Subgroups — C₅×#69401 #14279886

Order 1920.

1136 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#95	C₂	1	1	yes	maximal, characteristic
3	C₂×C₅×C₃⋊#95	C₂	1	2	yes	maximal
4	C₂×C₅×C₃⋊#95	C₂	1	2	yes	maximal
5	C₂×C₅×C₃⋊#95	C₂	1	1	yes	maximal, characteristic
6	C₅×#1434	—	3	1	no	maximal, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
8	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
9	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
10	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
11	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
12	C₂×C₄×C₅×Dic₃	—	2	4	no	—
13	C₂×C₄×C₅×Dic₃	C₄	1	4	yes	complemented
14	C₃×C₅×#95	C₄	1	4	yes	complemented
15	C₅×C₃⋊#95	—	2	4	no	—
16	C₅×C₃⋊#95	—	2	4	no	—
17	C₅×C₃⋊#95	C₄	1	4	yes	complemented
18	#69401	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₂²×C₄²×C₅	—	3	1	no	—
20	C₂×C₅×#95	—	3	1	no	—
21	C₂×C₅×#95	—	3	2	no	—
22	C₂×C₅×#95	—	3	2	no	—
23	C₂×C₅×#95	D₃	1	1	yes	characteristic
24	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
25	C₂²×C₃×C₄×C₅	—	2	2	no	—
26	C₂²×C₃×C₄×C₅	—	2	2	no	—
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	—	2	2	no	—
30	C₂²×C₃×C₄×C₅	—	2	2	no	—
31	C₂²×C₃×C₄×C₅	—	2	2	no	—
32	C₂²×C₃×C₄×C₅	—	2	2	no	—
33	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
34	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
35	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	2	yes	—
37	C₂²×C₅×Dic₃	—	2	2	no	—
38	C₂²×C₅×Dic₃	—	2	2	no	—
39	C₂²×C₅×Dic₃	—	2	2	no	—
40	C₂²×C₅×Dic₃	—	2	1	no	—
41	C₂²×C₅×Dic₃	—	2	1	no	—
42	C₂²×C₅×Dic₃	—	2	2	no	—
43	C₂²×C₅×Dic₃	—	2	2	no	—
44	C₂²×C₅×Dic₃	—	2	2	no	—
45	C₂²×C₅×Dic₃	—	2	2	no	—
46	C₂²×C₅×Dic₃	—	2	2	no	—
47	C₂²×C₅×Dic₃	—	2	2	no	—
48	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	—
49	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
50	C₂²×C₅×Dic₃	C₂×C₄	1	2	yes	—
51	C₂²×C₅×Dic₃	D₄	1	4	yes	—
52	C₂²×C₅×Dic₃	D₄	1	2	yes	—
53	C₂²×C₅×Dic₃	Q₈	1	2	yes	—
54	C₄×C₅×Dic₃	—	2	8	no	—
55	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic
56	C₂×C₃×#95	C₂×C₅	1	1	yes	characteristic
57	C₂×C₃⋊#95	C₂×C₅	1	2	yes	—
58	C₂×C₃⋊#95	C₂×C₅	1	2	yes	—
59	C₂×C₃⋊#95	C₂×C₅	1	1	yes	characteristic
60	C₂³×C₄×C₅	—	3	1	no	—
61	C₂³×C₄×C₅	—	3	1	no	—
62	C₂³×C₄×C₅	—	3	2	no	—
63	C₂³×C₄×C₅	C₂×D₃	1	2	yes	—
64	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
65	C₂×C₄²×C₅	—	3	4	no	—
66	C₂×C₄²×C₅	—	6	4	no	—
67	C₅×#95	—	3	4	no	—
68	C₅×#95	—	6	4	no	—
69	C₅×#95	—	6	4	no	—
70	C₅×#95	Dic₃	1	4	yes	complemented
71	#1434	—	3	1	no	Sylow
