Subgroups — C₅×#73755 #14321078

Order 1920.

1312 conjugacy classes of subgroups.

The subgroup lattice has 532 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×#872	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic
4	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₅×#4989	C₂	1	2	yes	maximal
6	C₅×#4976	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×C₄⋊Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4668	C₂	1	2	yes	maximal
11	C₅×#4647	C₂	1	2	yes	maximal, complemented
12	C₅×#2296	—	3	1	no	maximal, Hall
13	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
14	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
20	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
22	C₂×C₅×C₄⋊Dic₃	C₂²	1	2	yes	—
23	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
24	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
26	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
28	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
30	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
32	C₅×#872	—	2	4	no	—
33	C₅×#872	C₄	1	8	yes	complemented
34	C₄²×C₅×D₃	—	2	4	no	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₅×C₃⋊#95	C₂²	1	2	yes	—
37	C₅×C₃⋊#95	C₂²	1	2	yes	—
38	C₅×C₃⋊#95	C₂²	1	2	yes	—
39	#73755	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×#117	—	3	1	no	—
41	C₂×C₅×#117	—	3	1	no	—
42	C₂²×C₄²×C₅	—	3	1	no	—
43	C₅×#389	—	3	2	no	—
44	C₅×#389	—	3	2	no	—
45	C₅×#385	—	3	2	no	—
46	C₅×#385	—	3	2	no	—
47	C₄×C₅×C₄⋊C₄	—	3	1	no	—
48	C₄×C₅×C₄⋊C₄	—	3	1	no	—
49	C₄×C₅×C₄⋊C₄	—	3	1	no	—
50	C₄×C₅×C₄⋊C₄	D₃	1	1	yes	characteristic, complemented
51	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
60	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
61	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
62	C₂×C₄×C₅×D₃	—	2	4	no	—
63	C₂×C₄×C₅×D₃	—	2	4	no	—
64	C₂×C₄×C₅×D₃	—	2	4	no	—
65	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
66	C₂×C₄×C₅×D₃	D₄	1	4	yes	—
67	C₂×C₄×C₅×D₃	Q₈	1	4	yes	—
68	C₃×C₅×C₄⋊C₄	—	2	4	no	—
69	C₃×C₄²×C₅	—	2	2	no	—
70	C₃×C₄²×C₅	—	2	2	no	—
71	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
72	C₅×(C₂×D₃)⋊C₄	—	2	4	no	—
73	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
74	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	—
75	C₅×C₄⋊Dic₃	—	2	4	no	—
76	C₅×Dic₃⋊C₄	—	2	4	no	—
77	C₅×Dic₃⋊C₄	—	2	4	no	—
78	C₅×Dic₃⋊C₄	—	2	4	no	—
79	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
80	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
81	C₄×C₅×Dic₃	—	2	2	no	—
82	C₄×C₅×Dic₃	—	2	2	no	—
83	C₄×C₅×Dic₃	—	2	4	no	—
84	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
85	C₂×#872	C₂×C₅	1	1	yes	characteristic
86	C₂×#872	C₂×C₅	1	1	yes	characteristic
87	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic
88	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
89	#4989	C₂×C₅	1	2	yes	—
90	#4976	C₂×C₅	1	2	yes	complemented
91	C₄×C₄⋊Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
