Subgroups — C₅×#71669 #14301621

Order 1920.

1156 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	C₂×C₃×C₅×#120	C₂	1	1	yes	maximal, characteristic
2	C₅×#5798	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5247	C₂	1	2	yes	maximal, complemented
4	C₂×C₅×#834	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4527	C₂	1	2	yes	maximal, complemented
6	C₅×#1889	—	3	1	no	maximal, Hall
7	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
8	C₂²×C₃×C₅×D₄	—	2	1	no	—
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₃×C₅×#120	—	2	2	no	—
11	C₃×C₅×#120	C₄	1	4	yes	complemented
12	C₂×C₃×C₅×C₂²⋊C₄	—	2	1	no	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
14	C₂×C₅×#217	—	2	1	no	—
15	C₂×C₅×#217	—	2	4	no	—
16	C₂×C₅×#217	C₂²	1	2	yes	—
17	C₂×C₅×#217	C₂²	1	2	yes	—
18	C₅×D₄×Dic₃	—	2	4	no	—
19	C₅×#926	—	2	1	no	—
20	C₅×#834	—	2	2	no	—
21	#71669	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#120	D₃	1	1	yes	characteristic
23	C₅×#518	—	3	1	no	—
24	C₂×C₅×#99	—	3	1	no	—
25	C₅×#379	—	3	2	no	—
26	C₅×#342	—	3	2	no	—
27	C₂⁴×C₃×C₅	—	2	2	no	—
28	C₂⁴×C₃×C₅	—	2	1	no	—
29	C₂⁴×C₃×C₅	—	2	1	no	—
30	C₂⁴×C₃×C₅	—	2	2	no	—
31	C₂⁴×C₃×C₅	—	4	4	no	—
32	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	complemented
33	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
34	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
35	C₂×C₃×C₅×D₄	—	2	2	no	—
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	4	no	—
38	C₂×C₃×C₅×D₄	—	4	4	no	—
39	C₂×C₃×C₅×D₄	C₂×C₄	1	2	yes	—
40	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
41	C₂²×C₃×C₄×C₅	—	2	1	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
43	C₂²×C₅×Dic₃	—	2	2	no	—
44	C₂²×C₅×Dic₃	—	2	2	no	—
45	C₂²×C₅×Dic₃	D₄	1	4	yes	complemented
46	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
47	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
48	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	2	yes	complemented
49	C₅×#217	—	2	2	no	—
50	C₅×#217	—	2	2	no	—
51	C₅×#217	—	2	2	no	—
52	C₅×#217	—	2	2	no	—
53	C₅×#217	—	2	2	no	—
54	C₅×#217	—	4	8	no	—
55	C₅×C₄⋊Dic₃	—	2	2	no	—
56	C₄×C₅×Dic₃	—	2	2	no	—
57	C₂×C₃×#120	C₂×C₅	1	1	yes	characteristic
58	#5798	C₂×C₅	1	1	yes	characteristic, complemented
59	#5247	C₂×C₅	1	2	yes	complemented
60	C₂×#834	C₂×C₅	1	1	yes	characteristic, complemented
61	#4527	C₂×C₅	1	2	yes	complemented
62	C₂⁵×C₅	C₂×D₃	1	1	yes	characteristic
63	C₂²×C₅×D₄	—	2	1	no	—
64	C₂²×C₅×D₄	C₂×D₃	1	1	yes	characteristic
65	C₅×#120	—	2	2	no	—
66	C₅×#120	Dic₃	1	4	yes	complemented
67	C₄×C₅×D₄	—	6	4	no	—
68	C₅×#117	—	6	1	no	—
69	C₂×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