72	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
73	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
74	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
75	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
76	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
77	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
78	C₂³×C₃×C₅	#41	1	2	yes	—
79	C₂³×C₃×C₅	#41	1	2	yes	—
80	C₂³×C₃×C₅	#41	1	2	yes	—
81	C₂³×C₃×C₅	#41	1	1	yes	characteristic
82	C₂³×C₃×C₅	#41	1	1	yes	characteristic
83	C₂×C₃×C₄×C₅	—	2	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	4	no	—
86	C₂×C₃×C₄×C₅	—	2	4	no	—
87	C₂×C₃×C₄×C₅	—	2	4	no	—
88	C₂×C₃×C₄×C₅	—	2	4	no	—
89	C₂×C₃×C₄×C₅	—	2	4	no	—
90	C₂×C₃×C₄×C₅	—	4	2	no	—
91	C₂×C₃×C₄×C₅	—	4	2	no	—
92	C₂×C₃×C₄×C₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	C₄²	1	4	yes	—
95	C₂×C₅×Dic₃	—	2	2	no	—
96	C₂×C₅×Dic₃	—	2	2	no	—
97	C₂×C₅×Dic₃	—	2	2	no	—
98	C₂×C₅×Dic₃	—	2	2	no	—
99	C₂×C₅×Dic₃	—	2	4	no	—
100	C₂×C₅×Dic₃	—	2	4	no	—
101	C₂×C₅×Dic₃	—	2	4	no	—
102	C₂×C₅×Dic₃	—	2	4	no	—
103	C₂×C₅×Dic₃	—	2	4	no	—
104	C₂×C₅×Dic₃	—	2	4	no	—
105	C₂×C₅×Dic₃	—	2	4	no	—
106	C₂×C₅×Dic₃	—	4	2	no	—
107	C₂×C₅×Dic₃	—	4	2	no	—
108	C₂×C₅×Dic₃	—	4	2	no	—
109	C₂×C₅×Dic₃	—	4	2	no	—
110	C₂×C₅×Dic₃	C₂²⋊C₄	1	4	yes	—
111	C₂×C₅×Dic₃	C₄⋊C₄	1	4	yes	—
112	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
113	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
114	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
115	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
116	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
117	C₂×C₄×Dic₃	—	2	4	no	—
118	C₂×C₄×Dic₃	C₄×C₅	1	4	yes	complemented
119	C₃×#95	C₄×C₅	1	4	yes	complemented
120	C₃⋊#95	—	2	4	no	—
121	C₃⋊#95	—	2	4	no	—
122	C₃⋊#95	C₄×C₅	1	4	yes	complemented
123	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
124	C₂²×C₄×C₅	—	2	2	no	—
125	C₂²×C₄×C₅	—	2	2	no	—
126	C₂²×C₄×C₅	—	2	2	no	—
127	C₂²×C₄×C₅	—	2	2	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	—	2	2	no	—
130	C₂²×C₄×C₅	—	2	2	no	—
131	C₂²×C₄×C₅	—	2	2	no	—
132	C₂²×C₄×C₅	—	3	2	no	—
133	C₂²×C₄×C₅	—	3	2	no	—
134	C₂²×C₄×C₅	—	3	4	no	—
135	C₂²×C₄×C₅	—	3	2	no	—
136	C₂²×C₄×C₅	—	3	2	no	—
137	C₂²×C₄×C₅	—	3	4	no	—
138	C₂²×C₄×C₅	—	6	2	no	—
139	C₂²×C₄×C₅	—	6	2	no	—
140	C₂²×C₄×C₅	—	6	2	no	—
141	C₂²×C₄×C₅	—	6	1	no	—
142	C₂²×C₄×C₅	—	6	1	no	—
143	C₂²×C₄×C₅	—	6	2	no	—
144	C₂²×C₄×C₅	—	6	2	no	—
145	C₂²×C₄×C₅	—	6	2	no	—
146	C₂²×C₄×C₅	—	6	2	no	—
147	C₂²×C₄×C₅	—	6	2	no	—
148	C₂²×C₄×C₅	—	6	2	no	—
149	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