92	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
93	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
94	#4668	C₂×C₅	1	2	yes	—
95	#4647	C₂×C₅	1	2	yes	complemented
96	C₂³×C₄×C₅	—	3	1	no	—
97	C₂³×C₄×C₅	—	3	2	no	—
98	C₅×#117	—	3	8	no	—
99	C₅×#117	—	6	4	no	—
100	C₂×C₅×C₄⋊C₄	—	3	1	no	—
101	C₂×C₅×C₄⋊C₄	—	3	1	no	—
102	C₂×C₅×C₄⋊C₄	—	3	2	no	—
103	C₂×C₅×C₄⋊C₄	—	3	2	no	—
104	C₂×C₅×C₄⋊C₄	—	3	2	no	—
105	C₂×C₅×C₄⋊C₄	—	3	2	no	—
106	C₂×C₅×C₄⋊C₄	C₂×D₃	1	2	yes	—
107	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
108	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
109	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
110	C₂×C₄²×C₅	—	3	1	no	—
111	C₂×C₄²×C₅	—	3	2	no	—
112	C₂×C₄²×C₅	—	3	1	no	—
113	C₂×C₄²×C₅	—	3	1	no	—
114	C₂×C₄²×C₅	—	6	4	no	—
115	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
118	C₅×#95	—	3	2	no	—
119	C₅×#95	—	3	2	no	—
120	C₅×#95	—	3	2	no	—
121	C₅×#95	C₂×D₃	1	2	yes	—
122	#2296	—	3	1	no	Sylow
123	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
124	C₂²×C₅×D₃	—	2	2	no	—
125	C₂²×C₅×D₃	—	2	2	no	—
126	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
127	C₂²×C₅×D₃	C₂×D₄	1	2	yes	—
128	C₂²×C₅×D₃	C₂×Q₈	1	2	yes	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
141	C₂×C₃×C₄×C₅	#41	1	4	yes	—
142	C₂×C₅×Dic₃	—	2	2	no	—
143	C₂×C₅×Dic₃	—	2	2	no	—
144	C₂×C₅×Dic₃	—	2	2	no	—
145	C₂×C₅×Dic₃	—	2	2	no	—
146	C₂×C₅×Dic₃	—	2	2	no	—
147	C₂×C₅×Dic₃	—	2	2	no	—
148	C₂×C₅×Dic₃	—	2	2	no	—
149	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
150	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
151	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
152	C₂×C₅×Dic₃	C₂×D₄	1	2	yes	—
153	C₂×C₅×Dic₃	C₂×Q₈	1	2	yes	—
154	C₂×C₅×Dic₃	#41	1	4	yes	—
155	C₄×C₅×D₃	—	2	16	no	—
156	C₄×C₅×D₃	C₄⋊C₄	1	16	yes	complemented
157	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
158	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
162	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
163	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₄⋊Dic₃	C₂²×C₅	1	2	yes	—
167	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
168	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
169	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
170	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
171	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
173	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
176	#872	—	2	4	no	—
177	#872	C₄×C₅	1	8	yes	complemented
178	C₄²×D₃	—	2	4	no	—
179	C₃×#95	C₂²×C₅	1	2	yes	—
180	C₃⋊#95	C₂²×C₅	1	2	yes	—
181	C₃⋊#95	C₂²×C₅	1	2	yes	—
182	C₃⋊#95	C₂²×C₅	1	2	yes	—
183	C₂⁴×C₅	—	3	1	no	—
184	C₂²×C₄×C₅	—	3	1	no	—
185	C₂²×C₄×C₅	—	3	4	no	—
186	C₂²×C₄×C₅	—	3	4	no	—
187	C₂²×C₄×C₅	—	3	4	no	—
188	C₂²×C₄×C₅	—	3	2	no	—
189	C₂²×C₄×C₅	—	3	1	no	—
190	C₂²×C₄×C₅	—	3	1	no	—
191	C₂²×C₄×C₅	—	3	2	no	—
192	C₂²×C₄×C₅	—	6	4	no	—
193	C₂²×C₄×C₅	—	6	4	no	—
194	C₂²×C₄×C₅	—	6	4	no	—
195	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
