Subgroups — C₅×#71683 #14302146

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	C₂×C₃×C₅×#121	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₅×#208	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#833	C₂	1	2	yes	maximal, complemented
4	C₅×#5207	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4530	C₂	1	2	yes	maximal, complemented
6	C₅×#1900	—	3	1	no	maximal, Hall
7	C₂²×C₃×C₅×D₄	C₄	1	2	yes	—
8	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₃×C₅×#121	—	2	1	no	—
11	C₃×C₅×#121	—	2	1	no	—
12	C₃×C₅×#121	—	2	1	no	—
13	C₃×C₅×#121	—	2	1	no	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₂²⋊C₄	C₄	1	2	yes	—
16	C₂×C₅×#208	—	2	1	no	—
17	C₂×C₅×#208	—	2	4	no	—
18	C₂×C₅×#208	C₂²	1	2	yes	—
19	C₂×C₅×#208	C₂²	1	2	yes	—
20	C₂²×C₅×C₃⋊C₈	—	2	1	no	—
21	C₅×#833	—	2	4	no	—
22	C₅×#830	—	2	1	no	—
23	C₅×#830	—	2	1	no	—
24	#71683	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
25	C₂²×C₅×M₁₆	—	3	1	no	—
26	C₂×C₅×#121	D₃	1	1	yes	characteristic
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	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
32	C₂×C₃×C₅×D₄	—	2	2	no	—
33	C₂×C₃×C₅×D₄	—	2	2	no	—
34	C₂×C₃×C₅×D₄	—	2	2	no	—
35	C₂×C₃×C₅×D₄	—	2	1	no	—
36	C₂×C₃×C₅×D₄	—	2	1	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	—	4	4	no	—
39	C₂²×C₃×C₄×C₅	—	2	2	no	—
40	C₂²×C₃×C₄×C₅	—	2	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
42	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
48	C₃×C₅×C₄⋊C₄	—	2	1	no	—
49	C₃×C₅×C₄⋊C₄	—	2	1	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
52	C₅×#208	—	2	4	no	—
53	C₅×#208	—	2	2	no	—
54	C₅×#208	—	2	2	no	—
55	C₅×#208	—	2	2	no	—
56	C₅×#208	D₄	1	4	yes	complemented
57	C₂×C₅×C₃⋊C₈	—	2	4	no	—
58	C₂×C₅×C₃⋊C₈	—	2	2	no	—
59	C₂×C₅×C₃⋊C₈	—	2	2	no	—
60	C₂×C₃×#121	C₂×C₅	1	1	yes	characteristic
61	C₂²×#208	C₂×C₅	1	1	yes	characteristic, complemented
62	C₂×#833	C₂×C₅	1	2	yes	complemented
63	#5207	C₂×C₅	1	1	yes	characteristic, complemented
64	#4530	C₂×C₅	1	2	yes	complemented
65	C₂²×C₅×D₄	Dic₃	1	2	yes	—
66	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
67	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
68	C₂×C₅×M₁₆	—	3	2	no	—
69	C₂×C₅×M₁₆	—	3	2	no	—
70	C₂×C₅×M₁₆	—	6	4	no	—
71	C₂×C₅×M₁₆	—	6	1	no	—
72	C₂²×C₅×C₈	—	6	1	no	—
73	C₅×#121	—	2	1	no	—
74	C₅×#121	—	2	1	no	—
75	C₅×#121	—	2	1	no	—
76	C₅×#121	—	2	1	no	—
77	C₂×C₅×C₄⋊C₄	C₂×D₃	1	1	yes	characteristic
78	C₂×C₅×C₂²⋊C₄	Dic₃	1	2	yes	—
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	—	2	2	no	—
86	C₂³×C₃×C₅	—	2	4	no	—
87	C₂³×C₃×C₅	—	4	1	no	—
88	C₂³×C₃×C₅	—	4	2	no	—
89	C₂³×C₃×C₅	—	4	2	no	—
90	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
91	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
92	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
93	C₃×C₅×D₄	—	4	4	no	—
94	C₃×C₅×D₄	—	4	4	no	—
95	C₃×C₅×D₄	—	4	1	no	—
96	C₃×C₅×D₄	—	4	2	no	—
97	C₃×C₅×D₄	—	4	1	no	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	1	no	—
100	C₂×C₃×C₄×C₅	—	2	1	no	—
101	C₂×C₃×C₄×C₅	—	2	2	no	—
102	C₂×C₃×C₄×C₅	—	2	2	no	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	1	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	4	2	no	—