150	C₂²×C₄×C₅	C₄×D₃	1	2	yes	—
151	C₂²×C₄×C₅	C₂×Dic₃	1	4	yes	—
152	C₂²×C₄×C₅	C₂×Dic₃	1	2	yes	—
153	C₄²×C₅	—	6	8	no	—
154	C₂²×C₄²	—	3	1	no	—
155	C₂×#95	—	3	1	no	—
156	C₂×#95	—	3	2	no	—
157	C₂×#95	—	3	2	no	—
158	C₂×#95	C₅×D₃	1	1	yes	characteristic
159	C₂²×C₃×C₅	C₂×C₄²	1	1	yes	characteristic
160	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
161	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
162	C₂²×C₃×C₅	#117	1	1	yes	characteristic
163	C₂²×C₃×C₅	#117	1	1	yes	characteristic
164	C₂²×C₃×C₅	#117	1	2	yes	—
165	C₂²×C₃×C₅	#117	1	1	yes	characteristic
166	C₂²×C₃×C₅	#117	1	1	yes	characteristic
167	C₂²×C₃×C₅	#117	1	2	yes	—
168	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
169	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
170	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
171	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
172	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
173	C₂²×C₃×C₅	C₄×Q₈	1	1	yes	characteristic
174	C₂²×C₃×C₅	#121	1	2	yes	—
175	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
176	C₂²×C₃×C₅	#123	1	2	yes	—
177	C₂²×C₃×C₅	#123	1	2	yes	—
178	C₂²×C₃×C₅	#124	1	2	yes	—
179	C₂²×C₃×C₅	#125	1	2	yes	—
180	C₂²×C₃×C₅	#126	1	2	yes	—
181	C₂²×C₃×C₅	#126	1	2	yes	—
182	C₃×C₄×C₅	—	2	4	no	—
183	C₃×C₄×C₅	—	4	4	no	—
184	C₅×Dic₃	—	2	4	no	—
185	C₅×Dic₃	—	2	4	no	—
186	C₅×Dic₃	—	4	4	no	—
187	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	2	2	no	—
189	C₂²×C₃×C₄	—	2	2	no	—
190	C₂²×C₃×C₄	—	2	2	no	—
191	C₂²×C₃×C₄	—	2	2	no	—
192	C₂²×C₃×C₄	—	2	2	no	—
193	C₂²×C₃×C₄	—	2	2	no	—
194	C₂²×C₃×C₄	—	2	2	no	—
195	C₂²×C₃×C₄	—	2	2	no	—
196	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
197	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
198	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
199	C₂²×C₃×C₄	C₂×C₄×C₅	1	2	yes	—
200	C₂²×Dic₃	—	2	2	no	—
201	C₂²×Dic₃	—	2	2	no	—
202	C₂²×Dic₃	—	2	2	no	—
203	C₂²×Dic₃	—	2	1	no	—
204	C₂²×Dic₃	—	2	1	no	—
205	C₂²×Dic₃	—	2	2	no	—
206	C₂²×Dic₃	—	2	2	no	—
207	C₂²×Dic₃	—	2	2	no	—
208	C₂²×Dic₃	—	2	2	no	—
209	C₂²×Dic₃	—	2	2	no	—
210	C₂²×Dic₃	—	2	2	no	—
211	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	—
212	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
213	C₂²×Dic₃	C₂×C₄×C₅	1	2	yes	—
214	C₂²×Dic₃	C₅×D₄	1	4	yes	—
215	C₂²×Dic₃	C₅×D₄	1	2	yes	—
216	C₂²×Dic₃	C₅×Q₈	1	2	yes	—
217	C₄×Dic₃	—	2	8	no	—
218	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
219	C₂³×C₅	C₂×C₄×D₃	1	1	yes	characteristic
220	C₂³×C₅	#235	1	2	yes	—
