Subgroups — C₅×#83637 #14471597

Order 1920.

700 conjugacy classes of subgroups.

The subgroup lattice has 484 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₅×#5584	C₂	1	1	yes	maximal, characteristic, complemented
3	C₅×#5093	C₂	1	1	yes	maximal, characteristic, complemented
4	C₅×#5084	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#5068	C₂	1	2	yes	maximal, complemented
6	C₅×#5063	C₂	1	2	yes	maximal, complemented
7	C₅×Q₈×C₃⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₅×#5019	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×#214	C₂	1	2	yes	maximal, complemented
10	C₅×#5016	C₂	1	2	yes	maximal
11	C₄×C₅×#213	C₂	1	1	yes	maximal, characteristic
12	C₅×#3360	—	3	1	no	maximal, Hall
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×#125	C₂²	1	2	yes	—
15	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
16	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
17	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
21	C₅×#946	—	2	1	no	—
22	C₂×C₅×#214	C₂²	1	2	yes	—
23	C₂×C₅×#213	C₂²	1	1	yes	characteristic
24	C₅×#898	—	2	2	no	—
25	C₅×#892	—	2	1	no	—
26	C₅×#875	C₂²	1	2	yes	—
27	C₄×C₅×D₁₂	C₂²	1	1	yes	characteristic
28	C₅×#869	C₂²	1	1	yes	characteristic
29	C₄×C₅×Dic₆	C₂²	1	2	yes	—
30	C₅×#832	C₂²	1	1	yes	characteristic
31	C₅×#810	C₂²	1	2	yes	—
32	C₅×#810	C₂²	1	2	yes	—
33	C₅×#810	C₂²	1	2	yes	—
34	C₅×#809	C₂²	1	1	yes	characteristic
35	C₅×#809	C₂²	1	2	yes	—
36	C₅×#808	C₂²	1	2	yes	—
37	C₅×#807	C₂²	1	1	yes	characteristic
38	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	2	yes	—
39	C₅×C₄⋊(C₃⋊C₈)	C₂²	1	1	yes	characteristic
40	C₄×C₅×C₃⋊C₈	C₂²	1	1	yes	characteristic
41	C₄×C₅×C₃⋊C₈	C₂²	1	2	yes	—
42	#83637	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#556	—	3	1	no	—
44	C₅×#554	D₃	1	1	yes	characteristic, complemented
45	C₅×#488	—	3	2	no	—
46	C₅×#487	—	3	1	no	—
47	C₅×#479	—	3	2	no	—
48	C₅×#476	—	3	1	no	—
49	C₅×#463	—	3	2	no	—
50	C₅×#461	—	3	1	no	—
51	C₅×C₈×Q₈	—	3	1	no	—
52	C₄×C₅×SD₁₆	—	3	2	no	—
53	C₄×C₅×D₈	—	3	1	no	—
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	—	2	2	no	—
59	C₂×C₅×D₁₂	C₂³	1	1	yes	characteristic
60	C₂×C₄×C₅×D₃	—	2	1	no	—
61	C₂×C₅×Dic₆	C₂³	1	2	yes	—
62	C₃×C₅×C₄⋊C₄	—	2	2	no	—
63	C₃×C₅×C₄⋊C₄	—	2	1	no	—
64	C₃×C₅×C₄⋊C₄	—	2	2	no	—
65	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
68	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
69	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
71	C₃×C₄²×C₅	C₂³	1	2	yes	—
72	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
73	C₅×#214	—	2	4	no	—
74	C₅×#213	—	2	2	no	—
75	C₅×(C₂×D₃)⋊C₄	—	2	1	no	—
76	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
