Subgroups — C₅×#82267 #14319905

Order 1920.

2176 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	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#926	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4987	C₂	1	4	yes	maximal, complemented
5	C₅×#4955	C₂	1	2	yes	maximal
6	C₅×#4943	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	4	yes	maximal, complemented
8	C₅×#2280	—	3	1	no	maximal, Hall
9	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
12	C₂²×C₄×C₅×D₃	—	2	4	no	—
13	C₂²×C₄×C₅×D₃	—	2	4	no	—
14	C₂²×C₄×C₅×D₃	C₄	1	8	yes	complemented
15	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₃×C₅×#117	—	2	4	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
21	C₂×C₅×#217	C₂²	1	2	yes	—
22	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	8	yes	—
23	C₅×#926	—	2	4	no	—
24	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	complemented
25	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
26	C₅×C₃⋊#95	C₂²	1	8	yes	complemented
27	#82267	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂⁴×C₄×C₅	—	3	1	no	—
29	C₂×C₅×#117	—	3	1	no	—
30	C₂×C₅×#117	D₃	1	1	yes	characteristic, complemented
31	C₅×#381	—	3	2	no	—
32	C₅×#380	—	3	4	no	—
33	C₅×#379	—	3	2	no	—
34	C₄×C₅×C₂²⋊C₄	—	3	4	no	—
35	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
36	C₂³×C₅×D₃	—	2	2	no	—
37	C₂³×C₅×D₃	—	2	2	no	—
38	C₂³×C₅×D₃	—	2	8	no	—
39	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
40	C₂³×C₅×D₃	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
43	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₅×Dic₃	—	2	2	no	—
48	C₂²×C₅×Dic₃	—	2	2	no	—
49	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
50	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
51	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
52	C₂×C₄×C₅×D₃	—	2	32	no	—
53	C₂×C₄×C₅×D₃	—	2	4	no	—
54	C₂×C₄×C₅×D₃	—	2	4	no	—
55	C₂×C₄×C₅×D₃	—	2	4	no	—
56	C₂×C₄×C₅×D₃	—	2	4	no	—
57	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
58	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₅×#217	—	2	4	no	—
63	C₅×(C₂×D₃)⋊C₄	—	2	16	no	—
64	C₅×C₄⋊Dic₃	—	2	4	no	—
65	C₄×C₅×Dic₃	—	2	4	no	—
66	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
67	C₂×C₃×#117	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×#926	C₂×C₅	1	1	yes	characteristic, complemented
69	#4987	C₂×C₅	1	4	yes	complemented
70	#4955	C₂×C₅	1	2	yes	—
71	#4943	C₂×C₅	1	2	yes	complemented
72	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	4	yes	complemented
73	C₂⁵×C₅	—	3	1	no	—
74	C₂³×C₄×C₅	—	3	1	no	—
75	C₂³×C₄×C₅	—	3	8	no	—
76	C₂³×C₄×C₅	—	3	2	no	—
77	C₂³×C₄×C₅	—	3	2	no	—
78	C₂³×C₄×C₅	—	6	4	no	—
79	C₂³×C₄×C₅	—	6	4	no	—
80	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
81	C₅×#117	—	2	4	no	—
82	C₅×#117	—	6	4	no	—
83	C₂×C₅×C₄⋊C₄	—	3	2	no	—
84	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	complemented
85	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
86	C₂×C₅×C₂²⋊C₄	—	3	8	no	—
87	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
88	C₂×C₄²×C₅	—	3	2	no	—
89	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
90	C₅×#95	—	3	8	no	—
91	#2280	—	3	1	no	Sylow
92	C₂³×C₃×C₅	—	2	4	no	—
93	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
