Subgroups — C₅×#79325 #14419125

Order 1920.

760 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₅×#5479	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#432	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×C₅×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#4838	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4834	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#4831	C₂	1	1	yes	maximal, characteristic, complemented
7	C₅×#4830	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#4730	C₂	1	2	yes	maximal, complemented
9	C₅×#67⋊C₈	C₂	1	2	yes	maximal, complemented
10	C₅×#4709	C₂	1	2	yes	maximal, complemented
11	C₅×#4708	C₂	1	2	yes	maximal, complemented
12	C₅×#2966	—	3	1	no	maximal, Hall
13	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
14	C₅×#930	C₄	1	1	yes	characteristic
15	C₅×#929	C₄	1	2	yes	—
16	C₄×C₅×#67	C₂²	1	2	yes	—
17	C₅×#924	C₄	1	1	yes	characteristic
18	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
19	C₂²×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
20	C₂×C₅×ΓL(1,𝔽₂₅)	C₂²	1	2	yes	—
21	C₂×C₅×D₃×C₈	C₂²	1	2	yes	—
22	C₅×#876	C₄	1	2	yes	—
23	C₅×#875	C₄	1	1	yes	characteristic
24	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
25	C₅×#872	C₂²	1	2	yes	—
26	C₅×#870	C₄	1	1	yes	characteristic
27	C₄×C₅×Dic₆	C₂²	1	1	yes	characteristic
28	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
29	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
30	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
31	C₃×C₅×#97	C₂²	1	2	yes	—
32	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
33	C₅×(C₂×D₃)⋊C₈	C₂²	1	2	yes	—
34	C₅×#815	C₂²	1	2	yes	—
35	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
36	C₅×Dic₃⋊C₈	C₂²	1	2	yes	—
37	C₅×C₈×Dic₃	C₂²	1	2	yes	—
38	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
39	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
42	#79325	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#529	—	3	1	no	—
44	C₅×#446	—	3	1	no	—
45	C₅×C₈×Q₈	—	3	1	no	—
46	C₅×#436	—	3	1	no	—
47	C₅×#435	—	3	2	no	—
48	C₅×C₈×D₄	—	3	1	no	—
49	C₅×C₈×D₄	—	3	2	no	—
50	C₅×#433	—	3	2	no	—
51	C₅×#432	D₃	1	1	yes	characteristic, complemented
52	C₅×#405	—	3	2	no	—
53	C₂×C₄×C₅×C₈	—	3	1	no	—
54	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂×C₅×#67	C₂×C₄	1	2	yes	—
58	C₂×C₅×D₁₂	C₂×C₄	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	C₂³	1	2	yes	—
60	C₂×C₅×Dic₆	C₂×C₄	1	1	yes	characteristic
61	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
63	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
64	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic
65	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
66	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
67	C₅×#217	C₂×C₄	1	2	yes	—
68	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
69	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
70	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
71	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	2	yes	—
72	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
73	C₅×C₄⋊Dic₃	C₂×C₄	1	1	yes	characteristic
74	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
75	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
76	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
77	C₅×Dic₃⋊C₄	C₂×C₄	1	2	yes	—
78	C₄×C₅×Dic₃	C₂³	1	2	yes	—
79	C₂×C₅×C₃⋊C₈	—	2	2	no	—
80	C₂×C₅×C₃⋊C₈	—	2	2	no	—
81	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
82	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