196	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
197	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
198	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
199	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
200	C₅×C₄⋊C₄	—	2	4	no	—
201	C₅×C₄⋊C₄	—	3	4	no	—
202	C₅×C₄⋊C₄	—	3	4	no	—
203	C₅×C₄⋊C₄	—	6	4	no	—
204	C₅×C₄⋊C₄	—	6	4	no	—
205	C₅×C₄⋊C₄	—	6	4	no	—
206	C₅×C₄⋊C₄	—	6	4	no	—
207	C₅×C₂²⋊C₄	—	3	4	no	—
208	C₅×C₂²⋊C₄	—	3	4	no	—
209	C₅×C₂²⋊C₄	—	6	4	no	—
210	C₄²×C₅	—	2	2	no	—
211	C₄²×C₅	—	2	2	no	—
212	C₄²×C₅	—	3	4	no	—
213	C₄²×C₅	—	6	4	no	—
214	C₄²×C₅	—	6	2	no	—
215	C₄²×C₅	—	6	2	no	—
216	C₄²×C₅	C₄×D₃	1	4	yes	complemented
217	C₂×#117	—	3	1	no	—
218	C₂×#117	—	3	1	no	—
219	C₂²×C₄²	—	3	1	no	—
220	#389	—	3	2	no	—
221	#389	—	3	2	no	—
222	#385	—	3	2	no	—
223	#385	—	3	2	no	—
224	C₄×C₄⋊C₄	—	3	1	no	—
225	C₄×C₄⋊C₄	—	3	1	no	—
226	C₄×C₄⋊C₄	—	3	1	no	—
227	C₄×C₄⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
228	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
229	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
230	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
231	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
232	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
233	C₂×C₅×D₃	—	2	2	no	—
234	C₂×C₅×D₃	—	2	2	no	—
235	C₂×C₅×D₃	—	2	4	no	—
236	C₂×C₅×D₃	—	2	4	no	—
237	C₂×C₅×D₃	C₂×C₄⋊C₄	1	4	yes	—
238	C₃×C₄×C₅	—	2	2	no	—
239	C₃×C₄×C₅	—	2	2	no	—
240	C₃×C₄×C₅	—	2	4	no	—
241	C₃×C₄×C₅	—	4	2	no	—
242	C₃×C₄×C₅	C₂×C₄⋊C₄	1	4	yes	—
243	C₅×Dic₃	—	2	2	no	—
244	C₅×Dic₃	—	2	2	no	—
245	C₅×Dic₃	—	2	4	no	—
246	C₅×Dic₃	—	4	2	no	—
247	C₅×Dic₃	C₂×C₄⋊C₄	1	4	yes	—
248	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
250	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
253	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
255	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
256	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
257	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
258	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
259	C₂×C₄×D₃	—	2	4	no	—
260	C₂×C₄×D₃	—	2	4	no	—
261	C₂×C₄×D₃	—	2	4	no	—
262	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
263	C₂×C₄×D₃	C₅×D₄	1	4	yes	—
264	C₂×C₄×D₃	C₅×Q₈	1	4	yes	—
265	C₃×C₄⋊C₄	—	2	4	no	—
266	C₃×C₄²	—	2	2	no	—
267	C₃×C₄²	—	2	2	no	—
268	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
269	(C₂×D₃)⋊C₄	—	2	4	no	—
270	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
271	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	—
272	C₄⋊Dic₃	—	2	4	no	—
273	Dic₃⋊C₄	—	2	4	no	—
274	Dic₃⋊C₄	—	2	4	no	—
275	Dic₃⋊C₄	—	2	4	no	—
276	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
277	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
278	C₄×Dic₃	—	2	2	no	—
279	C₄×Dic₃	—	2	2	no	—
280	C₄×Dic₃	—	2	4	no	—
281	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
282	C₂³×C₅	—	3	2	no	—
283	C₂³×C₅	—	3	2	no	—
284	C₂³×C₅	—	3	2	no	—
285	C₂³×C₅	—	6	2	no	—
286	C₂³×C₅	—	6	2	no	—