94	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
95	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₅×D₃	—	2	16	no	—
98	C₂²×C₅×D₃	—	2	16	no	—
99	C₂²×C₅×D₃	—	2	8	no	—
100	C₂²×C₅×D₃	—	2	2	no	—
101	C₂²×C₅×D₃	—	2	2	no	—
102	C₂²×C₅×D₃	—	2	4	no	—
103	C₂²×C₅×D₃	—	2	16	no	—
104	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
105	C₂²×C₅×D₃	#41	1	8	yes	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	8	no	—
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₅×Dic₃	—	2	8	no	—
116	C₂×C₅×Dic₃	—	2	2	no	—
117	C₂×C₅×Dic₃	—	2	2	no	—
118	C₂×C₅×Dic₃	—	2	4	no	—
119	C₂×C₅×Dic₃	—	2	8	no	—
120	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
121	C₄×C₅×D₃	—	2	16	no	—
122	C₄×C₅×D₃	—	2	16	no	—
123	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
124	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
125	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
126	C₂²×C₄×D₃	—	2	4	no	—
127	C₂²×C₄×D₃	—	2	4	no	—
128	C₂²×C₄×D₃	C₄×C₅	1	8	yes	complemented
129	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
130	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
131	C₃×#117	—	2	4	no	—
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
133	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
135	C₂×#217	C₂²×C₅	1	2	yes	—
136	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	8	yes	—
137	#926	—	2	4	no	—
138	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	complemented
139	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
140	C₃⋊#95	C₂²×C₅	1	8	yes	complemented
141	C₂⁴×C₅	—	3	2	no	—
142	C₂⁴×C₅	—	3	4	no	—
143	C₂⁴×C₅	—	6	8	no	—
144	C₂⁴×C₅	—	6	2	no	—
145	C₂⁴×C₅	—	6	2	no	—
146	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
147	C₂²×C₄×C₅	—	3	4	no	—
148	C₂²×C₄×C₅	—	3	2	no	—
149	C₂²×C₄×C₅	—	3	8	no	—
150	C₂²×C₄×C₅	—	3	8	no	—
151	C₂²×C₄×C₅	—	3	4	no	—
152	C₂²×C₄×C₅	—	6	2	no	—
153	C₂²×C₄×C₅	—	6	2	no	—
154	C₂²×C₄×C₅	—	6	32	no	—
155	C₂²×C₄×C₅	—	6	4	no	—
156	C₂²×C₄×C₅	—	6	4	no	—
157	C₂²×C₄×C₅	—	6	4	no	—
158	C₂²×C₄×C₅	—	6	4	no	—
159	C₂²×C₄×C₅	C₄×D₃	1	4	yes	—
160	C₂²×C₄×C₅	D₁₂	1	4	yes	—
161	C₂²×C₄×C₅	#67	1	4	yes	—
162	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
163	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
164	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	6	4	no	—
167	C₅×C₂²⋊C₄	—	2	4	no	—
168	C₅×C₂²⋊C₄	—	6	16	no	—
169	C₅×C₂²⋊C₄	—	6	4	no	—
170	C₄²×C₅	—	2	4	no	—
171	C₄²×C₅	—	6	4	no	—
172	C₂⁴×C₄	—	3	1	no	—
173	C₂×#117	—	3	1	no	—
174	C₂×#117	C₅×D₃	1	1	yes	characteristic, complemented
175	#381	—	3	2	no	—
176	#380	—	3	4	no	—
177	#379	—	3	2	no	—
178	C₄×C₂²⋊C₄	—	3	4	no	—
179	C₂²×C₃×C₅	—	2	4	no	—
180	C₂²×C₃×C₅	—	2	4	no	—
181	C₂²×C₃×C₅	—	2	4	no	—
182	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
187	C₂×C₅×D₃	—	2	32	no	—
188	C₂×C₅×D₃	—	2	4	no	—
189	C₂×C₅×D₃	—	2	4	no	—
190	C₂×C₅×D₃	—	2	8	no	—
191	C₂×C₅×D₃	—	2	8	no	—
192	C₂×C₅×D₃	#117	1	8	yes	complemented
193	C₃×C₄×C₅	—	4	4	no	—
194	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
195	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
196	C₅×Dic₃	—	2	4	no	—
197	C₅×Dic₃	—	4	4	no	—
198	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
199	C₂³×D₃	—	2	2	no	—
200	C₂³×D₃	—	2	2	no	—
201	C₂³×D₃	—	2	8	no	—
202	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