77	C₅×(C₂×D₃)⋊C₄	—	2	2	no	—
78	C₅×C₄⋊Dic₃	—	2	1	no	—
79	C₅×C₄⋊Dic₃	—	2	1	no	—
80	C₅×C₄⋊Dic₃	C₂³	1	1	yes	characteristic
81	C₅×Dic₃⋊C₄	—	2	2	no	—
82	C₄×C₅×Dic₃	—	2	2	no	—
83	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
84	C₂×C₅×C₃⋊C₈	C₂³	1	2	yes	—
85	C₂×C₅×C₃⋊C₈	C₂³	1	1	yes	characteristic
86	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
87	#5584	C₂×C₅	1	1	yes	characteristic, complemented
88	#5093	C₂×C₅	1	1	yes	characteristic, complemented
89	#5084	C₂×C₅	1	1	yes	characteristic, complemented
90	#5068	C₂×C₅	1	2	yes	complemented
91	#5063	C₂×C₅	1	2	yes	complemented
92	Q₈×C₃⋊C₈	C₂×C₅	1	1	yes	characteristic, complemented
93	#5019	C₂×C₅	1	1	yes	characteristic, complemented
94	C₄×#214	C₂×C₅	1	2	yes	complemented
95	#5016	C₂×C₅	1	2	yes	—
96	C₄×#213	C₂×C₅	1	1	yes	characteristic
97	C₂×C₅×SD₁₆	—	3	2	no	—
98	C₂×C₅×D₈	—	3	1	no	—
99	C₅×C₄⋊Q₈	—	3	1	no	—
100	C₅×C₄⋊Q₈	C₂×D₃	1	1	yes	characteristic
101	C₅×#126	—	6	2	no	—
102	C₅×#125	C₂×D₃	1	2	yes	—
103	C₅×#124	—	3	2	no	—
104	C₅×C₂²⋊Q₈	—	2	1	no	—
105	C₅×C₂²⋊Q₈	—	2	2	no	—
106	C₅×C₂²⋊Q₈	—	6	1	no	—
107	C₄×C₅×Q₈	—	3	2	no	—
108	C₄×C₅×Q₈	C₂×D₃	1	1	yes	characteristic
109	C₄×C₅×D₄	—	3	1	no	—
110	C₄×C₅×D₄	C₂×D₃	1	1	yes	characteristic
111	C₄×C₅×D₄	C₂×D₃	1	2	yes	—
112	C₅×#117	—	6	1	no	—
113	C₂×C₅×C₄⋊C₄	—	2	1	no	—
114	C₅×#107	—	3	1	no	—
115	C₅×#106	—	3	2	no	—
116	C₅×C₄⋊C₈	—	3	1	no	—
117	C₅×C₄⋊C₈	—	3	2	no	—
118	C₅×#103	—	3	2	no	—
119	C₅×#103	—	3	2	no	—
120	C₅×#103	—	3	2	no	—
121	C₅×#102	—	3	1	no	—
122	C₅×#102	—	3	1	no	—
123	C₅×#102	—	3	2	no	—
124	C₄×C₅×C₈	—	3	1	no	—
125	C₄×C₅×C₈	—	3	2	no	—
126	#3360	—	3	1	no	Sylow
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂²×C₅×D₃	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	—	8	1	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	#41	1	2	yes	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	4	2	no	—
136	C₂×C₃×C₄×C₅	—	8	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂×C₅×Dic₃	—	2	1	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₅×D₁₂	—	2	1	no	—
145	C₅×D₁₂	—	2	1	no	—
146	C₄×C₅×D₃	—	4	2	no	—
147	C₅×Dic₆	—	2	2	no	—
148	C₅×Dic₆	—	2	2	no	—
149	C₅×C₃⋊C₈	—	2	1	no	—
150	C₅×C₃⋊C₈	—	2	2	no	—
151	C₅×C₃⋊C₈	—	2	1	no	—
152	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
153	C₃×#125	C₂²×C₅	1	2	yes	—
154	C₃×C₂²⋊Q₈	—	2	1	no	—
155	C₃×C₂²⋊Q₈	—	2	2	no	—
156	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
157	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
158	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	—	2	1	no	—
160	#946	—	2	1	no	—
161	C₂×#214	C₂²×C₅	1	2	yes	—
162	C₂×#213	C₂²×C₅	1	1	yes	characteristic
163	#898	—	2	2	no	—
164	#892	—	2	1	no	—