85	C₅×ΓL(1,𝔽₂₅)	—	2	4	no	—
86	C₅×D₃×C₈	—	2	4	no	—
87	#5479	C₂×C₅	1	1	yes	characteristic
88	C₃×#432	C₂×C₅	1	1	yes	characteristic, complemented
89	C₂×C₄×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
90	#4838	C₂×C₅	1	1	yes	characteristic, complemented
91	#4834	C₂×C₅	1	1	yes	characteristic, complemented
92	#4831	C₂×C₅	1	1	yes	characteristic, complemented
93	#4830	C₂×C₅	1	1	yes	characteristic, complemented
94	#4730	C₂×C₅	1	2	yes	complemented
95	#67⋊C₈	C₂×C₅	1	2	yes	complemented
96	#4709	C₂×C₅	1	2	yes	complemented
97	#4708	C₂×C₅	1	2	yes	complemented
98	C₂×C₅×M₁₆	—	3	2	no	—
99	C₂²×C₅×C₈	—	3	1	no	—
100	C₂²×C₅×C₈	—	3	1	no	—
101	C₂²×C₅×C₈	—	3	2	no	—
102	C₅×#126	—	3	2	no	—
103	C₅×#125	—	3	1	no	—
104	C₅×#124	—	3	1	no	—
105	C₅×#123	—	3	2	no	—
106	C₅×C₂²⋊Q₈	—	3	1	no	—
107	C₅×#121	—	3	1	no	—
108	C₄×C₅×Q₈	—	3	1	no	—
109	C₄×C₅×D₄	—	3	2	no	—
110	C₄×C₅×D₄	—	3	1	no	—
111	C₅×#117	—	3	2	no	—
112	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
113	C₅×C₄⋊C₈	—	3	2	no	—
114	C₅×C₄⋊C₈	—	3	2	no	—
115	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
116	C₅×C₄⋊C₈	C₂×D₃	1	1	yes	characteristic
117	C₅×C₂²⋊C₈	—	3	2	no	—
118	C₅×C₂²⋊C₈	—	3	2	no	—
119	C₅×C₂²⋊C₈	C₂×D₃	1	2	yes	—
120	C₅×#97	—	3	2	no	—
121	C₅×#97	C₂×D₃	1	2	yes	—
122	C₄×C₅×C₈	—	3	2	no	—
123	C₄×C₅×C₈	—	3	1	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	—	3	1	no	—
126	C₄×C₅×C₈	—	3	1	no	—
127	#2966	—	3	1	no	Sylow
128	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
129	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₅×#67	—	2	4	no	—
141	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
142	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
143	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
144	C₅×D₁₂	—	2	2	no	—
145	C₄×C₅×D₃	—	2	2	no	—
146	C₄×C₅×D₃	—	2	2	no	—
147	C₅×Dic₆	—	2	2	no	—
148	C₃×C₅×C₈	—	2	2	no	—
149	C₃×C₅×C₈	—	2	2	no	—
150	C₅×C₃⋊C₈	—	2	1	no	—
151	C₅×C₃⋊C₈	—	2	1	no	—
152	C₅×C₃⋊C₈	#41	1	2	yes	—
153	C₅×C₃⋊C₈	#41	1	2	yes	—
154	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
155	#930	C₄×C₅	1	1	yes	characteristic
156	#929	C₄×C₅	1	2	yes	—
157	C₄×#67	C₂²×C₅	1	2	yes	—
158	#924	C₄×C₅	1	1	yes	characteristic
159	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
160	C₂²×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
161	C₂×ΓL(1,𝔽₂₅)	C₂²×C₅	1	2	yes	—
162	C₂×D₃×C₈	C₂²×C₅	1	2	yes	—
163	#876	C₄×C₅	1	2	yes	—
164	#875	C₄×C₅	1	1	yes	characteristic
165	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
166	#872	C₂²×C₅	1	2	yes	—
167	#870	C₄×C₅	1	1	yes	characteristic
168	C₄×Dic₆	C₂²×C₅	1	1	yes	characteristic
169	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
171	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
172	C₃×#97	C₂²×C₅	1	2	yes	—
173	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
174	(C₂×D₃)⋊C₈	C₂²×C₅	1	2	yes	—
175	#815	C₂²×C₅	1	2	yes	—
176	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
177	Dic₃⋊C₈	C₂²×C₅	1	2	yes	—
178	C₈×Dic₃	C₂²×C₅	1	2	yes	—
179	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
180	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
181	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
182	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₅×Q₈	—	3	1	no	—
184	C₂×C₅×D₄	—	3	2	no	—
185	C₂×C₅×D₄	—	3	1	no	—
186	C₂²×C₄×C₅	—	3	2	no	—
187	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₄×D₃	1	1	yes	characteristic
189	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
190	C₅×M₁₆	—	6	4	no	—
