Subgroups — C₃×C₅×#2722 #14275756

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 440 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#126	C₂	1	2	yes	maximal
2	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#397	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#385	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#380	C₂	1	2	yes	maximal
10	C₅×#2722	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
12	C₃×C₅×#126	—	2	8	no	—
13	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₃×C₅×#95	C₂²	1	2	yes	—
27	C₃×C₅×#95	C₂²	1	2	yes	—
28	C₃×C₅×#95	C₂²	1	2	yes	—
29	C₃×C₅×#95	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	2	yes	—
31	C₃×C₅×#95	C₂²	1	2	yes	—
32	C₃×C₅×#95	C₂²	1	1	yes	characteristic
33	C₃×#2722	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#126	C₂×C₃	1	2	yes	—
35	C₅×#398	C₂×C₃	1	2	yes	complemented
36	C₅×#398	C₂×C₃	1	2	yes	complemented
37	C₅×#397	C₂×C₃	1	1	yes	characteristic
38	C₅×#397	C₂×C₃	1	1	yes	characteristic
39	C₅×#389	C₂×C₃	1	2	yes	complemented
40	C₅×#387	C₂×C₃	1	2	yes	complemented
41	C₅×#385	C₂×C₃	1	1	yes	characteristic
42	C₅×#380	C₂×C₃	1	2	yes	—
43	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	—	2	4	no	—
45	C₂²×C₃×C₄×C₅	—	4	1	no	—
46	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
47	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
49	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₃×C₅×C₄⋊C₄	—	2	4	no	—
55	C₃×C₅×C₄⋊C₄	—	2	4	no	—
56	C₃×C₅×C₄⋊C₄	—	2	4	no	—
57	C₃×C₅×C₄⋊C₄	—	2	4	no	—
58	C₃×C₅×C₄⋊C₄	—	2	4	no	—
59	C₃×C₅×C₄⋊C₄	—	4	2	no	—
60	C₃×C₅×C₄⋊C₄	—	4	1	no	—
61	C₃×C₅×C₄⋊C₄	—	4	1	no	—
62	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
63	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
64	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
65	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
66	C₃×C₄²×C₅	—	2	4	no	—
67	C₂×C₃×#126	C₂×C₅	1	2	yes	—
68	C₃×#398	C₂×C₅	1	2	yes	complemented
69	C₃×#398	C₂×C₅	1	2	yes	complemented
70	C₃×#397	C₂×C₅	1	1	yes	characteristic
71	C₃×#397	C₂×C₅	1	1	yes	characteristic
72	C₃×#389	C₂×C₅	1	2	yes	complemented
73	C₃×#387	C₂×C₅	1	2	yes	complemented
74	C₃×#385	C₂×C₅	1	1	yes	characteristic
75	C₃×#380	C₂×C₅	1	2	yes	—
76	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
77	C₅×#126	—	2	8	no	—
78	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
79	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
80	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
81	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
87	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
90	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
91	C₅×#95	C₂²×C₃	1	2	yes	—
92	C₅×#95	C₂²×C₃	1	2	yes	—
93	C₅×#95	C₂²×C₃	1	2	yes	—
94	C₅×#95	C₂²×C₃	1	1	yes	characteristic
95	C₅×#95	C₂²×C₃	1	2	yes	—
96	C₅×#95	C₂²×C₃	1	2	yes	—
97	C₅×#95	C₂²×C₃	1	1	yes	characteristic
98	#2722	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	2	1	no	—
101	C₂³×C₃×C₅	—	2	1	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
104	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	2	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	1	no	—
117	C₂×C₃×C₄×C₅	—	2	1	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	2	no	—
120	C₂×C₃×C₄×C₅	—	2	2	no	—
121	C₂×C₃×C₄×C₅	—	2	2	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	2	no	—
124	C₂×C₃×C₄×C₅	—	2	2	no	—
125	C₂×C₃×C₄×C₅	—	4	4	no	—
126	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
127	C₂×C₃×C₄×C₅	#41	1	4	yes	—
128	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
129	C₃×#126	—	2	8	no	—