165	#875	C₂²×C₅	1	2	yes	—
166	C₄×D₁₂	C₂²×C₅	1	1	yes	characteristic
167	#869	C₂²×C₅	1	1	yes	characteristic
168	C₄×Dic₆	C₂²×C₅	1	2	yes	—
169	#832	C₂²×C₅	1	1	yes	characteristic
170	#810	C₂²×C₅	1	2	yes	—
171	#810	C₂²×C₅	1	2	yes	—
172	#810	C₂²×C₅	1	2	yes	—
173	#809	C₂²×C₅	1	1	yes	characteristic
174	#809	C₂²×C₅	1	2	yes	—
175	#808	C₂²×C₅	1	2	yes	—
176	#807	C₂²×C₅	1	1	yes	characteristic
177	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	2	yes	—
178	C₄⋊(C₃⋊C₈)	C₂²×C₅	1	1	yes	characteristic
179	C₄×C₃⋊C₈	C₂²×C₅	1	1	yes	characteristic
180	C₄×C₃⋊C₈	C₂²×C₅	1	2	yes	—
181	C₂×C₅×Q₈	—	2	1	no	—
182	C₂×C₅×Q₈	—	3	2	no	—
183	C₂×C₅×Q₈	#67	1	1	yes	characteristic
184	C₂×C₅×D₄	—	3	1	no	—
185	C₂×C₅×D₄	C₂²×D₃	1	1	yes	characteristic
186	C₂²×C₄×C₅	—	2	1	no	—
187	C₂²×C₄×C₅	—	2	2	no	—
188	C₂²×C₄×C₅	—	6	1	no	—
189	C₅×SD₁₆	—	6	4	no	—
190	C₅×D₈	—	6	2	no	—
191	C₂×C₅×C₈	—	3	1	no	—
192	C₂×C₅×C₈	—	3	2	no	—
193	C₂×C₅×C₈	—	3	1	no	—
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	—	2	1	no	—
196	C₅×C₄⋊C₄	—	2	2	no	—
197	C₅×C₄⋊C₄	—	3	1	no	—
198	C₅×C₄⋊C₄	—	6	1	no	—
199	C₅×C₄⋊C₄	—	6	2	no	—
200	C₅×C₄⋊C₄	—	6	1	no	—
201	C₅×C₄⋊C₄	#67	1	1	yes	characteristic
202	C₅×C₄⋊C₄	#67	1	2	yes	—
203	C₅×C₄⋊C₄	C₂²×D₃	1	1	yes	characteristic
204	C₅×C₄⋊C₄	C₂²×D₃	1	2	yes	—
205	C₅×C₂²⋊C₄	—	2	1	no	—
206	C₅×C₂²⋊C₄	—	2	2	no	—
207	C₅×C₂²⋊C₄	—	6	2	no	—
208	C₅×C₂²⋊C₄	—	6	1	no	—
209	C₅×C₂²⋊C₄	—	6	2	no	—
210	C₄²×C₅	—	6	2	no	—
211	C₄²×C₅	C₂²×D₃	1	1	yes	characteristic
212	C₄²×C₅	C₂²×D₃	1	2	yes	—
213	#556	—	3	1	no	—
214	#554	C₅×D₃	1	1	yes	characteristic, complemented
215	#488	—	3	2	no	—
216	#487	—	3	1	no	—
217	#479	—	3	2	no	—
218	#476	—	3	1	no	—
219	#463	—	3	2	no	—
220	#461	—	3	1	no	—
221	C₈×Q₈	—	3	1	no	—
222	C₄×SD₁₆	—	3	2	no	—
223	C₄×D₈	—	3	1	no	—
224	C₂²×C₃×C₅	—	2	2	no	—
225	C₂²×C₃×C₅	—	4	1	no	—
226	C₂²×C₃×C₅	—	4	1	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂×C₅×D₃	—	4	1	no	—
229	C₂×C₅×D₃	—	4	1	no	—
230	C₂×C₅×D₃	—	4	1	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	2	2	no	—
233	C₃×C₄×C₅	—	2	1	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	—	4	2	no	—
236	C₃×C₄×C₅	#135	1	2	yes	—
237	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
238	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
239	C₅×Dic₃	—	4	2	no	—
240	C₅×Dic₃	—	4	1	no	—
241	C₂×C₃×Q₈	—	2	1	no	—
242	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
243	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	—	2	1	no	—
245	C₂²×C₃×C₄	—	2	2	no	—
246	C₂×D₁₂	C₂³×C₅	1	1	yes	characteristic
247	C₂×C₄×D₃	—	2	1	no	—
248	C₂×Dic₆	C₂³×C₅	1	2	yes	—
249	C₃×C₄⋊C₄	—	2	2	no	—
250	C₃×C₄⋊C₄	—	2	1	no	—
251	C₃×C₄⋊C₄	—	2	2	no	—