191	C₂×C₅×C₈	—	3	1	no	—
192	C₂×C₅×C₈	—	3	1	no	—
193	C₂×C₅×C₈	—	3	1	no	—
194	C₂×C₅×C₈	—	3	1	no	—
195	C₂×C₅×C₈	—	6	4	no	—
196	C₂×C₅×C₈	—	6	2	no	—
197	C₂×C₅×C₈	—	6	2	no	—
198	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
199	C₂×C₅×C₈	C₂²×D₃	1	2	yes	—
200	C₅×C₄⋊C₄	—	3	2	no	—
201	C₅×C₄⋊C₄	—	3	2	no	—
202	C₅×C₄⋊C₄	—	3	1	no	—
203	C₅×C₄⋊C₄	—	3	2	no	—
204	C₅×C₄⋊C₄	—	3	1	no	—
205	C₅×C₄⋊C₄	—	3	2	no	—
206	C₅×C₂²⋊C₄	—	3	2	no	—
207	C₅×C₂²⋊C₄	—	3	2	no	—
208	C₅×C₂²⋊C₄	—	3	2	no	—
209	C₅×C₂²⋊C₄	—	3	2	no	—
210	C₅×C₂²⋊C₄	—	3	2	no	—
211	C₄²×C₅	—	3	2	no	—
212	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
213	C₄²×C₅	C₄×D₃	1	1	yes	characteristic
214	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
215	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
216	#529	—	3	1	no	—
217	#446	—	3	1	no	—
218	C₈×Q₈	—	3	1	no	—
219	#436	—	3	1	no	—
220	#435	—	3	2	no	—
221	C₈×D₄	—	3	1	no	—
222	C₈×D₄	—	3	2	no	—
223	#433	—	3	2	no	—
224	#432	C₅×D₃	1	1	yes	characteristic, complemented
225	#405	—	3	2	no	—
226	C₂×C₄×C₈	—	3	1	no	—
227	C₂²×C₃×C₅	—	2	1	no	—
228	C₂²×C₃×C₅	—	2	1	no	—
229	C₂²×C₃×C₅	#131	1	2	yes	—
230	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
231	C₂×C₅×D₃	—	2	2	no	—
232	C₂×C₅×D₃	—	2	2	no	—
233	C₂×C₅×D₃	—	2	2	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	2	1	no	—
237	C₃×C₄×C₅	—	2	1	no	—
238	C₃×C₄×C₅	#131	1	2	yes	—
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₅×Dic₃	—	2	2	no	—
242	C₅×Dic₃	—	2	2	no	—
243	C₅×Dic₃	—	2	2	no	—
244	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
245	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂×#67	C₂×C₄×C₅	1	2	yes	—
248	C₂×D₁₂	C₂×C₄×C₅	1	1	yes	characteristic
249	C₂×C₄×D₃	C₂³×C₅	1	2	yes	—
250	C₂×Dic₆	C₂×C₄×C₅	1	1	yes	characteristic
251	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
252	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
253	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
254	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic
255	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
256	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
257	#217	C₂×C₄×C₅	1	2	yes	—
258	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
259	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
260	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
261	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	2	yes	—
262	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
263	C₄⋊Dic₃	C₂×C₄×C₅	1	1	yes	characteristic
264	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
265	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
266	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
267	Dic₃⋊C₄	C₂×C₄×C₅	1	2	yes	—
268	C₄×Dic₃	C₂³×C₅	1	2	yes	—
269	C₂×C₃⋊C₈	—	2	2	no	—
270	C₂×C₃⋊C₈	—	2	2	no	—
271	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
274	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
275	ΓL(1,𝔽₂₅)	—	2	4	no	—
276	D₃×C₈	—	2	4	no	—
277	C₂³×C₅	—	3	2	no	—
278	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
279	C₅×Q₈	—	6	2	no	—
280	C₅×D₄	—	6	4	no	—
281	C₅×D₄	—	6	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	1	no	—
286	C₂×C₄×C₅	—	3	2	no	—
287	C₂×C₄×C₅	—	3	2	no	—
288	C₂×C₄×C₅	—	3	2	no	—
289	C₂×C₄×C₅	—	6	2	no	—
290	C₂×C₄×C₅	—	6	2	no	—
291	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
292	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
295	C₂×C₄×C₅	C₂×C₄×D₃	1	1	yes	characteristic
296	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