130	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
131	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
132	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
133	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
134	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
136	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
138	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
142	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
143	C₃×#95	C₂²×C₅	1	2	yes	—
144	C₃×#95	C₂²×C₅	1	2	yes	—
145	C₃×#95	C₂²×C₅	1	2	yes	—
146	C₃×#95	C₂²×C₅	1	1	yes	characteristic
147	C₃×#95	C₂²×C₅	1	2	yes	—
148	C₃×#95	C₂²×C₅	1	2	yes	—
149	C₃×#95	C₂²×C₅	1	1	yes	characteristic
150	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
151	C₂²×C₄×C₅	—	2	4	no	—
152	C₂²×C₄×C₅	—	4	1	no	—
153	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
154	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
155	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
156	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
158	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₅×C₄⋊C₄	—	2	4	no	—
162	C₅×C₄⋊C₄	—	2	4	no	—
163	C₅×C₄⋊C₄	—	2	4	no	—
164	C₅×C₄⋊C₄	—	2	4	no	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₄⋊C₄	—	4	2	no	—
167	C₅×C₄⋊C₄	—	4	1	no	—
168	C₅×C₄⋊C₄	—	4	1	no	—
169	C₅×C₂²⋊C₄	—	2	4	no	—
170	C₅×C₂²⋊C₄	—	2	4	no	—
171	C₅×C₂²⋊C₄	—	4	1	no	—
172	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
173	C₄²×C₅	—	2	4	no	—
174	C₂×#126	C₂×C₃×C₅	1	2	yes	—
175	#398	C₂×C₃×C₅	1	2	yes	complemented
176	#398	C₂×C₃×C₅	1	2	yes	complemented
177	#397	C₂×C₃×C₅	1	1	yes	characteristic
178	#397	C₂×C₃×C₅	1	1	yes	characteristic
179	#389	C₂×C₃×C₅	1	2	yes	complemented
180	#387	C₂×C₃×C₅	1	2	yes	complemented
181	#385	C₂×C₃×C₅	1	1	yes	characteristic
182	#380	C₂×C₃×C₅	1	2	yes	—
183	C₂²×C₃×C₅	—	2	2	no	—
184	C₂²×C₃×C₅	—	2	4	no	—
185	C₂²×C₃×C₅	—	4	2	no	—
186	C₂²×C₃×C₅	—	4	1	no	—
187	C₂²×C₃×C₅	—	4	1	no	—
188	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
190	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
191	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
192	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
193	C₃×C₄×C₅	—	2	4	no	—
194	C₃×C₄×C₅	—	2	4	no	—
195	C₃×C₄×C₅	—	4	2	no	—
196	C₃×C₄×C₅	—	4	2	no	—
197	C₃×C₄×C₅	—	4	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	—	4	1	no	—
200	C₃×C₄×C₅	—	4	1	no	—
201	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
202	C₂²×C₃×C₄	—	2	4	no	—
203	C₂²×C₃×C₄	—	4	1	no	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
206	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
207	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
208	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
209	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
210	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
211	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
212	C₃×C₄⋊C₄	—	2	4	no	—
213	C₃×C₄⋊C₄	—	2	4	no	—
214	C₃×C₄⋊C₄	—	2	4	no	—
215	C₃×C₄⋊C₄	—	2	4	no	—
216	C₃×C₄⋊C₄	—	2	4	no	—
217	C₃×C₄⋊C₄	—	4	2	no	—
218	C₃×C₄⋊C₄	—	4	1	no	—
219	C₃×C₄⋊C₄	—	4	1	no	—
220	C₃×C₂²⋊C₄	—	2	4	no	—
221	C₃×C₂²⋊C₄	—	2	4	no	—
222	C₃×C₂²⋊C₄	—	4	1	no	—
223	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
224	C₃×C₄²	—	2	4	no	—
225	C₂³×C₅	—	2	2	no	—
226	C₂³×C₅	—	2	1	no	—
227	C₂³×C₅	—	2	1	no	—
228	C₂³×C₅	—	2	2	no	—
229	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
230	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
231	C₂×C₄×C₅	—	2	2	no	—
232	C₂×C₄×C₅	—	2	2	no	—
233	C₂×C₄×C₅	—	2	2	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	2	no	—
