×D₄	—	3	1	no	—
252	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
253	C₂×M₁₆	—	2	1	no	—
254	C₂×M₁₆	—	2	4	no	—
255	C₂×M₁₆	—	3	2	no	—
256	C₂×M₁₆	C₂×C₅×D₃	1	2	yes	—
257	C₂²×C₈	—	2	1	no	—
258	#121	—	6	1	no	—
259	#121	—	6	1	no	—
260	#121	—	6	1	no	—
261	#121	—	6	1	no	—
262	C₂×C₄⋊C₄	—	3	1	no	—
263	C₂×C₂²⋊C₄	—	3	2	no	—
264	#100	—	6	4	no	—
265	C₂²⋊C₈	—	6	1	no	—
266	C₂²⋊C₈	—	6	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	C₅×D₃	—	8	2	no	—
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	4	1	no	—
277	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
278	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
279	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
280	C₂²×D₃	—	2	2	no	—
281	C₂²×D₃	—	2	4	no	—
282	C₂²×D₃	—	4	2	no	—
283	C₂²×D₃	—	4	2	no	—
284	C₂×C₃×C₄	—	2	2	no	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	1	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	1	no	—
290	C₂×C₃×C₄	—	2	1	no	—
291	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
295	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃×C₄	C₅×#41	1	2	yes	—
297	#67	—	4	4	no	—
298	#67	—	4	4	no	—
299	C₂×Dic₃	—	2	2	no	—
300	C₂×Dic₃	—	4	2	no	—
301	D₁₂	—	4	1	no	—
302	D₁₂	—	4	2	no	—
303	D₁₂	—	4	1	no	—
304	C₃×C₈	—	2	4	no	—
305	C₃⋊C₈	—	4	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	—	12	2	no	—
315	C₂²×C₅	—	12	2	no	—
316	C₂²×C₅	—	12	2	no	—
317	C₂²×C₅	—	24	4	no	—
318	C₂²×C₅	#823	1	2	yes	complemented
319	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	1	yes	characteristic
320	C₂²×C₅	C₄×#67	1	2	yes	—
321	C₄×C₅	—	2	1	no	—
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	12	2	no	—
324	C₄×C₅	#929	1	1	yes	characteristic
325	C₄×C₅	#930	1	2	yes	—
326	C₄×C₅	#953	1	1	yes	characteristic
327	C₂⁴	—	3	2	no	—
328	C₂⁴	C₄×C₅×D₃	1	1	yes	characteristic
329	C₂×D₄	—	6	2	no	—
330	C₂×D₄	—	6	2	no	—
331	C₂×D₄	—	6	1	no	—
332	C₂×D₄	—	6	2	no	—
333	C₂×D₄	—	6	2	no	—
334	C₂×D₄	—	6	1	no	—
335	C₂×D₄	—	12	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	—	3	2	no	—
339	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
340	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
341	C₂²×C₄	C₅×D₁₂	1	1	yes	characteristic
342	C₂²×C₄	C₅×#67	1	1	yes	characteristic
343	C₂²×C₄	C₅×#67	1	1	yes	characteristic
344	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
345	M₁₆	—	2	4	no	—
346	M₁₆	—	2	2	no	—
347	M₁₆	—	6	2	no	—
348	M₁₆	—	6	2	no	—
349	M₁₆	C₅×#67	1	4	yes	complemented
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	—	2	2	no	—
352	C₂×C₈	—	6	2	no	—
353	C₄⋊C₄	—	6	1	no	—
354	C₄⋊C₄	—	6	1	no	—
355	C₂²⋊C₄	—	6	2	no	—
356	C₂²⋊C₄	—	6	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	C₅×#100	1	2	yes	complemented
367	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
368	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
369	C₂×D₃	—	4	2	no	—
370	C₂×D₃	—	4	2	no	—
371	C₂×D₃	—	4	2	no	—
372	C₂×D₃	—	8	4	no	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	C₅×#120	1	1	yes	characteristic
376	C₃×C₄	C₅×#121	1	2	yes	—
377	C₃×C₄	C₅×#123	1	1	yes	characteristic
378	Dic₃	—	4	2	no	—
379	C₂×C₅	—	2	2	no	—
380	C₂×C₅	—	2	2	no	—
381	C₂×C₅	—	4	1	no	—
382	C₂×C₅	—	24	2	no	—