71	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
72	C₂×C₅×C₂²⋊C₄	—	6	1	no	—
73	C₂×C₅×C₂²⋊C₄	—	6	4	no	—
74	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	1	yes	characteristic
75	C₅×#99	—	6	2	no	—
76	#1889	—	3	1	no	Sylow
77	C₂³×C₃×C₅	—	2	8	no	—
78	C₂³×C₃×C₅	—	2	4	no	—
79	C₂³×C₃×C₅	—	2	2	no	—
80	C₂³×C₃×C₅	—	2	4	no	—
81	C₂³×C₃×C₅	—	2	1	no	—
82	C₂³×C₃×C₅	—	2	1	no	—
83	C₂³×C₃×C₅	—	4	4	no	—
84	C₂³×C₃×C₅	—	4	2	no	—
85	C₂³×C₃×C₅	—	4	4	no	—
86	C₂³×C₃×C₅	—	4	2	no	—
87	C₂³×C₃×C₅	—	4	4	no	—
88	C₂³×C₃×C₅	—	4	8	no	—
89	C₂³×C₃×C₅	—	4	2	no	—
90	C₂³×C₃×C₅	—	4	1	no	—
91	C₂³×C₃×C₅	—	4	2	no	—
92	C₂³×C₃×C₅	—	4	1	no	—
93	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	complemented
94	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
95	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
97	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
98	C₂³×C₃×C₅	#41	1	2	yes	—
99	C₃×C₅×D₄	—	2	4	no	—
100	C₃×C₅×D₄	—	2	4	no	—
101	C₃×C₅×D₄	—	4	8	no	—
102	C₂×C₃×C₄×C₅	—	2	1	no	—
103	C₂×C₃×C₄×C₅	—	2	1	no	—
104	C₂×C₃×C₄×C₅	—	2	2	no	—
105	C₂×C₃×C₄×C₅	—	4	2	no	—
106	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	2	yes	complemented
107	C₂×C₅×Dic₃	—	2	4	no	—
108	C₂×C₅×Dic₃	—	4	4	no	—
109	C₂×C₅×Dic₃	—	4	4	no	—
110	C₂×C₅×Dic₃	—	4	2	no	—
111	C₂×C₅×Dic₃	—	8	2	no	—
112	C₂⁵×C₃	C₂²×C₅	1	1	yes	characteristic
113	C₂²×C₃×D₄	—	2	1	no	—
114	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
115	C₃×#120	—	2	2	no	—
116	C₃×#120	C₄×C₅	1	4	yes	complemented
117	C₂×C₃×C₂²⋊C₄	—	2	1	no	—
118	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
119	C₂×#217	—	2	1	no	—
120	C₂×#217	—	2	4	no	—
121	C₂×#217	C₂²×C₅	1	2	yes	—
122	C₂×#217	C₂²×C₅	1	2	yes	—
123	D₄×Dic₃	—	2	4	no	—
124	#926	—	2	1	no	—
125	#834	—	2	2	no	—
126	C₂⁴×C₅	—	2	2	no	—
127	C₂⁴×C₅	—	2	1	no	—
128	C₂⁴×C₅	—	2	2	no	—
129	C₂⁴×C₅	—	2	1	no	—
130	C₂⁴×C₅	—	4	4	no	—
131	C₂⁴×C₅	C₂×Dic₃	1	2	yes	complemented
132	C₂⁴×C₅	#67	1	1	yes	characteristic
133	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
134	C₂×C₅×D₄	—	2	2	no	—
135	C₂×C₅×D₄	—	2	2	no	—
136	C₂×C₅×D₄	—	2	4	no	—
137	C₂×C₅×D₄	—	4	4	no	—
138	C₂×C₅×D₄	C₂×Dic₃	1	2	yes	—
139	C₂×C₅×D₄	#67	1	2	yes	—
140	C₂²×C₄×C₅	—	2	1	no	—
141	C₂²×C₄×C₅	—	3	4	no	—
142	C₂²×C₄×C₅	—	6	2	no	—
143	C₂²×C₄×C₅	—	6	2	no	—
144	C₂²×C₄×C₅	#67	1	1	yes	characteristic
145	C₅×C₄⋊C₄	—	6	2	no	—
146	C₅×C₂²⋊C₄	—	2	1	no	—
147	C₅×C₂²⋊C₄	—	2	4	no	—
148	C₅×C₂²⋊C₄	—	6	2	no	—
149	C₅×C₂²⋊C₄	—	6	2	no	—
150	C₅×C₂²⋊C₄	—	6	2	no	—
151	C₅×C₂²⋊C₄	—	6	2	no	—
152	C₅×C₂²⋊C₄	—	6	2	no	—
153	C₅×C₂²⋊C₄	—	12	8	no	—
154	C₅×C₂²⋊C₄	C₂×Dic₃	1	2	yes	complemented
155	C₄²×C₅	—	6	2	no	—
156	C₂×#120	C₅×D₃	1	1	yes	characteristic
157	#518	—	3	1	no	—