107	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	2	yes	—
113	C₅×C₃⋊C₈	—	2	4	no	—
114	C₅×C₃⋊C₈	—	4	2	no	—
115	C₂²×C₃×D₄	C₄×C₅	1	2	yes	—
116	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
117	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
118	C₃×#121	—	2	1	no	—
119	C₃×#121	—	2	1	no	—
120	C₃×#121	—	2	1	no	—
121	C₃×#121	—	2	1	no	—
122	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
123	C₂×C₃×C₂²⋊C₄	C₄×C₅	1	2	yes	—
124	C₂×#208	—	2	1	no	—
125	C₂×#208	—	2	4	no	—
126	C₂×#208	C₂²×C₅	1	2	yes	—
127	C₂×#208	C₂²×C₅	1	2	yes	—
128	C₂²×C₃⋊C₈	—	2	1	no	—
129	#833	—	2	4	no	—
130	#830	—	2	1	no	—
131	#830	—	2	1	no	—
132	C₂⁴×C₅	C₂×Dic₃	1	1	yes	characteristic
133	C₂⁴×C₅	C₂×Dic₃	1	2	yes	—
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	2	2	no	—
137	C₂×C₅×D₄	—	2	2	no	—
138	C₂×C₅×D₄	—	2	1	no	—
139	C₂×C₅×D₄	—	2	1	no	—
140	C₂×C₅×D₄	—	4	4	no	—
141	C₂²×C₄×C₅	—	2	2	no	—
142	C₂²×C₄×C₅	—	2	2	no	—
143	C₂²×C₄×C₅	C₂×Dic₃	1	1	yes	characteristic
144	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
145	C₂²×C₄×C₅	#67	1	1	yes	characteristic
146	C₂²×C₄×C₅	#67	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	—	3	4	no	—
151	C₅×M₁₆	—	6	4	no	—
152	C₅×M₁₆	—	6	2	no	—
153	C₅×M₁₆	—	6	2	no	—
154	C₅×M₁₆	—	6	2	no	—
155	C₂×C₅×C₈	—	6	4	no	—
156	C₂×C₅×C₈	—	6	2	no	—
157	C₂×C₅×C₈	—	6	2	no	—
158	C₅×C₄⋊C₄	—	2	1	no	—
159	C₅×C₄⋊C₄	—	2	1	no	—
160	C₅×C₂²⋊C₄	—	2	2	no	—
161	C₅×C₂²⋊C₄	—	2	2	no	—
162	C₂²×M₁₆	—	3	1	no	—
163	C₂×#121	C₅×D₃	1	1	yes	characteristic
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	—	4	2	no	—
176	C₂²×C₃×C₅	—	4	2	no	—
177	C₂²×C₃×C₅	—	4	2	no	—
178	C₂²×C₃×C₅	—	8	4	no	—
179	C₂²×C₃×C₅	#100	1	2	yes	complemented
180	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
182	C₃×C₄×C₅	—	2	1	no	—
183	C₃×C₄×C₅	—	2	1	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₃×C₄×C₅	#120	1	1	yes	characteristic
186	C₃×C₄×C₅	#121	1	2	yes	—
187	C₃×C₄×C₅	#123	1	1	yes	characteristic
188	C₂⁴×C₃	C₂×C₄×C₅	1	1	yes	characteristic
189	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	—
190	C₂×C₃×D₄	—	2	2	no	—
191	C₂×C₃×D₄	—	2	2	no	—
192	C₂×C₃×D₄	—	2	2	no	—
193	C₂×C₃×D₄	—	2	1	no	—
194	C₂×C₃×D₄	—	2	1	no	—
195	C₂×C₃×D₄	—	2	2	no	—
196	C₂×C₃×D₄	—	4	4	no	—
197	C₂²×C₃×C₄	—	2	2	no	—
198	C₂²×C₃×C₄	—	2	2	no	—
199	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
200	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
201	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
203	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
204	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
206	C₃×C₄⋊C₄	—	2	1	no	—
207	C₃×C₄⋊C₄	—	2	1	no	—
208	C₃×C₂²⋊C₄	—	2	2	no	—
209	C₃×C₂²⋊C₄	—	2	2	no	—
210	#208	—	2	4	no	—
211	#208	—	2	2	no	—
212	#208	—	2	2	no	—
213	#208	—	2	2	no	—
214	#208	C₅×D₄	1	4	yes	complemented
215	C₂×C₃⋊C₈	—	2	4	no	—
216	C₂×C₃⋊C₈	—	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	—	2	2	no	—
221	C₂³×C₅	—	2	4	no	—
222	C₂³×C₅	—	4	1	no	—
223	C₂³×C₅	—	4	2	no	—
224	C₂³×C₅	—	4	2	no	—
225	C₂³×C₅	#217	1	1	yes	characteristic
226	C₂³×C₅	#217	1	1	yes	characteristic
227	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
228	C₅×D₄	—	4	4	no	—
229	C₅×D₄	—	4	4	no	—