221	C₂³×C₅	#235	1	2	yes	—
222	C₂³×C₅	D₃×D₄	1	2	yes	—
223	C₂³×C₅	D₃×D₄	1	1	yes	characteristic
224	C₂³×C₅	#237	1	2	yes	—
225	C₂³×C₅	#237	1	1	yes	characteristic
226	C₂³×C₅	D₃×Q₈	1	1	yes	characteristic
227	C₂³×C₅	#239	1	1	yes	characteristic
228	C₂³×C₅	C₂²×Dic₃	1	1	yes	characteristic
229	C₂×C₄×C₅	—	2	2	no	—
230	C₂×C₄×C₅	—	2	2	no	—
231	C₂×C₄×C₅	—	2	4	no	—
232	C₂×C₄×C₅	—	2	4	no	—
233	C₂×C₄×C₅	—	2	4	no	—
234	C₂×C₄×C₅	—	2	4	no	—
235	C₂×C₄×C₅	—	2	4	no	—
236	C₂×C₄×C₅	—	3	4	no	—
237	C₂×C₄×C₅	—	3	4	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	—	4	2	no	—
240	C₂×C₄×C₅	—	4	2	no	—
241	C₂×C₄×C₅	—	4	2	no	—
242	C₂×C₄×C₅	—	6	2	no	—
243	C₂×C₄×C₅	—	6	2	no	—
244	C₂×C₄×C₅	—	6	2	no	—
245	C₂×C₄×C₅	—	6	4	no	—
246	C₂×C₄×C₅	—	6	4	no	—
247	C₂×C₄×C₅	—	6	2	no	—
248	C₂×C₄×C₅	—	6	4	no	—
249	C₂×C₄×C₅	—	6	4	no	—
250	C₂×C₄×C₅	—	6	4	no	—
251	C₂×C₄×C₅	—	6	4	no	—
252	C₂×C₄×C₅	—	6	4	no	—
253	C₂×C₄×C₅	—	12	2	no	—
254	C₂×C₄×C₅	—	12	2	no	—
255	C₂×C₄×C₅	—	12	2	no	—
256	C₂×C₄×C₅	—	12	2	no	—
257	C₂×C₄×C₅	C₄×Dic₃	1	4	yes	—
258	C₂³×C₄	—	3	1	no	—
259	C₂³×C₄	—	3	1	no	—
260	C₂³×C₄	—	3	2	no	—
261	C₂³×C₄	C₂×C₅×D₃	1	2	yes	—
262	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
263	C₂×C₄²	—	3	4	no	—
264	C₂×C₄²	—	6	4	no	—
265	#95	—	3	4	no	—
266	#95	—	6	4	no	—
267	#95	—	6	4	no	—
268	#95	C₅×Dic₃	1	4	yes	complemented
269	C₂×C₃×C₅	#376	1	1	yes	characteristic
270	C₂×C₃×C₅	C₄×C₂²⋊C₄	1	1	yes	characteristic
271	C₂×C₃×C₅	C₄×C₄⋊C₄	1	1	yes	characteristic
272	C₂×C₃×C₅	#380	1	1	yes	characteristic
273	C₂×C₃×C₅	#381	1	1	yes	characteristic
274	C₂×C₃×C₅	#382	1	1	yes	characteristic
275	C₂×C₃×C₅	#383	1	1	yes	characteristic
276	C₂×C₃×C₅	#387	1	2	yes	—
277	C₂×C₃×C₅	#387	1	2	yes	—
278	C₂×C₃×C₅	#388	1	2	yes	—
279	C₂×C₃×C₅	#388	1	2	yes	—
280	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
281	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
282	C₂³×C₃	C₂²×C₄×C₅	1	1	yes	characteristic
283	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
284	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
285	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
286	C₂³×C₃	C₅×#41	1	2	yes	—
287	C₂³×C₃	C₅×#41	1	2	yes	—
288	C₂³×C₃	C₅×#41	1	2	yes	—
289	C₂³×C₃	C₅×#41	1	1	yes	characteristic
290	C₂³×C₃	C₅×#41	1	1	yes	characteristic
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	4	no	—
294	C₂×C₃×C₄	—	2	4	no	—
295	C₂×C₃×C₄	—	2	4	no	—
296	C₂×C₃×C₄	—	2	4	no	—
297	C₂×C₃×C₄	—	2	4	no	—
298	C₂×C₃×C₄	—	4	2	no	—
299	C₂×C₃×C₄	—	4	2	no	—
300	C₂×C₃×C₄	—	4	2	no	—
301	C₂×C₃×C₄	—	4	2	no	—
302	C₂×C₃×C₄	C₄²×C₅	1	4	yes	—