252	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
253	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
254	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
255	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
256	C₃×C₂²⋊C₄	—	2	1	no	—
257	C₃×C₂²⋊C₄	—	2	2	no	—
258	C₃×C₄²	C₂³×C₅	1	2	yes	—
259	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
260	#214	—	2	4	no	—
261	#213	—	2	2	no	—
262	(C₂×D₃)⋊C₄	—	2	1	no	—
263	(C₂×D₃)⋊C₄	—	2	2	no	—
264	(C₂×D₃)⋊C₄	—	2	2	no	—
265	C₄⋊Dic₃	—	2	1	no	—
266	C₄⋊Dic₃	—	2	1	no	—
267	C₄⋊Dic₃	C₂³×C₅	1	1	yes	characteristic
268	Dic₃⋊C₄	—	2	2	no	—
269	C₄×Dic₃	—	2	2	no	—
270	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
271	C₂×C₃⋊C₈	C₂³×C₅	1	1	yes	characteristic
272	C₂×C₃⋊C₈	C₂³×C₅	1	2	yes	—
273	C₂³×C₅	—	2	1	no	—
274	C₂³×C₅	—	6	1	no	—
275	C₅×Q₈	—	2	2	no	—
276	C₅×Q₈	—	6	2	no	—
277	C₅×Q₈	—	6	2	no	—
278	C₅×Q₈	—	8	1	no	—
279	C₅×D₄	—	2	1	no	—
280	C₅×D₄	—	6	1	no	—
281	C₅×D₄	—	6	1	no	—
282	C₅×D₄	#239	1	2	yes	—
283	C₂×C₄×C₅	—	2	1	no	—
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	4	2	no	—
286	C₂×C₄×C₅	—	6	1	no	—
287	C₂×C₄×C₅	—	6	2	no	—
288	C₂×C₄×C₅	—	8	2	no	—
289	C₂×C₄×C₅	—	12	2	no	—
290	C₂×C₄×C₅	C₂×#67	1	2	yes	—
291	C₂×C₄×C₅	C₂×#67	1	2	yes	—
292	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
293	C₂×C₄×C₅	C₂×#67	1	1	yes	characteristic
294	C₂×C₄×C₅	C₂³×D₃	1	1	yes	characteristic
295	C₅×C₈	—	6	1	no	—
296	C₅×C₈	—	6	2	no	—
297	C₅×C₈	—	6	1	no	—
298	C₂×SD₁₆	—	3	2	no	—
299	C₂×D₈	—	3	1	no	—
300	C₄⋊Q₈	—	3	1	no	—
301	C₄⋊Q₈	C₂×C₅×D₃	1	1	yes	characteristic
302	#126	—	6	2	no	—
303	#125	C₂×C₅×D₃	1	2	yes	—
304	#124	—	3	2	no	—
305	C₂²⋊Q₈	—	2	1	no	—
306	C₂²⋊Q₈	—	2	2	no	—
307	C₂²⋊Q₈	—	6	1	no	—
308	C₄×Q₈	—	3	2	no	—
309	C₄×Q₈	C₂×C₅×D₃	1	1	yes	characteristic
310	C₄×D₄	—	3	1	no	—
311	C₄×D₄	C₂×C₅×D₃	1	1	yes	characteristic
312	C₄×D₄	C₂×C₅×D₃	1	2	yes	—
313	#117	—	6	1	no	—
314	C₂×C₄⋊C₄	—	2	1	no	—
315	#107	—	3	1	no	—
316	#106	—	3	2	no	—
317	C₄⋊C₈	—	3	1	no	—
318	C₄⋊C₈	—	3	2	no	—
319	#103	—	3	2	no	—
320	#103	—	3	2	no	—
321	#103	—	3	2	no	—
322	#102	—	3	1	no	—
323	#102	—	3	1	no	—
324	#102	—	3	2	no	—
325	C₄×C₈	—	3	1	no	—
326	C₄×C₈	—	3	2	no	—
327	C₂×C₃×C₅	—	4	2	no	—
328	C₂×C₃×C₅	#548	1	1	yes	characteristic
329	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
330	C₂×C₃×C₅	#577	1	1	yes	characteristic
331	C₅×D₃	—	8	1	no	—
332	C₂³×C₃	—	2	1	no	—
333	C₂²×D₃	—	2	1	no	—
334	C₃×Q₈	—	2	2	no	—
335	C₃×Q₈	—	8	1	no	—
336	C₃×D₄	—	2	1	no	—
337	C₃×D₄	C₅×#41	1	2	yes	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	2	no	—
340	C₂×C₃×C₄	—	4	2	no	—
341	C₂×C₃×C₄	—	8	2	no	—
342	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