230	C₅×D₄	—	4	1	no	—
231	C₅×D₄	—	4	1	no	—
232	C₅×D₄	—	4	2	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	1	no	—
237	C₂×C₄×C₅	—	2	1	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	#217	1	1	yes	characteristic
243	C₂×C₄×C₅	#217	1	1	yes	characteristic
244	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
245	C₂×C₄×C₅	#237	1	2	yes	—
246	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
248	C₅×C₈	—	6	4	no	—
249	C₅×C₈	—	12	2	no	—
250	C₂²×D₄	C₅×Dic₃	1	2	yes	—
251	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
252	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
253	C₂×M₁₆	—	3	2	no	—
254	C₂×M₁₆	—	3	2	no	—
255	C₂×M₁₆	—	6	4	no	—
256	C₂×M₁₆	—	6	1	no	—
257	C₂²×C₈	—	6	1	no	—
258	#121	—	2	1	no	—
259	#121	—	2	1	no	—
260	#121	—	2	1	no	—
261	#121	—	2	1	no	—
262	C₂×C₄⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂×C₂²⋊C₄	C₅×Dic₃	1	2	yes	—
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	—	8	2	no	—
271	C₂×C₃×C₅	#386	1	1	yes	characteristic
272	C₂×C₃×C₅	C₂×#100	1	1	yes	characteristic
273	C₂×C₃×C₅	#413	1	1	yes	characteristic
274	C₂³×C₃	—	2	2	no	—
275	C₂³×C₃	—	2	2	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	4	no	—
278	C₂³×C₃	—	4	1	no	—
279	C₂³×C₃	—	4	2	no	—
280	C₂³×C₃	—	4	2	no	—
281	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
282	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
283	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
284	C₃×D₄	—	4	4	no	—
285	C₃×D₄	—	4	4	no	—
286	C₃×D₄	—	4	1	no	—
287	C₃×D₄	—	4	2	no	—
288	C₃×D₄	—	4	1	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	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	1	no	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	4	2	no	—
298	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
303	C₂×C₃×C₄	C₅×#41	1	2	yes	—
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	—	4	2	no	—
315	C₂²×C₅	—	4	2	no	—
316	C₂²×C₅	—	4	2	no	—
317	C₂²×C₅	—	8	4	no	—
318	C₂²×C₅	#833	1	2	yes	complemented
319	C₂²×C₅	D₄×Dic₃	1	2	yes	—
320	C₂²×C₅	C₂×#217	1	1	yes	characteristic
321	C₄×C₅	—	2	1	no	—
322	C₄×C₅	—	2	1	no	—
323	C₄×C₅	—	4	2	no	—
324	C₄×C₅	#935	1	1	yes	characteristic
325	C₄×C₅	#937	1	1	yes	characteristic
326	C₄×C₅	#939	1	2	yes	—
327	C₂⁴	C₂×C₅×Dic₃	1	1	yes	characteristic
328	C₂⁴	C₂×C₅×Dic₃	1	2	yes	—
329	C₂×D₄	—	2	2	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	2	1	no	—
335	C₂×D₄	—	4	4	no	—
336	C₂²×C₄	—	2	2	no	—
337	C₂²×C₄	—	2	2	no	—
338	C₂²×C₄	C₂×C₅×Dic₃	1	1	yes	characteristic
339	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
340	C₂²×C₄	C₅×#67	1	1	yes	characteristic
341	C₂²×C₄	C₅×#67	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	—	3	4	no	—
346	M₁₆	—	6	4	no	—
347	M₁₆	—	6	2	no	—
348	M₁₆	—	6	2	no	—
349	M₁₆	—	6	2	no	—
350	C₂×C₈	—	6	4	no	—
351	C₂×C₈	—	6	2	no	—
352	C₂×C₈	—	6	2	no	—
353	C₄⋊C₄	—	2	1	no	—
354	C₄⋊C₄	—	2	1	no	—
355	C₂²⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	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	—	4	2	no	—
367	C₂²×C₃	—	4	2	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	8	4	no	—
370	C₂²×C₃	C₅×#100	1	2	yes	complemented
371	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