303	C₂×Dic₃	—	2	2	no	—
304	C₂×Dic₃	—	2	2	no	—
305	C₂×Dic₃	—	2	2	no	—
306	C₂×Dic₃	—	2	2	no	—
307	C₂×Dic₃	—	2	4	no	—
308	C₂×Dic₃	—	2	4	no	—
309	C₂×Dic₃	—	2	4	no	—
310	C₂×Dic₃	—	2	4	no	—
311	C₂×Dic₃	—	2	4	no	—
312	C₂×Dic₃	—	2	4	no	—
313	C₂×Dic₃	—	2	4	no	—
314	C₂×Dic₃	—	4	2	no	—
315	C₂×Dic₃	—	4	2	no	—
316	C₂×Dic₃	—	4	2	no	—
317	C₂×Dic₃	—	4	2	no	—
318	C₂×Dic₃	C₅×C₂²⋊C₄	1	4	yes	—
319	C₂×Dic₃	C₅×C₄⋊C₄	1	4	yes	—
320	C₂²×C₅	#872	1	1	yes	characteristic
321	C₂²×C₅	#872	1	1	yes	characteristic
322	C₂²×C₅	#872	1	2	yes	—
323	C₂²×C₅	#877	1	1	yes	characteristic
324	C₂²×C₅	#879	1	2	yes	—
325	C₂²×C₅	D₃×C₂²⋊C₄	1	1	yes	characteristic
326	C₂²×C₅	#67⋊C₄	1	2	yes	—
327	C₂²×C₅	#883	1	2	yes	—
328	C₂²×C₅	#884	1	2	yes	—
329	C₂²×C₅	#885	1	2	yes	—
330	C₂²×C₅	#887	1	1	yes	characteristic
331	C₂²×C₅	#889	1	2	yes	—
332	C₂²×C₅	D₃×C₄⋊C₄	1	1	yes	characteristic
333	C₂²×C₅	#892	1	1	yes	characteristic
334	C₂²×C₅	#893	1	1	yes	characteristic
335	C₂²×C₅	#894	1	2	yes	—
336	C₂²×C₅	#896	1	2	yes	—
337	C₂²×C₅	#898	1	2	yes	—
338	C₂²×C₅	C₂×C₄×Dic₃	1	1	yes	characteristic
339	C₂²×C₅	#926	1	2	yes	—
340	C₂²×C₅	D₄×Dic₃	1	2	yes	—
341	C₂²×C₅	D₄×Dic₃	1	1	yes	characteristic
342	C₂²×C₅	Q₈×Dic₃	1	1	yes	characteristic
343	C₄×C₅	—	2	4	no	—
344	C₄×C₅	—	4	4	no	—
345	C₄×C₅	—	6	4	no	—
346	C₄×C₅	—	6	4	no	—
347	C₄×C₅	—	12	4	no	—
348	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
349	C₂²×C₄	—	2	2	no	—
350	C₂²×C₄	—	2	2	no	—
351	C₂²×C₄	—	2	2	no	—
352	C₂²×C₄	—	2	2	no	—
353	C₂²×C₄	—	2	2	no	—
354	C₂²×C₄	—	2	2	no	—
355	C₂²×C₄	—	2	2	no	—
356	C₂²×C₄	—	2	2	no	—
357	C₂²×C₄	—	3	2	no	—
358	C₂²×C₄	—	3	2	no	—
359	C₂²×C₄	—	3	2	no	—
360	C₂²×C₄	—	3	4	no	—
361	C₂²×C₄	—	3	2	no	—
362	C₂²×C₄	—	3	4	no	—
363	C₂²×C₄	—	6	2	no	—
364	C₂²×C₄	—	6	2	no	—
365	C₂²×C₄	—	6	2	no	—
366	C₂²×C₄	—	6	1	no	—
367	C₂²×C₄	—	6	1	no	—
368	C₂²×C₄	—	6	2	no	—
369	C₂²×C₄	—	6	2	no	—
370	C₂²×C₄	—	6	2	no	—
371	C₂²×C₄	—	6	2	no	—
372	C₂²×C₄	—	6	2	no	—
373	C₂²×C₄	—	6	2	no	—
374	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
375	C₂²×C₄	C₄×C₅×D₃	1	2	yes	—
376	C₂²×C₄	C₂×C₅×Dic₃	1	4	yes	—
377	C₂²×C₄	C₂×C₅×Dic₃	1	2	yes	—
378	C₄²	—	6	8	no	—
379	C₃×C₅	#1434	1	1	yes	characteristic, complemented, Hall
380	C₂²×C₃	C₂×C₄²×C₅	1	1	yes	characteristic
381	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
382	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
383	C₂²×C₃	C₅×#117	1	1	yes	characteristic
384	C₂²×C₃	C₅×#117	1	1	yes	characteristic
385	C₂²×C₃	C₅×#117	1	2	yes	—
386	C₂²×C₃	C₅×#117	1	1	yes	characteristic
387	C₂²×C₃	C₅×#117	1	1	yes	characteristic