158	C₂×#99	—	3	1	no	—
159	#379	—	3	2	no	—
160	#342	—	3	2	no	—
161	C₂²×C₃×C₅	—	2	4	no	—
162	C₂²×C₃×C₅	—	2	2	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	—	2	8	no	—
165	C₂²×C₃×C₅	—	2	2	no	—
166	C₂²×C₃×C₅	—	4	1	no	—
167	C₂²×C₃×C₅	—	4	1	no	—
168	C₂²×C₃×C₅	—	4	2	no	—
169	C₂²×C₃×C₅	—	4	2	no	—
170	C₂²×C₃×C₅	—	4	8	no	—
171	C₂²×C₃×C₅	—	4	2	no	—
172	C₂²×C₃×C₅	—	4	4	no	—
173	C₂²×C₃×C₅	—	4	4	no	—
174	C₂²×C₃×C₅	—	4	2	no	—
175	C₂²×C₃×C₅	—	4	2	no	—
176	C₂²×C₃×C₅	—	4	4	no	—
177	C₂²×C₃×C₅	—	8	1	no	—
178	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
179	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
180	C₂²×C₃×C₅	#120	1	1	yes	characteristic
181	C₂²×C₃×C₅	#121	1	2	yes	—
182	C₂²×C₃×C₅	#123	1	1	yes	characteristic
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	4	2	no	—
185	C₅×Dic₃	—	4	4	no	—
186	C₅×Dic₃	—	8	2	no	—
187	C₂⁴×C₃	—	2	2	no	—
188	C₂⁴×C₃	—	2	1	no	—
189	C₂⁴×C₃	—	2	1	no	—
190	C₂⁴×C₃	—	2	2	no	—
191	C₂⁴×C₃	—	4	4	no	—
192	C₂⁴×C₃	C₂×C₄×C₅	1	2	yes	complemented
193	C₂⁴×C₃	C₅×D₄	1	1	yes	characteristic
194	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
195	C₂×C₃×D₄	—	2	2	no	—
196	C₂×C₃×D₄	—	2	2	no	—
197	C₂×C₃×D₄	—	2	4	no	—
198	C₂×C₃×D₄	—	4	4	no	—
199	C₂×C₃×D₄	C₂×C₄×C₅	1	2	yes	—
200	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
201	C₂²×C₃×C₄	—	2	1	no	—
202	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
203	C₂²×Dic₃	—	2	2	no	—
204	C₂²×Dic₃	—	2	2	no	—
205	C₂²×Dic₃	C₅×D₄	1	4	yes	complemented
206	C₃×C₂²⋊C₄	—	2	1	no	—
207	C₃×C₂²⋊C₄	—	2	4	no	—
208	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	2	yes	complemented
209	#217	—	2	2	no	—
210	#217	—	2	2	no	—
211	#217	—	2	2	no	—
212	#217	—	2	2	no	—
213	#217	—	2	2	no	—
214	#217	—	4	8	no	—
215	C₄⋊Dic₃	—	2	2	no	—
216	C₄×Dic₃	—	2	2	no	—
217	C₂³×C₅	—	2	8	no	—
218	C₂³×C₅	—	2	4	no	—
219	C₂³×C₅	—	2	4	no	—
220	C₂³×C₅	—	2	1	no	—
221	C₂³×C₅	—	2	2	no	—
222	C₂³×C₅	—	2	1	no	—
223	C₂³×C₅	—	4	4	no	—
224	C₂³×C₅	—	4	2	no	—
225	C₂³×C₅	—	4	2	no	—
226	C₂³×C₅	—	4	4	no	—
227	C₂³×C₅	—	4	4	no	—
228	C₂³×C₅	—	4	8	no	—
229	C₂³×C₅	—	4	2	no	—
230	C₂³×C₅	—	4	1	no	—
231	C₂³×C₅	—	4	1	no	—
232	C₂³×C₅	—	4	2	no	—
233	C₂³×C₅	#217	1	2	yes	complemented
234	C₂³×C₅	D₃×D₄	1	2	yes	—
235	C₂³×C₅	#237	1	2	yes	—
236	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
237	C₂³×C₅	C₂×#67	1	1	yes	characteristic
238	C₂³×C₅	C₂×#67	1	1	yes	characteristic
239	C₅×D₄	—	2	4	no	—
240	C₅×D₄	—	2	4	no	—
241	C₅×D₄	—	4	8	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	4	2	no	—
246	C₂×C₄×C₅	—	6	4	no	—
247	C₂×C₄×C₅	—	12	4	no	—
248	C₂×C₄×C₅	—	12	4	no	—
249	C₂×C₄×C₅	—	12	2	no	—
250	C₂×C₄×C₅	—	24	2	no	—
251	C₂×C₄×C₅	#217	1	2	yes	complemented