203	C₂³×D₃	C₂³×C₅	1	2	yes	—
204	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
205	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
206	C₂²×C₃×C₄	C₅×D₄	1	4	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
210	C₂²×Dic₃	—	2	2	no	—
211	C₂²×Dic₃	—	2	2	no	—
212	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
213	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
214	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
215	C₂×C₄×D₃	—	2	32	no	—
216	C₂×C₄×D₃	—	2	4	no	—
217	C₂×C₄×D₃	—	2	4	no	—
218	C₂×C₄×D₃	—	2	4	no	—
219	C₂×C₄×D₃	—	2	4	no	—
220	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
221	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	—
222	C₃×C₄⋊C₄	—	2	4	no	—
223	C₃×C₂²⋊C₄	—	2	4	no	—
224	C₃×C₄²	—	2	4	no	—
225	#217	—	2	4	no	—
226	(C₂×D₃)⋊C₄	—	2	16	no	—
227	C₄⋊Dic₃	—	2	4	no	—
228	C₄×Dic₃	—	2	4	no	—
229	C₂³×C₅	—	2	4	no	—
230	C₂³×C₅	—	3	4	no	—
231	C₂³×C₅	—	3	8	no	—
232	C₂³×C₅	—	6	16	no	—
233	C₂³×C₅	—	6	16	no	—
234	C₂³×C₅	—	6	16	no	—
235	C₂³×C₅	—	6	8	no	—
236	C₂³×C₅	—	6	2	no	—
237	C₂³×C₅	—	6	4	no	—
238	C₂³×C₅	—	6	2	no	—
239	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
240	C₂³×C₅	C₂×D₁₂	1	2	yes	—
241	C₂³×C₅	C₂×#67	1	2	yes	—
242	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
243	C₂×C₄×C₅	—	2	8	no	—
244	C₂×C₄×C₅	—	2	4	no	—
245	C₂×C₄×C₅	—	3	4	no	—
246	C₂×C₄×C₅	—	6	8	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	2	no	—
249	C₂×C₄×C₅	—	6	16	no	—
250	C₂×C₄×C₅	—	6	16	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	8	no	—
253	C₂×C₄×C₅	(C₂×D₃)⋊C₄	1	16	yes	complemented
254	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
255	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
256	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
257	C₂×C₄×C₅	C₂×D₁₂	1	2	yes	—
258	C₂×C₄×C₅	C₂×#67	1	2	yes	—
259	C₂×C₄×C₅	C₂×#67	1	2	yes	—
260	C₂⁵	—	3	1	no	—
261	C₂³×C₄	—	3	1	no	—
262	C₂³×C₄	—	3	8	no	—
263	C₂³×C₄	—	3	2	no	—
264	C₂³×C₄	—	3	2	no	—
265	C₂³×C₄	—	6	4	no	—
266	C₂³×C₄	—	6	4	no	—
267	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
268	#117	—	2	4	no	—
269	#117	—	6	4	no	—
270	C₂×C₄⋊C₄	—	3	2	no	—
271	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	complemented
272	C₂×C₂²⋊C₄	—	3	2	no	—
273	C₂×C₂²⋊C₄	—	3	8	no	—
274	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
275	C₂×C₄²	—	3	2	no	—
276	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
277	#95	—	3	8	no	—
278	C₂×C₃×C₅	—	2	4	no	—
279	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₃×C₅	C₂×#117	1	2	yes	—
281	C₂×C₃×C₅	#525	1	2	yes	—
282	C₂×C₃×C₅	#525	1	2	yes	—
283	C₅×D₃	—	2	8	no	—
284	C₂³×C₃	—	2	4	no	—
285	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
286	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
287	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
288	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
289	C₂²×D₃	—	2	16	no	—
290	C₂²×D₃	—	2	16	no	—
291	C₂²×D₃	—	2	8	no	—
292	C₂²×D₃	—	2	2	no	—
293	C₂²×D₃	—	2	2	no	—
294	C₂²×D₃	—	2	4	no	—
295	C₂²×D₃	—	2	16	no	—
296	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
297	C₂²×D₃	C₅×#41	1	8	yes	—
298	C₂×C₃×C₄	—	2	4	no	—
299	C₂×C₃×C₄	—	2	8	no	—
300	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	16	yes	complemented