237	C₂×C₄×C₅	—	2	2	no	—
238	C₂×C₄×C₅	—	2	2	no	—
239	C₂×C₄×C₅	—	2	2	no	—
240	C₂×C₄×C₅	—	2	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	2	1	no	—
243	C₂×C₄×C₅	—	2	1	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	4	4	no	—
252	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
253	C₂×C₄×C₅	C₃×#41	1	4	yes	—
254	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
255	#126	—	2	8	no	—
256	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
257	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
258	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
259	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
260	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
261	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
262	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
264	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
265	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
266	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
267	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
268	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
269	#95	C₂²×C₃×C₅	1	2	yes	—
270	#95	C₂²×C₃×C₅	1	2	yes	—
271	#95	C₂²×C₃×C₅	1	2	yes	—
272	#95	C₂²×C₃×C₅	1	1	yes	characteristic
273	#95	C₂²×C₃×C₅	1	2	yes	—
274	#95	C₂²×C₃×C₅	1	2	yes	—
275	#95	C₂²×C₃×C₅	1	1	yes	characteristic
276	C₂×C₃×C₅	—	4	2	no	—
277	C₂×C₃×C₅	#537	1	1	yes	characteristic
278	C₂×C₃×C₅	#541	1	2	yes	—
279	C₂×C₃×C₅	#547	1	2	yes	—
280	C₂×C₃×C₅	#551	1	1	yes	characteristic
281	C₂×C₃×C₅	#563	1	1	yes	characteristic
282	C₂³×C₃	—	2	2	no	—
283	C₂³×C₃	—	2	1	no	—
284	C₂³×C₃	—	2	1	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
287	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
288	C₂×C₃×C₄	—	2	2	no	—
289	C₂×C₃×C₄	—	2	2	no	—
290	C₂×C₃×C₄	—	2	2	no	—
291	C₂×C₃×C₄	—	2	2	no	—
292	C₂×C₃×C₄	—	2	2	no	—
293	C₂×C₃×C₄	—	2	2	no	—
294	C₂×C₃×C₄	—	2	2	no	—
295	C₂×C₃×C₄	—	2	2	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	1	no	—
300	C₂×C₃×C₄	—	2	1	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	2	no	—
307	C₂×C₃×C₄	—	2	2	no	—
308	C₂×C₃×C₄	—	4	4	no	—
309	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
310	C₂×C₃×C₄	C₅×#41	1	4	yes	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	2	4	no	—
313	C₂²×C₅	—	4	1	no	—
314	C₂²×C₅	—	4	2	no	—
315	C₂²×C₅	—	4	1	no	—
316	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
318	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
319	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
320	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
321	C₄×C₅	—	2	4	no	—
322	C₄×C₅	—	2	4	no	—
323	C₄×C₅	—	4	1	no	—
324	C₄×C₅	—	4	2	no	—
325	C₄×C₅	—	4	2	no	—
326	C₄×C₅	—	4	2	no	—
327	C₄×C₅	—	4	2	no	—
328	C₄×C₅	—	4	1	no	—
329	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
330	C₂²×C₄	—	2	4	no	—
331	C₂²×C₄	—	4	1	no	—
332	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
333	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
334	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
335	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
336	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
337	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
338	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
339	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
340	C₄⋊C₄	—	2	4	no	—
341	C₄⋊C₄	—	2	4	no	—
342	C₄⋊C₄	—	2	4	no	—
343	C₄⋊C₄	—	2	4	no	—
344	C₄⋊C₄	—	2	4	no	—
345	C₄⋊C₄	—	4	2	no	—
346	C₄⋊C₄	—	4	1	no	—
347	C₄⋊C₄	—	4	1	no	—
348	C₂²⋊C₄	—	2	4	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	4	1	no	—