343	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
344	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
345	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
346	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
347	C₂×Dic₃	—	2	1	no	—
348	C₂×Dic₃	—	2	2	no	—
349	D₁₂	—	2	1	no	—
350	D₁₂	—	2	1	no	—
351	C₄×D₃	—	4	2	no	—
352	Dic₆	—	2	2	no	—
353	Dic₆	—	2	2	no	—
354	C₃⋊C₈	—	2	1	no	—
355	C₃⋊C₈	—	2	2	no	—
356	C₃⋊C₈	—	2	1	no	—
357	C₂²×C₅	—	2	2	no	—
358	C₂²×C₅	—	4	1	no	—
359	C₂²×C₅	—	4	1	no	—
360	C₂²×C₅	—	12	1	no	—
361	C₂²×C₅	—	12	1	no	—
362	C₂²×C₅	—	12	1	no	—
363	C₂²×C₅	C₂²×#67	1	1	yes	characteristic
364	C₄×C₅	—	2	2	no	—
365	C₄×C₅	—	2	2	no	—
366	C₄×C₅	—	2	1	no	—
367	C₄×C₅	—	4	1	no	—
368	C₄×C₅	—	4	2	no	—
369	C₄×C₅	—	12	2	no	—
370	C₄×C₅	—	12	1	no	—
371	C₄×C₅	#950	1	2	yes	—
372	C₄×C₅	C₂×#239	1	1	yes	characteristic
373	C₄×C₅	#1007	1	1	yes	characteristic
374	C₂×Q₈	—	2	1	no	—
375	C₂×Q₈	—	3	2	no	—
376	C₂×Q₈	C₅×#67	1	1	yes	characteristic
377	C₂×D₄	—	3	1	no	—
378	C₂×D₄	C₂²×C₅×D₃	1	1	yes	characteristic
379	C₂²×C₄	—	2	1	no	—
380	C₂²×C₄	—	2	2	no	—
381	C₂²×C₄	—	6	1	no	—
382	SD₁₆	—	6	4	no	—
383	D₈	—	6	2	no	—
384	C₂×C₈	—	3	1	no	—
385	C₂×C₈	—	3	2	no	—
386	C₂×C₈	—	3	1	no	—
387	C₄⋊C₄	—	2	2	no	—
388	C₄⋊C₄	—	2	1	no	—
389	C₄⋊C₄	—	2	2	no	—
390	C₄⋊C₄	—	3	1	no	—
391	C₄⋊C₄	—	6	1	no	—
392	C₄⋊C₄	—	6	2	no	—
393	C₄⋊C₄	—	6	1	no	—
394	C₄⋊C₄	C₅×#67	1	1	yes	characteristic
395	C₄⋊C₄	C₅×#67	1	2	yes	—
396	C₄⋊C₄	C₂²×C₅×D₃	1	2	yes	—
397	C₄⋊C₄	C₂²×C₅×D₃	1	1	yes	characteristic
398	C₂²⋊C₄	—	2	1	no	—
399	C₂²⋊C₄	—	2	2	no	—
400	C₂²⋊C₄	—	6	2	no	—
401	C₂²⋊C₄	—	6	1	no	—
402	C₂²⋊C₄	—	6	2	no	—
403	C₄²	—	6	2	no	—
404	C₄²	C₂²×C₅×D₃	1	1	yes	characteristic
405	C₄²	C₂²×C₅×D₃	1	2	yes	—
406	C₃×C₅	#3360	1	1	yes	characteristic, complemented, Hall
407	C₂²×C₃	—	2	2	no	—
408	C₂²×C₃	—	4	1	no	—
409	C₂²×C₃	—	4	1	no	—
410	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
411	C₂×D₃	—	4	1	no	—
412	C₂×D₃	—	4	1	no	—
413	C₂×D₃	—	4	1	no	—
414	C₃×C₄	—	2	2	no	—
415	C₃×C₄	—	2	2	no	—
416	C₃×C₄	—	2	1	no	—
417	C₃×C₄	—	4	1	no	—
418	C₃×C₄	—	4	2	no	—
419	C₃×C₄	C₅×#135	1	2	yes	—
420	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
421	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
422	Dic₃	—	4	2	no	—
423	Dic₃	—	4	1	no	—
424	C₂×C₅	—	4	2	no	—
425	C₂×C₅	—	24	1	no	—
426	C₂×C₅	#5817	1	1	yes	characteristic
427	C₂×C₅	C₂×#950	1	1	yes	characteristic
428	C₂×C₅	#5836	1	1	yes	characteristic
429	C₂³	—	2	1	no	—
430	C₂³	—	6	1	no	—
431	Q₈	—	2	2	no	—
432	Q₈	—	6	2	no	—
433	Q₈	—	6	2	no	—
434	Q₈	—	8	1	no	—
435	D₄	—	2	1	no	—
436	D₄	—	6	1	no	—
437	D₄	—	6	1	no	—
438	D₄	C₅×#239	1	2	yes	—
439	C₂×C₄	—	2	1	no	—