301	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
302	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
303	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
304	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
305	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
306	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
307	C₂×Dic₃	—	2	8	no	—
308	C₂×Dic₃	—	2	2	no	—
309	C₂×Dic₃	—	2	2	no	—
310	C₂×Dic₃	—	2	4	no	—
311	C₂×Dic₃	—	2	8	no	—
312	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
313	C₄×D₃	—	2	16	no	—
314	C₄×D₃	—	2	16	no	—
315	C₂²×C₅	—	2	4	no	—
316	C₂²×C₅	—	2	4	no	—
317	C₂²×C₅	—	2	4	no	—
318	C₂²×C₅	—	3	8	no	—
319	C₂²×C₅	—	6	32	no	—
320	C₂²×C₅	—	6	4	no	—
321	C₂²×C₅	—	6	8	no	—
322	C₂²×C₅	—	6	4	no	—
323	C₂²×C₅	—	6	8	no	—
324	C₂²×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
325	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
326	C₂²×C₅	C₂²×D₁₂	1	1	yes	characteristic
327	C₂²×C₅	D₃×#41	1	4	yes	—
328	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
329	C₄×C₅	—	4	4	no	—
330	C₄×C₅	—	6	4	no	—
331	C₄×C₅	—	12	4	no	—
332	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
333	C₄×C₅	C₂×(C₂×D₃)⋊C₄	1	4	yes	—
334	C₂⁴	—	3	2	no	—
335	C₂⁴	—	3	4	no	—
336	C₂⁴	—	6	8	no	—
337	C₂⁴	—	6	2	no	—
338	C₂⁴	—	6	2	no	—
339	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
340	C₂²×C₄	—	3	4	no	—
341	C₂²×C₄	—	3	2	no	—
342	C₂²×C₄	—	3	8	no	—
343	C₂²×C₄	—	3	8	no	—
344	C₂²×C₄	—	3	4	no	—
345	C₂²×C₄	—	6	2	no	—
346	C₂²×C₄	—	6	2	no	—
347	C₂²×C₄	—	6	32	no	—
348	C₂²×C₄	—	6	4	no	—
349	C₂²×C₄	—	6	4	no	—
350	C₂²×C₄	—	6	4	no	—
351	C₂²×C₄	—	6	4	no	—
352	C₂²×C₄	C₄×C₅×D₃	1	4	yes	—
353	C₂²×C₄	C₅×D₁₂	1	4	yes	—
354	C₂²×C₄	C₅×#67	1	4	yes	—
355	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
356	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	6	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	6	16	no	—
362	C₂²⋊C₄	—	6	4	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	6	4	no	—
365	C₃×C₅	#2280	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
370	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
371	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
372	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
373	C₂²×C₃	C₂×C₅×#41	1	4	yes	—
374	C₂×D₃	—	2	32	no	—
375	C₂×D₃	—	2	4	no	—
376	C₂×D₃	—	2	4	no	—
377	C₂×D₃	—	2	8	no	—
378	C₂×D₃	—	2	8	no	—
379	C₂×D₃	C₅×#117	1	8	yes	complemented
380	C₃×C₄	—	4	4	no	—
381	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
382	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	—
383	Dic₃	—	2	4	no	—
384	Dic₃	—	4	4	no	—
385	C₂×C₅	—	2	4	no	—
386	C₂×C₅	—	6	8	no	—
387	C₂×C₅	D₃×#117	1	2	yes	—
388	C₂×C₅	#5524	1	2	yes	—
389	C₂×C₅	C₂²×(C₂×D₃)⋊C₄	1	1	yes	characteristic
390	C₂×C₅	#5828	1	2	yes	—
391	C₂³	—	2	4	no	—
392	C₂³	—	3	4	no	—
393	C₂³	—	3	8	no	—
394	C₂³	—	6	16	no	—
395	C₂³	—	6	16	no	—
396	C₂³	—	6	16	no	—
397	C₂³	—	6	8	no	—
398	C₂³	—	6	2	no	—
399	C₂³	—	6	4	no	—
400	C₂³	—	6	2	no	—
401	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
402	C₂³	C₂×C₅×D₁₂	1	2	yes	—
403	C₂³	C₂×C₅×#67	1	2	yes	—
404	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	3	4	no	—
408	C₂×C₄	—	6	8	no	—
409	C₂×C₄	—	6	2	no	—
410	C₂×C₄	—	6	2	no	—