351	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
352	C₄²	—	2	4	no	—
353	C₃×C₅	#2722	1	1	yes	characteristic, direct product factor, Hall
354	C₂²×C₃	—	2	2	no	—
355	C₂²×C₃	—	2	4	no	—
356	C₂²×C₃	—	4	2	no	—
357	C₂²×C₃	—	4	1	no	—
358	C₂²×C₃	—	4	1	no	—
359	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
360	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
361	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
362	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
363	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
364	C₃×C₄	—	2	4	no	—
365	C₃×C₄	—	2	4	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	4	2	no	—
368	C₃×C₄	—	4	2	no	—
369	C₃×C₄	—	4	2	no	—
370	C₃×C₄	—	4	1	no	—
371	C₃×C₄	—	4	1	no	—
372	C₂×C₅	—	4	2	no	—
373	C₂×C₅	C₃×#537	1	1	yes	characteristic
374	C₂×C₅	C₃×#541	1	2	yes	—
375	C₂×C₅	C₃×#547	1	2	yes	—
376	C₂×C₅	C₃×#551	1	1	yes	characteristic
377	C₂×C₅	C₃×#563	1	1	yes	characteristic
378	C₂³	—	2	2	no	—
379	C₂³	—	2	1	no	—
380	C₂³	—	2	1	no	—
381	C₂³	—	2	2	no	—
382	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
383	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
384	C₂×C₄	—	2	2	no	—
385	C₂×C₄	—	2	2	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	2	no	—
388	C₂×C₄	—	2	2	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	2	2	no	—
392	C₂×C₄	—	2	2	no	—
393	C₂×C₄	—	2	2	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	1	no	—
396	C₂×C₄	—	2	1	no	—
397	C₂×C₄	—	2	2	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	4	4	no	—
405	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
406	C₂×C₄	C₃×C₅×#41	1	4	yes	—
407	C₂×C₃	—	4	2	no	—
408	C₂×C₃	C₅×#537	1	1	yes	characteristic
409	C₂×C₃	C₅×#541	1	2	yes	—
410	C₂×C₃	C₅×#547	1	2	yes	—
411	C₂×C₃	C₅×#551	1	1	yes	characteristic
412	C₂×C₃	C₅×#563	1	1	yes	characteristic
413	C₅	C₃×#2722	1	1	yes	characteristic, direct product factor, Sylow
414	C₂²	—	2	2	no	—
415	C₂²	—	2	4	no	—
416	C₂²	—	4	2	no	—
417	C₂²	—	4	1	no	—
418	C₂²	—	4	1	no	—
419	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
420	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
421	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
423	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
424	C₄	—	2	4	no	—
425	C₄	—	2	4	no	—
426	C₄	—	4	2	no	—
427	C₄	—	4	2	no	—
428	C₄	—	4	2	no	—
429	C₄	—	4	2	no	—
430	C₄	—	4	1	no	—
431	C₄	—	4	1	no	—
432	C₃	C₅×#2722	1	1	yes	characteristic, direct product factor, Sylow
433	C₂	—	4	2	no	—
434	C₂	C₃×C₅×#537	1	1	yes	characteristic
435	C₂	C₃×C₅×#541	1	2	yes	—
436	C₂	C₃×C₅×#547	1	2	yes	—
437	C₂	C₃×C₅×#551	1	1	yes	characteristic
438	C₂	C₃×C₅×#563	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#398	C₂	semidirect
3. C₃×C₅×#398	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#387	C₂	semidirect
10. C₅×#2722	C₃	direct (N × H)
33. C₃×#2722	C₅	direct (N × H)
35. C₅×#398	C₂×C₃	semidirect
36. C₅×#398	C₂×C₃	semidirect
39. C₅×#389	C₂×C₃	semidirect
40. C₅×#387	C₂×C₃	semidirect
68. C₃×#398	C₂×C₅	semidirect
69. C₃×#398	C₂×C₅	semidirect
72. C₃×#389	C₂×C₅	semidirect
73. C₃×#387	C₂×C₅	semidirect
98. #2722	C₃×C₅	direct (N × H)
175. #398	C₂×C₃×C₅	semidirect
176. #398	C₂×C₃×C₅	semidirect
179. #389	C₂×C₃×C₅	semidirect
180. #387	C₂×C₃×C₅	semidirect
353. C₃×C₅	#2722	direct (N × H)
413. C₅	C₃×#2722	direct (N × H)
432. C₃	C₅×#2722	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#126	2
C₃×C₅×#398	2
C₃×C₅×#397	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₅×#380	2
C₅×#2722	3
C₃×#2722	5

Subgroups — C3×C5×#2722 #14275756

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2722 #14275756