252	C₂⁵	C₂×C₅×D₃	1	1	yes	characteristic
253	C₂²×D₄	—	2	1	no	—
254	C₂²×D₄	C₂×C₅×D₃	1	1	yes	characteristic
255	#120	—	2	2	no	—
256	#120	C₅×Dic₃	1	4	yes	complemented
257	C₄×D₄	—	6	4	no	—
258	#117	—	6	1	no	—
259	C₂×C₂²⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	—	3	2	no	—
261	C₂×C₂²⋊C₄	—	3	2	no	—
262	C₂×C₂²⋊C₄	—	6	1	no	—
263	C₂×C₂²⋊C₄	—	6	4	no	—
264	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	1	yes	characteristic
265	#99	—	6	2	no	—
266	C₂×C₃×C₅	—	2	2	no	—
267	C₂×C₃×C₅	—	2	1	no	—
268	C₂×C₃×C₅	—	2	2	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	—	4	4	no	—
271	C₂×C₃×C₅	—	4	2	no	—
272	C₂×C₃×C₅	#386	1	1	yes	characteristic
273	C₂×C₃×C₅	B(4,𝔽₂)	1	2	yes	—
274	C₂³×C₃	—	2	8	no	—
275	C₂³×C₃	—	2	4	no	—
276	C₂³×C₃	—	2	2	no	—
277	C₂³×C₃	—	2	4	no	—
278	C₂³×C₃	—	2	1	no	—
279	C₂³×C₃	—	2	1	no	—
280	C₂³×C₃	—	4	4	no	—
281	C₂³×C₃	—	4	2	no	—
282	C₂³×C₃	—	4	4	no	—
283	C₂³×C₃	—	4	2	no	—
284	C₂³×C₃	—	4	4	no	—
285	C₂³×C₃	—	4	8	no	—
286	C₂³×C₃	—	4	2	no	—
287	C₂³×C₃	—	4	1	no	—
288	C₂³×C₃	—	4	2	no	—
289	C₂³×C₃	—	4	1	no	—
290	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	complemented
291	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
292	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
293	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂³×C₃	C₅×#41	1	2	yes	—
296	C₃×D₄	—	2	4	no	—
297	C₃×D₄	—	2	4	no	—
298	C₃×D₄	—	4	8	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	4	2	no	—
303	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	2	yes	complemented
304	C₂×Dic₃	—	2	4	no	—
305	C₂×Dic₃	—	4	4	no	—
306	C₂×Dic₃	—	4	4	no	—
307	C₂×Dic₃	—	4	2	no	—
308	C₂×Dic₃	—	8	2	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	2	4	no	—
311	C₂²×C₅	—	2	4	no	—
312	C₂²×C₅	—	2	8	no	—
313	C₂²×C₅	—	2	2	no	—
314	C₂²×C₅	—	4	2	no	—
315	C₂²×C₅	—	4	1	no	—
316	C₂²×C₅	—	4	1	no	—
317	C₂²×C₅	—	4	2	no	—
318	C₂²×C₅	—	4	2	no	—
319	C₂²×C₅	—	4	8	no	—
320	C₂²×C₅	—	4	4	no	—
321	C₂²×C₅	—	4	4	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	—	4	2	no	—
324	C₂²×C₅	—	4	4	no	—
325	C₂²×C₅	—	8	1	no	—
326	C₂²×C₅	D₄×Dic₃	1	2	yes	—
327	C₂²×C₅	#935	1	1	yes	characteristic
328	C₂²×C₅	#937	1	1	yes	characteristic
329	C₂²×C₅	#939	1	2	yes	—
330	C₂²×C₅	C₂×#217	1	1	yes	characteristic
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	4	2	no	—
333	C₄×C₅	—	12	4	no	—
334	C₄×C₅	—	24	2	no	—
335	C₂⁴	—	2	2	no	—
336	C₂⁴	—	2	1	no	—
337	C₂⁴	—	2	2	no	—
338	C₂⁴	—	2	1	no	—
339	C₂⁴	—	4	4	no	—
340	C₂⁴	C₂×C₅×Dic₃	1	2	yes	complemented
341	C₂⁴	C₅×#67	1	1	yes	characteristic
342	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
343	C₂×D₄	—	2	2	no	—
344	C₂×D₄	—	2	2	no	—