287	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	2	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	3	2	no	—
296	C₂×C₄×C₅	—	3	2	no	—
297	C₂×C₄×C₅	—	3	2	no	—
298	C₂×C₄×C₅	—	3	16	no	—
299	C₂×C₄×C₅	—	3	2	no	—
300	C₂×C₄×C₅	—	3	2	no	—
301	C₂×C₄×C₅	—	3	4	no	—
302	C₂×C₄×C₅	—	6	16	no	—
303	C₂×C₄×C₅	—	6	2	no	—
304	C₂×C₄×C₅	—	6	2	no	—
305	C₂×C₄×C₅	—	6	2	no	—
306	C₂×C₄×C₅	—	6	2	no	—
307	C₂×C₄×C₅	—	6	2	no	—
308	C₂×C₄×C₅	—	6	2	no	—
309	C₂×C₄×C₅	—	6	2	no	—
310	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
311	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
312	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
313	C₂×C₄×C₅	#235	1	4	yes	—
314	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
315	C₂×C₄×C₅	D₃×Q₈	1	2	yes	—
316	C₂³×C₄	—	3	1	no	—
317	C₂³×C₄	—	3	2	no	—
318	#117	—	3	8	no	—
319	#117	—	6	4	no	—
320	C₂×C₄⋊C₄	—	3	1	no	—
321	C₂×C₄⋊C₄	—	3	1	no	—
322	C₂×C₄⋊C₄	—	3	2	no	—
323	C₂×C₄⋊C₄	—	3	2	no	—
324	C₂×C₄⋊C₄	—	3	2	no	—
325	C₂×C₄⋊C₄	—	3	2	no	—
326	C₂×C₄⋊C₄	C₂×C₅×D₃	1	2	yes	—
327	C₂×C₂²⋊C₄	—	3	1	no	—
328	C₂×C₂²⋊C₄	—	3	1	no	—
329	C₂×C₂²⋊C₄	—	3	2	no	—
330	C₂×C₄²	—	3	1	no	—
331	C₂×C₄²	—	3	1	no	—
332	C₂×C₄²	—	3	1	no	—
333	C₂×C₄²	—	3	2	no	—
334	C₂×C₄²	—	6	4	no	—
335	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
336	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
337	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
338	#95	—	3	2	no	—
339	#95	—	3	2	no	—
340	#95	—	3	2	no	—
341	#95	C₂×C₅×D₃	1	2	yes	—
342	C₂×C₃×C₅	C₂²×C₄⋊C₄	1	1	yes	characteristic
343	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
344	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
345	C₂×C₃×C₅	#525	1	2	yes	—
346	C₂×C₃×C₅	#533	1	2	yes	—
347	C₅×D₃	—	2	4	no	—
348	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
349	C₂²×D₃	—	2	2	no	—
350	C₂²×D₃	—	2	2	no	—
351	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
352	C₂²×D₃	C₂×C₅×D₄	1	2	yes	—
353	C₂²×D₃	C₂×C₅×Q₈	1	2	yes	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
362	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
363	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
365	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
366	C₂×C₃×C₄	C₅×#41	1	4	yes	—
367	C₂×Dic₃	—	2	2	no	—
368	C₂×Dic₃	—	2	2	no	—
369	C₂×Dic₃	—	2	2	no	—
370	C₂×Dic₃	—	2	2	no	—
371	C₂×Dic₃	—	2	2	no	—
372	C₂×Dic₃	—	2	2	no	—
373	C₂×Dic₃	—	2	2	no	—
374	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
375	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
376	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
377	C₂×Dic₃	C₂×C₅×D₄	1	2	yes	—
378	C₂×Dic₃	C₂×C₅×Q₈	1	2	yes	—
379	C₂×Dic₃	C₅×#41	1	4	yes	—
380	C₄×D₃	—	2	16	no	—
381	C₄×D₃	C₅×C₄⋊C₄	1	16	yes	complemented
382	C₂²×C₅	—	3	4	no	—
383	C₂²×C₅	—	6	2	no	—
384	C₂²×C₅	—	6	2	no	—
385	C₂²×C₅	—	6	4	no	—
386	C₂²×C₅	—	6	4	no	—
387	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
388	C₂²×C₅	C₂×#235	1	2	yes	—
389	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
390	C₂²×C₅	C₂×D₃×Q₈	1	1	yes	characteristic