440	C₂×C₄	—	2	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	6	1	no	—
443	C₂×C₄	—	6	2	no	—
444	C₂×C₄	—	8	2	no	—
445	C₂×C₄	—	12	2	no	—
446	C₂×C₄	C₂×C₅×#67	1	2	yes	—
447	C₂×C₄	C₂×C₅×#67	1	2	yes	—
448	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
449	C₂×C₄	C₂×C₅×#67	1	1	yes	characteristic
450	C₂×C₄	C₂³×C₅×D₃	1	1	yes	characteristic
451	C₈	—	6	1	no	—
452	C₈	—	6	2	no	—
453	C₈	—	6	1	no	—
454	C₂×C₃	—	4	2	no	—
455	C₂×C₃	C₅×#548	1	1	yes	characteristic
456	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
457	C₂×C₃	C₅×#577	1	1	yes	characteristic
458	D₃	—	8	1	no	—
459	C₅	#83637	1	1	yes	characteristic, direct product factor, Sylow
460	C₂²	—	2	2	no	—
461	C₂²	—	4	1	no	—
462	C₂²	—	4	1	no	—
463	C₂²	—	12	1	no	—
464	C₂²	—	12	1	no	—
465	C₂²	—	12	1	no	—
466	C₂²	C₂²×C₅×#67	1	1	yes	characteristic
467	C₄	—	2	2	no	—
468	C₄	—	2	2	no	—
469	C₄	—	2	1	no	—
470	C₄	—	4	1	no	—
471	C₄	—	4	2	no	—
472	C₄	—	12	2	no	—
473	C₄	—	12	1	no	—
474	C₄	C₅×#950	1	2	yes	—
475	C₄	C₂×C₅×#239	1	1	yes	characteristic
476	C₄	C₅×#1007	1	1	yes	characteristic
477	C₃	C₅×#3360	1	1	yes	characteristic, complemented, Sylow
478	C₂	—	4	2	no	—
479	C₂	—	24	1	no	—
480	C₂	C₅×#5817	1	1	yes	characteristic
481	C₂	C₂×C₅×#950	1	1	yes	characteristic
482	C₂	C₅×#5836	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₅	C₂²×#67
commutator, cosocle	C₂×C₃×C₄	C₂⁴×C₅
Frattini	C₂×C₄	C₂³×C₅×D₃
Fitting	C₃×C₅×#554	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₅×#213	C₂²
hypercenter	C₅×#554	D₃
hypocenter	C₃	C₅×#3360
LCS	G ▷ C₂×C₃×C₄ ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₅ ◁ C₄×C₅×Q₈ ◁ C₅×#554

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#554	C₂	semidirect
2. C₅×#5584	C₂	semidirect
3. C₅×#5093	C₂	semidirect
4. C₅×#5084	C₂	semidirect
5. C₅×#5068	C₂	semidirect
6. C₅×#5063	C₂	semidirect
7. C₅×Q₈×C₃⋊C₈	C₂	semidirect
8. C₅×#5019	C₂	semidirect
9. C₄×C₅×#214	C₂	semidirect
42. #83637	C₅	direct (N × H)
44. C₅×#554	D₃	semidirect
86. C₃×#554	C₂×C₅	semidirect
87. #5584	C₂×C₅	semidirect
88. #5093	C₂×C₅	semidirect
89. #5084	C₂×C₅	semidirect
90. #5068	C₂×C₅	semidirect
91. #5063	C₂×C₅	semidirect
92. Q₈×C₃⋊C₈	C₂×C₅	semidirect
93. #5019	C₂×C₅	semidirect
94. C₄×#214	C₂×C₅	semidirect
214. #554	C₅×D₃	semidirect
406. C₃×C₅	#3360	semidirect
459. C₅	#83637	direct (N × H)
477. C₃	C₅×#3360	semidirect

Maximal subgroups

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

subgroup	index
C₃×C₅×#554	2
C₅×#5584	2
C₅×#5093	2
C₅×#5084	2
C₅×#5068	2
C₅×#5063	2
C₅×Q₈×C₃⋊C₈	2
C₅×#5019	2
C₄×C₅×#214	2
C₅×#5016	2
C₄×C₅×#213	2
C₅×#3360	3
#83637	5

Subgroups — C5×#83637 #14471597

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#83637 #14471597