383	C₂×C₅	C₂×#823	1	1	yes	characteristic
384	C₂×C₅	#5132	1	1	yes	characteristic
385	C₂×C₅	#5213	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	4	1	no	—
389	C₂³	—	6	2	no	—
390	C₂³	—	6	4	no	—
391	C₂³	—	12	2	no	—
392	C₂³	—	12	2	no	—
393	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
394	C₂³	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
395	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
396	D₄	—	12	4	no	—
397	D₄	—	12	4	no	—
398	D₄	—	12	1	no	—
399	D₄	—	12	2	no	—
400	D₄	—	12	1	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	1	no	—
403	C₂×C₄	—	2	1	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	1	no	—
407	C₂×C₄	—	2	1	no	—
408	C₂×C₄	—	6	2	no	—
409	C₂×C₄	—	12	2	no	—
410	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
411	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
412	C₂×C₄	C₂×C₅×D₁₂	1	1	yes	characteristic
413	C₂×C₄	C₅×#235	1	2	yes	—
414	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
415	C₂×C₄	C₂×C₅×#67	1	2	yes	—
416	C₈	—	2	4	no	—
417	C₈	—	12	2	no	—
418	C₂×C₃	—	2	2	no	—
419	C₂×C₃	—	2	2	no	—
420	C₂×C₃	—	4	1	no	—
421	C₂×C₃	C₅×#386	1	1	yes	characteristic
422	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
423	C₂×C₃	C₅×#413	1	1	yes	characteristic
424	D₃	—	8	2	no	—
425	C₅	#72002	1	1	yes	characteristic, direct product factor, 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	—	12	2	no	—
435	C₂²	—	12	2	no	—
436	C₂²	—	12	2	no	—
437	C₂²	—	24	4	no	—
438	C₂²	C₅×#823	1	2	yes	complemented
439	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
440	C₂²	C₄×C₅×#67	1	2	yes	—
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	12	2	no	—
444	C₄	C₅×#929	1	1	yes	characteristic
445	C₄	C₅×#930	1	2	yes	—
446	C₄	C₅×#953	1	1	yes	characteristic
447	C₃	C₅×#1900	1	1	yes	characteristic, complemented, Sylow
448	C₂	—	2	2	no	—
449	C₂	—	2	2	no	—
450	C₂	—	4	1	no	—
451	C₂	—	24	2	no	—
452	C₂	C₂×C₅×#823	1	1	yes	characteristic
453	C₂	C₅×#5132	1	1	yes	characteristic
454	C₂	C₅×#5213	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×(C₂×D₃)⋊C₄
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₅×#930	C₂
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂²×C₅×M₁₆	D₃
hypocenter	C₃	C₅×#1900
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂²×C₅×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. C₅×#5207	C₂	semidirect
4. C₂×C₅×#823	C₂	semidirect
5. C₅×#4554	C₂	semidirect
24. #72002	C₅	direct (N × H)
25. C₂²×C₅×M₁₆	D₃	semidirect
50. C₃×C₅×M₁₆	D₄	semidirect
60. C₂²×C₃×M₁₆	C₂×C₅	semidirect
62. #5207	C₂×C₅	semidirect
63. C₂×#823	C₂×C₅	semidirect
64. #4554	C₂×C₅	semidirect
154. C₅×M₁₆	#67	semidirect
162. C₂²×M₁₆	C₅×D₃	semidirect
175. C₂²×C₃×C₅	#100	semidirect
208. C₃×M₁₆	C₅×D₄	semidirect
318. C₂²×C₅	#823	semidirect
349. M₁₆	C₅×#67	semidirect
357. C₃×C₅	#1900	semidirect
366. C₂²×C₃	C₅×#100	semidirect
425. C₅	#72002	direct (N × H)
438. C₂²	C₅×#823	semidirect
447. C₃	C₅×#1900	semidirect

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×C₅×#930	2
C₅×#5207	2
C₂×C₅×#823	2
C₅×#4554	2
C₅×#1900	3
#72002	5

Subgroups — C5×#72002 #14302143

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#72002 #14302143