391	C₂²×C₅	D₃×#41	1	2	yes	—
392	C₄×C₅	—	2	2	no	—
393	C₄×C₅	—	2	2	no	—
394	C₄×C₅	—	2	4	no	—
395	C₄×C₅	—	3	4	no	—
396	C₄×C₅	—	4	2	no	—
397	C₄×C₅	—	6	2	no	—
398	C₄×C₅	—	6	2	no	—
399	C₄×C₅	—	6	4	no	—
400	C₄×C₅	—	12	2	no	—
401	C₄×C₅	D₃×C₄⋊C₄	1	4	yes	—
402	C₂⁴	—	3	1	no	—
403	C₂²×C₄	—	3	1	no	—
404	C₂²×C₄	—	3	4	no	—
405	C₂²×C₄	—	3	4	no	—
406	C₂²×C₄	—	3	4	no	—
407	C₂²×C₄	—	3	2	no	—
408	C₂²×C₄	—	3	1	no	—
409	C₂²×C₄	—	3	1	no	—
410	C₂²×C₄	—	3	2	no	—
411	C₂²×C₄	—	6	4	no	—
412	C₂²×C₄	—	6	4	no	—
413	C₂²×C₄	—	6	4	no	—
414	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
415	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
416	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
417	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
418	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
419	C₄⋊C₄	—	2	4	no	—
420	C₄⋊C₄	—	3	4	no	—
421	C₄⋊C₄	—	3	4	no	—
422	C₄⋊C₄	—	6	4	no	—
423	C₄⋊C₄	—	6	4	no	—
424	C₄⋊C₄	—	6	4	no	—
425	C₄⋊C₄	—	6	4	no	—
426	C₂²⋊C₄	—	3	4	no	—
427	C₂²⋊C₄	—	3	4	no	—
428	C₂²⋊C₄	—	6	4	no	—
429	C₄²	—	2	2	no	—
430	C₄²	—	2	2	no	—
431	C₄²	—	3	4	no	—
432	C₄²	—	6	4	no	—
433	C₄²	—	6	2	no	—
434	C₄²	—	6	2	no	—
435	C₄²	C₄×C₅×D₃	1	4	yes	complemented
436	C₃×C₅	#2296	1	1	yes	characteristic, complemented, Hall
437	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
438	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
439	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
440	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
441	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
442	C₂×D₃	—	2	2	no	—
443	C₂×D₃	—	2	2	no	—
444	C₂×D₃	—	2	4	no	—
445	C₂×D₃	—	2	4	no	—
446	C₂×D₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	2	2	no	—
449	C₃×C₄	—	2	4	no	—
450	C₃×C₄	—	4	2	no	—
451	C₃×C₄	C₂×C₅×C₄⋊C₄	1	4	yes	—
452	Dic₃	—	2	2	no	—
453	Dic₃	—	2	2	no	—
454	Dic₃	—	2	4	no	—
455	Dic₃	—	4	2	no	—
456	Dic₃	C₂×C₅×C₄⋊C₄	1	4	yes	—
457	C₂×C₅	—	6	4	no	—
458	C₂×C₅	C₄×#235	1	1	yes	characteristic
459	C₂×C₅	C₂×D₃×C₄⋊C₄	1	1	yes	characteristic
460	C₂×C₅	#5522	1	1	yes	characteristic
461	C₂×C₅	#5547	1	2	yes	—
462	C₂×C₅	#5578	1	2	yes	—
463	C₂³	—	3	2	no	—
464	C₂³	—	3	2	no	—
465	C₂³	—	3	2	no	—
466	C₂³	—	6	2	no	—
467	C₂³	—	6	2	no	—
468	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	2	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	2	no	—
474	C₂×C₄	—	2	2	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	3	2	no	—
477	C₂×C₄	—	3	2	no	—
478	C₂×C₄	—	3	2	no	—
479	C₂×C₄	—	3	16	no	—
480	C₂×C₄	—	3	2	no	—
481	C₂×C₄	—	3	2	no	—
482	C₂×C₄	—	3	4	no	—
483	C₂×C₄	—	6	16	no	—
484	C₂×C₄	—	6	2	no	—
485	C₂×C₄	—	6	2	no	—
486	C₂×C₄	—	6	2	no	—
487	C₂×C₄	—	6	2	no	—
488	C₂×C₄	—	6	2	no	—
489	C₂×C₄	—	6	2	no	—
490	C₂×C₄	—	6	2	no	—
491	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
492	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
493	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
494	C₂×C₄	C₅×#235	1	4	yes	—
495	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