388	C₂²×C₃	C₅×#117	1	2	yes	—
389	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
390	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
391	C₂²×C₃	C₄×C₅×D₄	1	2	yes	—
392	C₂²×C₃	C₄×C₅×D₄	1	1	yes	characteristic
393	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
394	C₂²×C₃	C₄×C₅×Q₈	1	1	yes	characteristic
395	C₂²×C₃	C₅×#121	1	2	yes	—
396	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
397	C₂²×C₃	C₅×#123	1	2	yes	—
398	C₂²×C₃	C₅×#123	1	2	yes	—
399	C₂²×C₃	C₅×#124	1	2	yes	—
400	C₂²×C₃	C₅×#125	1	2	yes	—
401	C₂²×C₃	C₅×#126	1	2	yes	—
402	C₂²×C₃	C₅×#126	1	2	yes	—
403	C₃×C₄	—	2	4	no	—
404	C₃×C₄	—	4	4	no	—
405	Dic₃	—	2	4	no	—
406	Dic₃	—	2	4	no	—
407	Dic₃	—	4	4	no	—
408	C₂×C₅	#4650	1	1	yes	characteristic
409	C₂×C₅	#4651	1	1	yes	characteristic
410	C₂×C₅	#4652	1	2	yes	—
411	C₂×C₅	#4664	1	1	yes	characteristic
412	C₂×C₅	#4667	1	1	yes	characteristic
413	C₂×C₅	#4669	1	2	yes	—
414	C₂×C₅	#4932	1	1	yes	characteristic
415	C₂×C₅	Dic₃×C₂²⋊C₄	1	1	yes	characteristic
416	C₂×C₅	#4951	1	2	yes	—
417	C₂×C₅	Dic₃×C₄⋊C₄	1	1	yes	characteristic
418	C₂×C₅	#4980	1	2	yes	—
419	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
420	C₂³	C₂×C₄×C₅×D₃	1	1	yes	characteristic
421	C₂³	C₅×#235	1	2	yes	—
422	C₂³	C₅×#235	1	2	yes	—
423	C₂³	C₅×D₃×D₄	1	2	yes	—
424	C₂³	C₅×D₃×D₄	1	1	yes	characteristic
425	C₂³	C₅×#237	1	2	yes	—
426	C₂³	C₅×#237	1	1	yes	characteristic
427	C₂³	C₅×D₃×Q₈	1	1	yes	characteristic
428	C₂³	C₅×#239	1	1	yes	characteristic
429	C₂³	C₂²×C₅×Dic₃	1	1	yes	characteristic
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	4	no	—
433	C₂×C₄	—	2	4	no	—
434	C₂×C₄	—	2	4	no	—
435	C₂×C₄	—	2	4	no	—
436	C₂×C₄	—	2	4	no	—
437	C₂×C₄	—	3	4	no	—
438	C₂×C₄	—	3	4	no	—
439	C₂×C₄	—	4	2	no	—
440	C₂×C₄	—	4	2	no	—
441	C₂×C₄	—	4	2	no	—
442	C₂×C₄	—	4	2	no	—
443	C₂×C₄	—	6	2	no	—
444	C₂×C₄	—	6	2	no	—
445	C₂×C₄	—	6	2	no	—
446	C₂×C₄	—	6	4	no	—
447	C₂×C₄	—	6	4	no	—
448	C₂×C₄	—	6	2	no	—
449	C₂×C₄	—	6	4	no	—
450	C₂×C₄	—	6	4	no	—
451	C₂×C₄	—	6	4	no	—
452	C₂×C₄	—	6	4	no	—
453	C₂×C₄	—	6	4	no	—
454	C₂×C₄	—	12	2	no	—
455	C₂×C₄	—	12	2	no	—
456	C₂×C₄	—	12	2	no	—
457	C₂×C₄	—	12	2	no	—
458	C₂×C₄	C₄×C₅×Dic₃	1	4	yes	—
459	C₂×C₃	C₅×#376	1	1	yes	characteristic
460	C₂×C₃	C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic
461	C₂×C₃	C₄×C₅×C₄⋊C₄	1	1	yes	characteristic
462	C₂×C₃	C₅×#380	1	1	yes	characteristic
463	C₂×C₃	C₅×#381	1	1	yes	characteristic
464	C₂×C₃	C₅×#382	1	1	yes	characteristic
465	C₂×C₃	C₅×#383	1	1	yes	characteristic
466	C₂×C₃	C₅×#387	1	2	yes	—
467	C₂×C₃	C₅×#387	1	2	yes	—