372	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
373	C₃×C₄	—	2	1	no	—
374	C₃×C₄	—	2	1	no	—
375	C₃×C₄	—	4	2	no	—
376	C₃×C₄	C₅×#120	1	1	yes	characteristic
377	C₃×C₄	C₅×#121	1	2	yes	—
378	C₃×C₄	C₅×#123	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	—	8	2	no	—
383	C₂×C₅	C₂×#833	1	1	yes	characteristic
384	C₂×C₅	#5220	1	1	yes	characteristic
385	C₂×C₅	#5237	1	1	yes	characteristic
386	C₂³	—	2	2	no	—
387	C₂³	—	2	2	no	—
388	C₂³	—	2	2	no	—
389	C₂³	—	2	4	no	—
390	C₂³	—	4	1	no	—
391	C₂³	—	4	2	no	—
392	C₂³	—	4	2	no	—
393	C₂³	C₅×#217	1	1	yes	characteristic
394	C₂³	C₅×#217	1	1	yes	characteristic
395	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
396	D₄	—	4	4	no	—
397	D₄	—	4	4	no	—
398	D₄	—	4	1	no	—
399	D₄	—	4	1	no	—
400	D₄	—	4	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	—	2	2	no	—
409	C₂×C₄	—	4	2	no	—
410	C₂×C₄	C₅×#217	1	1	yes	characteristic
411	C₂×C₄	C₅×#217	1	1	yes	characteristic
412	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
413	C₂×C₄	C₅×#237	1	2	yes	—
414	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
415	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
416	C₈	—	6	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	—	8	2	no	—
422	C₂×C₃	C₅×#386	1	1	yes	characteristic
423	C₂×C₃	C₂×C₅×#100	1	1	yes	characteristic
424	C₂×C₃	C₅×#413	1	1	yes	characteristic
425	C₅	#71683	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	—	4	2	no	—
435	C₂²	—	4	2	no	—
436	C₂²	—	4	2	no	—
437	C₂²	—	8	4	no	—
438	C₂²	C₅×#833	1	2	yes	complemented
439	C₂²	C₅×D₄×Dic₃	1	2	yes	—
440	C₂²	C₂×C₅×#217	1	1	yes	characteristic
441	C₄	—	2	1	no	—
442	C₄	—	2	1	no	—
443	C₄	—	4	2	no	—
444	C₄	C₅×#935	1	1	yes	characteristic
445	C₄	C₅×#937	1	1	yes	characteristic
446	C₄	C₅×#939	1	2	yes	—
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	—	8	2	no	—
452	C₂	C₂×C₅×#833	1	1	yes	characteristic
453	C₂	C₅×#5220	1	1	yes	characteristic
454	C₂	C₅×#5237	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂×#217
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂²×C₄	C₂²×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#121	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
cosocle	C₂²×C₃×C₄	C₂³×C₅
hypercenter	C₂×C₅×#121	D₃
hypocenter	C₃	C₅×#1900
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂³×C₄×C₅ ◁ C₂×C₅×#121

Complements

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

N	H ≅ G/N	type
2. C₂²×C₅×#208	C₂	semidirect
3. C₂×C₅×#833	C₂	semidirect
4. C₅×#5207	C₂	semidirect
5. C₅×#4530	C₂	semidirect
24. #71683	C₅	direct (N × H)
56. C₅×#208	D₄	semidirect
61. C₂²×#208	C₂×C₅	semidirect
62. C₂×#833	C₂×C₅	semidirect
63. #5207	C₂×C₅	semidirect
64. #4530	C₂×C₅	semidirect
179. C₂²×C₃×C₅	#100	semidirect
214. #208	C₅×D₄	semidirect
318. C₂²×C₅	#833	semidirect
357. C₃×C₅	#1900	semidirect
370. C₂²×C₃	C₅×#100	semidirect
425. C₅	#71683	direct (N × H)
438. C₂²	C₅×#833	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
C₂×C₃×C₅×#121	2
C₂²×C₅×#208	2
C₂×C₅×#833	2
C₅×#5207	2
C₅×#4530	2
C₅×#1900	3
#71683	5

Subgroups — C5×#71683 #14302146

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71683 #14302146