297	C₅×C₈	—	2	2	no	—
298	C₅×C₈	—	2	2	no	—
299	C₅×C₈	—	3	2	no	—
300	C₅×C₈	—	3	2	no	—
301	C₅×C₈	—	6	1	no	—
302	C₅×C₈	—	6	1	no	—
303	C₂×M₁₆	—	3	2	no	—
304	C₂²×C₈	—	3	1	no	—
305	C₂²×C₈	—	3	1	no	—
306	C₂²×C₈	—	3	2	no	—
307	#126	—	3	2	no	—
308	#125	—	3	1	no	—
309	#124	—	3	1	no	—
310	#123	—	3	2	no	—
311	C₂²⋊Q₈	—	3	1	no	—
312	#121	—	3	1	no	—
313	C₄×Q₈	—	3	1	no	—
314	C₄×D₄	—	3	2	no	—
315	C₄×D₄	—	3	1	no	—
316	#117	—	3	2	no	—
317	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
318	C₄⋊C₈	—	3	2	no	—
319	C₄⋊C₈	—	3	2	no	—
320	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
321	C₄⋊C₈	C₂×C₅×D₃	1	1	yes	characteristic
322	C₂²⋊C₈	—	3	2	no	—
323	C₂²⋊C₈	—	3	2	no	—
324	C₂²⋊C₈	C₂×C₅×D₃	1	2	yes	—
325	#97	—	3	2	no	—
326	#97	C₂×C₅×D₃	1	2	yes	—
327	C₄×C₈	—	3	2	no	—
328	C₄×C₈	—	3	1	no	—
329	C₄×C₈	—	3	1	no	—
330	C₄×C₈	—	3	1	no	—
331	C₄×C₈	—	3	1	no	—
332	C₂×C₃×C₅	—	2	2	no	—
333	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
334	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
335	C₂×C₃×C₅	C₂×#131	1	1	yes	characteristic
336	C₅×D₃	—	4	2	no	—
337	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
338	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
344	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
347	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
348	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
349	#67	—	2	4	no	—
350	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
351	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
352	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
353	D₁₂	—	2	2	no	—
354	C₄×D₃	—	2	2	no	—
355	C₄×D₃	—	2	2	no	—
356	Dic₆	—	2	2	no	—
357	C₃×C₈	—	2	2	no	—
358	C₃×C₈	—	2	2	no	—
359	C₃⋊C₈	—	2	1	no	—
360	C₃⋊C₈	—	2	1	no	—
361	C₃⋊C₈	C₅×#41	1	2	yes	—
362	C₃⋊C₈	C₅×#41	1	2	yes	—
363	C₂²×C₅	—	2	1	no	—
364	C₂²×C₅	—	2	1	no	—
365	C₂²×C₅	—	6	2	no	—
366	C₂²×C₅	—	6	2	no	—
367	C₂²×C₅	—	6	2	no	—
368	C₂²×C₅	#907	1	2	yes	—
369	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	1	no	—
372	C₄×C₅	—	2	1	no	—
373	C₄×C₅	—	2	1	no	—
374	C₄×C₅	—	6	2	no	—
375	C₄×C₅	—	6	2	no	—
376	C₄×C₅	—	6	2	no	—
377	C₄×C₅	#907	1	2	yes	—
378	C₄×C₅	D₃×#41	1	1	yes	characteristic
379	C₄×C₅	D₃×#41	1	1	yes	characteristic
380	C₂×Q₈	—	3	1	no	—
381	C₂×D₄	—	3	2	no	—
382	C₂×D₄	—	3	1	no	—
383	C₂²×C₄	—	3	2	no	—
384	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
385	C₂²×C₄	C₄×C₅×D₃	1	1	yes	characteristic
386	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
387	M₁₆	—	6	4	no	—
388	C₂×C₈	—	3	1	no	—
389	C₂×C₈	—	3	1	no	—
390	C₂×C₈	—	3	1	no	—
391	C₂×C₈	—	3	1	no	—
392	C₂×C₈	—	6	4	no	—
393	C₂×C₈	—	6	2	no	—
394	C₂×C₈	—	6	2	no	—
395	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
396	C₂×C₈	C₂²×C₅×D₃	1	2	yes	—
397	C₄⋊C₄	—	3	2	no	—
398	C₄⋊C₄	—	3	2	no	—
399	C₄⋊C₄	—	3	1	no	—
400	C₄⋊C₄	—	3	2	no	—
401	C₄⋊C₄	—	3	1	no	—
402	C₄⋊C₄	—	3	2	no	—
403	C₂²⋊C₄	—	3	2	no	—
404	C₂²⋊C₄	—	3	2	no	—
405	C₂²⋊C₄	—	3	2	no	—
406	C₂²⋊C₄	—	3	2	no	—
407	C₂²⋊C₄	—	3	2	no	—
408	C₄²	—	3	2	no	—
409	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
410	C₄²	C₄×C₅×D₃	1	1	yes	characteristic
411	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
412	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
413	C₃×C₅	#2966	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	2	1	no	—
415	C₂²×C₃	—	2	1	no	—
416	C₂²×C₃	C₅×#131	1	2	yes	—
417	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
418	C₂×D₃	—	2	2	no	—
419	C₂×D₃	—	2	2	no	—
420	C₂×D₃	—	2	2	no	—
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	1	no	—