468	C₂×C₃	C₅×#388	1	2	yes	—
469	C₂×C₃	C₅×#388	1	2	yes	—
470	C₅	#69401	1	1	yes	characteristic, direct product factor, Sylow
471	C₂²	C₅×#872	1	1	yes	characteristic
472	C₂²	C₅×#872	1	1	yes	characteristic
473	C₂²	C₅×#872	1	2	yes	—
474	C₂²	C₅×#877	1	1	yes	characteristic
475	C₂²	C₅×#879	1	2	yes	—
476	C₂²	C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
477	C₂²	C₅×#67⋊C₄	1	2	yes	—
478	C₂²	C₅×#883	1	2	yes	—
479	C₂²	C₅×#884	1	2	yes	—
480	C₂²	C₅×#885	1	2	yes	—
481	C₂²	C₅×#887	1	1	yes	characteristic
482	C₂²	C₅×#889	1	2	yes	—
483	C₂²	C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
484	C₂²	C₅×#892	1	1	yes	characteristic
485	C₂²	C₅×#893	1	1	yes	characteristic
486	C₂²	C₅×#894	1	2	yes	—
487	C₂²	C₅×#896	1	2	yes	—
488	C₂²	C₅×#898	1	2	yes	—
489	C₂²	C₂×C₄×C₅×Dic₃	1	1	yes	characteristic
490	C₂²	C₅×#926	1	2	yes	—
491	C₂²	C₅×D₄×Dic₃	1	2	yes	—
492	C₂²	C₅×D₄×Dic₃	1	1	yes	characteristic
493	C₂²	C₅×Q₈×Dic₃	1	1	yes	characteristic
494	C₄	—	2	4	no	—
495	C₄	—	4	4	no	—
496	C₄	—	6	4	no	—
497	C₄	—	6	4	no	—
498	C₄	—	12	4	no	—
499	C₃	C₅×#1434	1	1	yes	characteristic, complemented, Sylow
500	C₂	C₅×#4650	1	1	yes	characteristic
501	C₂	C₅×#4651	1	1	yes	characteristic
502	C₂	C₅×#4652	1	2	yes	—
503	C₂	C₅×#4664	1	1	yes	characteristic
504	C₂	C₅×#4667	1	1	yes	characteristic
505	C₂	C₅×#4669	1	2	yes	—
506	C₂	C₅×#4932	1	1	yes	characteristic
507	C₂	C₅×Dic₃×C₂²⋊C₄	1	1	yes	characteristic
508	C₂	C₅×#4951	1	2	yes	—
509	C₂	C₅×Dic₃×C₄⋊C₄	1	1	yes	characteristic
510	C₂	C₅×#4980	1	2	yes	—

	subgroup	G/H
center	C₂⁴×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂×C₄²×C₅
Frattini	C₂⁴	C₂²×C₅×D₃
Fitting	C₂×C₃×C₅×#95	C₂
socle, prime radical	C₂⁴×C₃×C₅	C₂³
cosocle	C₂⁴×C₃	C₂³×C₅
hypercenter	C₂×C₅×#95	D₃
hypocenter	C₃	C₅×#1434
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂⁴×C₅ ◁ C₂×C₅×#95

Complements

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

N	H ≅ G/N	type
13. C₂×C₄×C₅×Dic₃	C₄	semidirect
14. C₃×C₅×#95	C₄	semidirect
17. C₅×C₃⋊#95	C₄	semidirect
18. #69401	C₅	direct (N × H)
70. C₅×#95	Dic₃	semidirect
118. C₂×C₄×Dic₃	C₄×C₅	semidirect
119. C₃×#95	C₄×C₅	semidirect
122. C₃⋊#95	C₄×C₅	semidirect
268. #95	C₅×Dic₃	semidirect
379. C₃×C₅	#1434	semidirect
470. C₅	#69401	direct (N × H)
499. C₃	C₅×#1434	semidirect

Maximal subgroups

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

subgroup	index
C₂²×C₄×C₅×Dic₃	2
C₂×C₃×C₅×#95	2
C₂×C₅×C₃⋊#95	2
C₅×#1434	3
#69401	5

Subgroups — C5×#69401 #14279886

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#69401 #14279886