345	C₂×D₄	—	2	4	no	—
346	C₂×D₄	—	4	4	no	—
347	C₂×D₄	C₂×C₅×Dic₃	1	2	yes	—
348	C₂×D₄	C₅×#67	1	2	yes	—
349	C₂²×C₄	—	2	1	no	—
350	C₂²×C₄	—	3	4	no	—
351	C₂²×C₄	—	6	2	no	—
352	C₂²×C₄	—	6	2	no	—
353	C₂²×C₄	C₅×#67	1	1	yes	characteristic
354	C₄⋊C₄	—	6	2	no	—
355	C₂²⋊C₄	—	2	1	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	6	2	no	—
358	C₂²⋊C₄	—	6	2	no	—
359	C₂²⋊C₄	—	6	2	no	—
360	C₂²⋊C₄	—	6	2	no	—
361	C₂²⋊C₄	—	6	2	no	—
362	C₂²⋊C₄	—	12	8	no	—
363	C₂²⋊C₄	C₂×C₅×Dic₃	1	2	yes	complemented
364	C₄²	—	6	2	no	—
365	C₃×C₅	#1889	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	2	no	—
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	2	8	no	—
370	C₂²×C₃	—	2	2	no	—
371	C₂²×C₃	—	4	1	no	—
372	C₂²×C₃	—	4	1	no	—
373	C₂²×C₃	—	4	2	no	—
374	C₂²×C₃	—	4	2	no	—
375	C₂²×C₃	—	4	8	no	—
376	C₂²×C₃	—	4	2	no	—
377	C₂²×C₃	—	4	4	no	—
378	C₂²×C₃	—	4	4	no	—
379	C₂²×C₃	—	4	2	no	—
380	C₂²×C₃	—	4	2	no	—
381	C₂²×C₃	—	4	4	no	—
382	C₂²×C₃	—	8	1	no	—
383	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
384	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
385	C₂²×C₃	C₅×#120	1	1	yes	characteristic
386	C₂²×C₃	C₅×#121	1	2	yes	—
387	C₂²×C₃	C₅×#123	1	1	yes	characteristic
388	C₃×C₄	—	2	2	no	—
389	C₃×C₄	—	4	2	no	—
390	Dic₃	—	4	4	no	—
391	Dic₃	—	8	2	no	—
392	C₂×C₅	—	2	1	no	—
393	C₂×C₅	—	2	2	no	—
394	C₂×C₅	—	2	2	no	—
395	C₂×C₅	—	2	1	no	—
396	C₂×C₅	—	4	4	no	—
397	C₂×C₅	—	4	2	no	—
398	C₂×C₅	#5032	1	2	yes	—
399	C₂×C₅	#5220	1	1	yes	characteristic
400	C₂³	—	2	8	no	—
401	C₂³	—	2	4	no	—
402	C₂³	—	2	4	no	—
403	C₂³	—	2	1	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	1	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	4	2	no	—
408	C₂³	—	4	2	no	—
409	C₂³	—	4	4	no	—
410	C₂³	—	4	4	no	—
411	C₂³	—	4	8	no	—
412	C₂³	—	4	2	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	4	1	no	—
415	C₂³	—	4	2	no	—
416	C₂³	C₅×#217	1	2	yes	complemented
417	C₂³	C₅×D₃×D₄	1	2	yes	—
418	C₂³	C₅×#237	1	2	yes	—
419	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
420	C₂³	C₂×C₅×#67	1	1	yes	characteristic
421	C₂³	C₂×C₅×#67	1	1	yes	characteristic
422	D₄	—	2	4	no	—
423	D₄	—	2	4	no	—
424	D₄	—	4	8	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	1	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	4	2	no	—
429	C₂×C₄	—	6	4	no	—
430	C₂×C₄	—	12	4	no	—
431	C₂×C₄	—	12	4	no	—
432	C₂×C₄	—	12	2	no	—
433	C₂×C₄	—	24	2	no	—
434	C₂×C₄	C₅×#217	1	2	yes	complemented
435	C₂×C₃	—	2	2	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	2	2	no	—
438	C₂×C₃	—	2	1	no	—
439	C₂×C₃	—	4	4	no	—
440	C₂×C₃	—	4	2	no	—
441	C₂×C₃	C₅×#386	1	1	yes	characteristic
442	C₂×C₃	C₅×B(4,𝔽₂)	1	2	yes	—