424	C₃×C₄	—	2	1	no	—
425	C₃×C₄	C₅×#131	1	2	yes	—
426	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
427	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
428	Dic₃	—	2	2	no	—
429	Dic₃	—	2	2	no	—
430	Dic₃	—	2	2	no	—
431	C₂×C₅	—	2	2	no	—
432	C₂×C₅	—	12	2	no	—
433	C₂×C₅	#5522	1	1	yes	characteristic
434	C₂×C₅	C₂×#907	1	1	yes	characteristic
435	C₂×C₅	C₂×#907	1	1	yes	characteristic
436	C₂³	—	3	2	no	—
437	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
438	Q₈	—	6	2	no	—
439	D₄	—	6	4	no	—
440	D₄	—	6	2	no	—
441	C₂×C₄	—	2	2	no	—
442	C₂×C₄	—	2	2	no	—
443	C₂×C₄	—	2	1	no	—
444	C₂×C₄	—	2	1	no	—
445	C₂×C₄	—	3	2	no	—
446	C₂×C₄	—	3	2	no	—
447	C₂×C₄	—	3	2	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	2	no	—
450	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
451	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
452	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
453	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
454	C₂×C₄	C₂×C₄×C₅×D₃	1	1	yes	characteristic
455	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
456	C₈	—	2	2	no	—
457	C₈	—	2	2	no	—
458	C₈	—	3	2	no	—
459	C₈	—	3	2	no	—
460	C₈	—	6	1	no	—
461	C₈	—	6	1	no	—
462	C₂×C₃	—	2	2	no	—
463	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
464	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
465	C₂×C₃	C₂×C₅×#131	1	1	yes	characteristic
466	D₃	—	4	2	no	—
467	C₅	#79325	1	1	yes	characteristic, direct product factor, Sylow
468	C₂²	—	2	1	no	—
469	C₂²	—	2	1	no	—
470	C₂²	—	6	2	no	—
471	C₂²	—	6	2	no	—
472	C₂²	—	6	2	no	—
473	C₂²	C₅×#907	1	2	yes	—
474	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	1	no	—
478	C₄	—	2	1	no	—
479	C₄	—	6	2	no	—
480	C₄	—	6	2	no	—
481	C₄	—	6	2	no	—
482	C₄	C₅×#907	1	2	yes	—
483	C₄	C₅×D₃×#41	1	1	yes	characteristic
484	C₄	C₅×D₃×#41	1	1	yes	characteristic
485	C₃	C₅×#2966	1	1	yes	characteristic, complemented, Sylow
486	C₂	—	2	2	no	—
487	C₂	—	12	2	no	—
488	C₂	C₅×#5522	1	1	yes	characteristic
489	C₂	C₂×C₅×#907	1	1	yes	characteristic
490	C₂	C₂×C₅×#907	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₅	C₂³×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#432	C₂
socle	C₂²×C₃×C₅	C₂³×C₄
prime radical	C₅×#930	C₄
cosocle	C₂×C₃×C₄	C₂⁴×C₅
hypercenter	C₅×#432	D₃
hypocenter	C₃	C₅×#2966
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₄×C₅ ◁ C₅×#432

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#432	C₂	semidirect
3. C₂×C₄×C₅×C₃⋊C₈	C₂	semidirect
4. C₅×#4838	C₂	semidirect
5. C₅×#4834	C₂	semidirect
6. C₅×#4831	C₂	semidirect
7. C₅×#4830	C₂	semidirect
8. C₅×#4730	C₂	semidirect
9. C₅×#67⋊C₈	C₂	semidirect
10. C₅×#4709	C₂	semidirect
11. C₅×#4708	C₂	semidirect
42. #79325	C₅	direct (N × H)
51. C₅×#432	D₃	semidirect
88. C₃×#432	C₂×C₅	semidirect
89. C₂×C₄×C₃⋊C₈	C₂×C₅	semidirect
90. #4838	C₂×C₅	semidirect
91. #4834	C₂×C₅	semidirect
92. #4831	C₂×C₅	semidirect
93. #4830	C₂×C₅	semidirect
94. #4730	C₂×C₅	semidirect
95. #67⋊C₈	C₂×C₅	semidirect
96. #4709	C₂×C₅	semidirect
97. #4708	C₂×C₅	semidirect
224. #432	C₅×D₃	semidirect
413. C₃×C₅	#2966	semidirect
467. C₅	#79325	direct (N × H)
485. C₃	C₅×#2966	semidirect

Maximal subgroups

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

subgroup	index
C₅×#5479	2
C₃×C₅×#432	2
C₂×C₄×C₅×C₃⋊C₈	2
C₅×#4838	2
C₅×#4834	2
C₅×#4831	2
C₅×#4830	2
C₅×#4730	2
C₅×#67⋊C₈	2
C₅×#4709	2
C₅×#4708	2
C₅×#2966	3
#79325	5

Subgroups — C5×#79325 #14419125

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#79325 #14419125