496	C₂×C₄	C₅×D₃×Q₈	1	2	yes	—
497	C₂×C₃	C₂²×C₅×C₄⋊C₄	1	1	yes	characteristic
498	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
499	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
500	C₂×C₃	C₅×#525	1	2	yes	—
501	C₂×C₃	C₅×#533	1	2	yes	—
502	D₃	—	2	4	no	—
503	C₅	#73755	1	1	yes	characteristic, direct product factor, Sylow
504	C₂²	—	3	4	no	—
505	C₂²	—	6	2	no	—
506	C₂²	—	6	2	no	—
507	C₂²	—	6	4	no	—
508	C₂²	—	6	4	no	—
509	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
510	C₂²	C₂×C₅×#235	1	2	yes	—
511	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
512	C₂²	C₂×C₅×D₃×Q₈	1	1	yes	characteristic
513	C₂²	C₅×D₃×#41	1	2	yes	—
514	C₄	—	2	2	no	—
515	C₄	—	2	2	no	—
516	C₄	—	2	4	no	—
517	C₄	—	3	4	no	—
518	C₄	—	4	2	no	—
519	C₄	—	6	2	no	—
520	C₄	—	6	2	no	—
521	C₄	—	6	4	no	—
522	C₄	—	12	2	no	—
523	C₄	C₅×D₃×C₄⋊C₄	1	4	yes	—
524	C₃	C₅×#2296	1	1	yes	characteristic, complemented, Sylow
525	C₂	—	6	4	no	—
526	C₂	C₄×C₅×#235	1	1	yes	characteristic
527	C₂	C₂×C₅×D₃×C₄⋊C₄	1	1	yes	characteristic
528	C₂	C₅×#5522	1	1	yes	characteristic
529	C₂	C₅×#5547	1	2	yes	—
530	C₂	C₅×#5578	1	2	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂²×C₃	C₂³×C₄×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₄⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂³×C₅×D₃	C₂³
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₄⋊C₄	D₃
hypocenter	C₃	C₅×#2296
LCS	G ▷ C₂²×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
6. C₅×#4976	C₂	semidirect
7. C₄×C₅×C₄⋊Dic₃	C₂	semidirect
8. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
9. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
11. C₅×#4647	C₂	semidirect
33. C₅×#872	C₄	semidirect
39. #73755	C₅	direct (N × H)
50. C₄×C₅×C₄⋊C₄	D₃	semidirect
71. C₃×C₄²×C₅	C₂×C₄	semidirect
79. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
80. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
84. C₄×C₅×Dic₃	C₂×C₄	semidirect
88. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
90. #4976	C₂×C₅	semidirect
91. C₄×C₄⋊Dic₃	C₂×C₅	semidirect
92. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
93. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
95. #4647	C₂×C₅	semidirect
156. C₄×C₅×D₃	C₄⋊C₄	semidirect
177. #872	C₄×C₅	semidirect
216. C₄²×C₅	C₄×D₃	semidirect
227. C₄×C₄⋊C₄	C₅×D₃	semidirect
268. C₃×C₄²	C₂×C₄×C₅	semidirect
276. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
277. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
281. C₄×Dic₃	C₂×C₄×C₅	semidirect
381. C₄×D₃	C₅×C₄⋊C₄	semidirect
435. C₄²	C₄×C₅×D₃	semidirect
436. C₃×C₅	#2296	semidirect
503. C₅	#73755	direct (N × H)
524. C₃	C₅×#2296	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₅×#872	2
C₂×C₄²×C₅×D₃	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#4989	2
C₅×#4976	2
C₄×C₅×C₄⋊Dic₃	2
C₄×C₅×Dic₃⋊C₄	2
C₅×#4668	2
C₅×#4647	2
C₅×#2296	3
#73755	5

Subgroups — C5×#73755 #14321078

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₅×#73755 #14321078