411	C₂×C₄	—	6	16	no	—
412	C₂×C₄	—	6	16	no	—
413	C₂×C₄	—	6	4	no	—
414	C₂×C₄	—	6	8	no	—
415	C₂×C₄	C₅×(C₂×D₃)⋊C₄	1	16	yes	complemented
416	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
417	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
418	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
419	C₂×C₄	C₂×C₅×D₁₂	1	2	yes	—
420	C₂×C₄	C₂×C₅×#67	1	2	yes	—
421	C₂×C₄	C₂×C₅×#67	1	2	yes	—
422	C₂×C₃	—	2	4	no	—
423	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
424	C₂×C₃	C₂×C₅×#117	1	2	yes	—
425	C₂×C₃	C₅×#525	1	2	yes	—
426	C₂×C₃	C₅×#525	1	2	yes	—
427	D₃	—	2	8	no	—
428	C₅	#82267	1	1	yes	characteristic, direct product factor, Sylow
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	3	8	no	—
433	C₂²	—	6	32	no	—
434	C₂²	—	6	4	no	—
435	C₂²	—	6	8	no	—
436	C₂²	—	6	4	no	—
437	C₂²	—	6	8	no	—
438	C₂²	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
439	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
440	C₂²	C₂²×C₅×D₁₂	1	1	yes	characteristic
441	C₂²	C₅×D₃×#41	1	4	yes	—
442	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
443	C₄	—	4	4	no	—
444	C₄	—	6	4	no	—
445	C₄	—	12	4	no	—
446	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
447	C₄	C₂×C₅×(C₂×D₃)⋊C₄	1	4	yes	—
448	C₃	C₅×#2280	1	1	yes	characteristic, complemented, Sylow
449	C₂	—	2	4	no	—
450	C₂	—	6	8	no	—
451	C₂	C₅×D₃×#117	1	2	yes	—
452	C₂	C₅×#5524	1	2	yes	—
453	C₂	C₂²×C₅×(C₂×D₃)⋊C₄	1	1	yes	characteristic
454	C₂	C₅×#5828	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₂×C₅×#117	D₃
hypocenter	C₃	C₅×#2280
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₂×C₅×#117

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₂×C₅×#926	C₂	semidirect
4. C₅×#4987	C₂	semidirect
6. C₅×#4943	C₂	semidirect
7. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
14. C₂²×C₄×C₅×D₃	C₄	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
20. C₂×C₃×C₄²×C₅	C₂²	semidirect
24. C₂×C₅×C₄⋊Dic₃	C₂²	semidirect
25. C₂×C₄×C₅×Dic₃	C₂²	semidirect
26. C₅×C₃⋊#95	C₂²	semidirect
27. #82267	C₅	direct (N × H)
30. C₂×C₅×#117	D₃	semidirect
67. C₂×C₃×#117	C₂×C₅	semidirect
68. C₂×#926	C₂×C₅	semidirect
69. #4987	C₂×C₅	semidirect
71. #4943	C₂×C₅	semidirect
72. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
84. C₂×C₅×C₄⋊C₄	C₂×D₃	semidirect
89. C₂×C₄²×C₅	C₂×D₃	semidirect
108. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
128. C₂²×C₄×D₃	C₄×C₅	semidirect
132. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
134. C₂×C₃×C₄²	C₂²×C₅	semidirect
138. C₂×C₄⋊Dic₃	C₂²×C₅	semidirect
139. C₂×C₄×Dic₃	C₂²×C₅	semidirect
140. C₃⋊#95	C₂²×C₅	semidirect
174. C₂×#117	C₅×D₃	semidirect
192. C₂×C₅×D₃	#117	semidirect
253. C₂×C₄×C₅	(C₂×D₃)⋊C₄	semidirect
271. C₂×C₄⋊C₄	C₂×C₅×D₃	semidirect
276. C₂×C₄²	C₂×C₅×D₃	semidirect
300. C₂×C₃×C₄	C₅×C₂²⋊C₄	semidirect
365. C₃×C₅	#2280	semidirect
379. C₂×D₃	C₅×#117	semidirect
415. C₂×C₄	C₅×(C₂×D₃)⋊C₄	semidirect
428. C₅	#82267	direct (N × H)
448. C₃	C₅×#2280	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₄×C₅×D₃	2
C₂×C₃×C₅×#117	2
C₂×C₅×#926	2
C₅×#4987	2
C₅×#4955	2
C₅×#4943	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#2280	3
#82267	5

Subgroups — C5×#82267 #14319905

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#82267 #14319905