443	C₅	#71669	1	1	yes	characteristic, direct product factor, Sylow
444	C₂²	—	2	2	no	—
445	C₂²	—	2	4	no	—
446	C₂²	—	2	4	no	—
447	C₂²	—	2	8	no	—
448	C₂²	—	2	2	no	—
449	C₂²	—	4	2	no	—
450	C₂²	—	4	1	no	—
451	C₂²	—	4	1	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	8	no	—
455	C₂²	—	4	4	no	—
456	C₂²	—	4	4	no	—
457	C₂²	—	4	2	no	—
458	C₂²	—	4	2	no	—
459	C₂²	—	4	4	no	—
460	C₂²	—	8	1	no	—
461	C₂²	C₅×D₄×Dic₃	1	2	yes	—
462	C₂²	C₅×#935	1	1	yes	characteristic
463	C₂²	C₅×#937	1	1	yes	characteristic
464	C₂²	C₅×#939	1	2	yes	—
465	C₂²	C₂×C₅×#217	1	1	yes	characteristic
466	C₄	—	2	2	no	—
467	C₄	—	4	2	no	—
468	C₄	—	12	4	no	—
469	C₄	—	24	2	no	—
470	C₃	C₅×#1889	1	1	yes	characteristic, complemented, Sylow
471	C₂	—	2	1	no	—
472	C₂	—	2	2	no	—
473	C₂	—	2	2	no	—
474	C₂	—	2	1	no	—
475	C₂	—	4	4	no	—
476	C₂	—	4	2	no	—
477	C₂	C₅×#5032	1	2	yes	—
478	C₂	C₅×#5220	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	#937
commutator	C₂³×C₃	C₂²×C₄×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting, prime radical	C₂×C₃×C₅×#120	C₂
socle	C₂²×C₃×C₅	#120
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₂×C₅×#120	D₃
hypocenter	C₃	C₅×#1889
LCS	G ▷ C₂³×C₃ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₂⁴×C₅ ◁ C₂×C₅×#120

Complements

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

N	H ≅ G/N	type
2. C₅×#5798	C₂	semidirect
3. C₅×#5247	C₂	semidirect
4. C₂×C₅×#834	C₂	semidirect
5. C₅×#4527	C₂	semidirect
11. C₃×C₅×#120	C₄	semidirect
21. #71669	C₅	direct (N × H)
32. C₂⁴×C₃×C₅	C₂×C₄	semidirect
45. C₂²×C₅×Dic₃	D₄	semidirect
48. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
58. #5798	C₂×C₅	semidirect
59. #5247	C₂×C₅	semidirect
60. C₂×#834	C₂×C₅	semidirect
61. #4527	C₂×C₅	semidirect
66. C₅×#120	Dic₃	semidirect
93. C₂³×C₃×C₅	C₂²⋊C₄	semidirect
106. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
116. C₃×#120	C₄×C₅	semidirect
131. C₂⁴×C₅	C₂×Dic₃	semidirect
154. C₅×C₂²⋊C₄	C₂×Dic₃	semidirect
192. C₂⁴×C₃	C₂×C₄×C₅	semidirect
205. C₂²×Dic₃	C₅×D₄	semidirect
208. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
233. C₂³×C₅	#217	semidirect
251. C₂×C₄×C₅	#217	semidirect
256. #120	C₅×Dic₃	semidirect
290. C₂³×C₃	C₅×C₂²⋊C₄	semidirect
303. C₂×C₃×C₄	C₅×C₂²⋊C₄	semidirect
340. C₂⁴	C₂×C₅×Dic₃	semidirect
363. C₂²⋊C₄	C₂×C₅×Dic₃	semidirect
365. C₃×C₅	#1889	semidirect
416. C₂³	C₅×#217	semidirect
434. C₂×C₄	C₅×#217	semidirect
443. C₅	#71669	direct (N × H)
470. C₃	C₅×#1889	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×#120	2
C₅×#5798	2
C₅×#5247	2
C₂×C₅×#834	2
C₅×#4527	2
C₅×#1889	3
#71669	5

Subgroups — C5×#71669 #14301621

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#71669 #14301621