Subgroups — C₃×C₅×#2337 #14275371

Order 1920.

1080 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#391	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#386	C₂	1	2	yes	maximal
6	C₃×C₅×#385	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#383	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
10	C₅×#2337	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₃×C₅×#124	C₄	1	8	yes	complemented
15	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×#2337	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
35	C₅×#391	C₂×C₃	1	2	yes	complemented
36	C₅×#388	C₂×C₃	1	2	yes	complemented
37	C₅×#388	C₂×C₃	1	2	yes	complemented
38	C₅×#386	C₂×C₃	1	2	yes	—
39	C₅×#385	C₂×C₃	1	2	yes	complemented
40	C₅×#383	C₂×C₃	1	1	yes	characteristic, complemented
41	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
42	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
43	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
44	C₂×C₃×C₅×Q₈	—	4	2	no	—
45	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
46	C₂×C₃×C₅×D₄	—	4	2	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	—	4	2	no	—
50	C₂²×C₃×C₄×C₅	—	4	2	no	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
56	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₄⋊C₄	—	4	2	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
63	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
64	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
65	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
66	C₃×C₄²×C₅	—	4	1	no	—
67	C₃×C₄²×C₅	—	4	1	no	—
68	C₃×C₄²×C₅	—	4	2	no	—
69	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
70	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
71	C₃×#391	C₂×C₅	1	2	yes	complemented
72	C₃×#388	C₂×C₅	1	2	yes	complemented
73	C₃×#388	C₂×C₅	1	2	yes	complemented
74	C₃×#386	C₂×C₅	1	2	yes	—
75	C₃×#385	C₂×C₅	1	2	yes	complemented
76	C₃×#383	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
79	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
81	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
82	C₅×#124	C₃×C₄	1	8	yes	complemented
83	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
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	2	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
91	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
92	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
93	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₅×#95	C₂²×C₃	1	2	yes	—
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	C₅×#95	C₂²×C₃	1	2	yes	—
99	C₅×#95	C₂²×C₃	1	1	yes	characteristic
100	C₅×#95	C₂²×C₃	1	2	yes	—
101	#2337	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	2	no	—
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	2	no	—
107	C₂³×C₃×C₅	—	2	2	no	—
108	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
109	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
110	C₃×C₅×Q₈	—	4	4	no	—
111	C₃×C₅×D₄	—	4	4	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	1	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	2	no	—
118	C₂×C₃×C₄×C₅	—	2	2	no	—
119	C₂×C₃×C₄×C₅	—	2	1	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	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	4	8	no	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
134	C₂×C₃×C₄×C₅	#41	1	4	yes	—
135	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
136	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
137	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
138	C₃×#124	C₄×C₅	1	8	yes	complemented
139	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
141	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
144	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
146	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
147	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
148	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
149	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
150	C₃×#95	C₂²×C₅	1	2	yes	—
151	C₃×#95	C₂²×C₅	1	2	yes	—
152	C₃×#95	C₂²×C₅	1	2	yes	—
153	C₃×#95	C₂²×C₅	1	1	yes	characteristic
154	C₃×#95	C₂²×C₅	1	2	yes	—
155	C₃×#95	C₂²×C₅	1	1	yes	characteristic
156	C₃×#95	C₂²×C₅	1	2	yes	—
157	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
158	C₂×C₅×Q₈	—	4	2	no	—
159	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
160	C₂×C₅×D₄	—	4	2	no	—
161	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
162	C₂²×C₄×C₅	—	2	4	no	—
163	C₂²×C₄×C₅	—	4	2	no	—
164	C₂²×C₄×C₅	—	4	2	no	—
165	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
166	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
167	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
168	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
169	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
170	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
171	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
172	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
173	C₅×C₄⋊C₄	—	2	4	no	—
174	C₅×C₄⋊C₄	—	4	2	no	—
175	C₅×C₂²⋊C₄	—	2	4	no	—
176	C₅×C₂²⋊C₄	—	4	2	no	—
177	C₅×C₂²⋊C₄	—	4	2	no	—
178	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
179	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
180	C₄²×C₅	—	4	1	no	—
181	C₄²×C₅	—	4	1	no	—
182	C₄²×C₅	—	4	2	no	—
183	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
184	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
185	#391	C₂×C₃×C₅	1	2	yes	complemented
186	#388	C₂×C₃×C₅	1	2	yes	complemented
187	#388	C₂×C₃×C₅	1	2	yes	complemented
188	#386	C₂×C₃×C₅	1	2	yes	—
189	#385	C₂×C₃×C₅	1	2	yes	complemented
190	#383	C₂×C₃×C₅	1	1	yes	characteristic, complemented
191	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
192	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
193	C₂²×C₃×C₅	—	2	4	no	—
194	C₂²×C₃×C₅	—	2	4	no	—
195	C₂²×C₃×C₅	—	2	4	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	4	2	no	—
198	C₂²×C₃×C₅	—	4	2	no	—
199	C₂²×C₃×C₅	—	4	2	no	—
200	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
202	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
203	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
204	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
205	C₃×C₄×C₅	—	2	2	no	—
206	C₃×C₄×C₅	—	2	2	no	—
207	C₃×C₄×C₅	—	2	4	no	—
208	C₃×C₄×C₅	—	2	2	no	—
209	C₃×C₄×C₅	—	2	4	no	—
210	C₃×C₄×C₅	—	4	2	no	—
211	C₃×C₄×C₅	—	4	2	no	—
212	C₃×C₄×C₅	—	4	2	no	—
213	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
214	C₂×C₃×Q₈	—	4	2	no	—
215	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
216	C₂×C₃×D₄	—	4	2	no	—
217	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
218	C₂²×C₃×C₄	—	2	4	no	—
219	C₂²×C₃×C₄	—	4	2	no	—
220	C₂²×C₃×C₄	—	4	2	no	—
221	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
222	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
223	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
224	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
225	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
226	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
227	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
228	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
229	C₃×C₄⋊C₄	—	2	4	no	—
230	C₃×C₄⋊C₄	—	4	2	no	—
231	C₃×C₂²⋊C₄	—	2	4	no	—
232	C₃×C₂²⋊C₄	—	4	2	no	—
233	C₃×C₂²⋊C₄	—	4	2	no	—
234	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
235	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
236	C₃×C₄²	—	4	1	no	—
237	C₃×C₄²	—	4	1	no	—
238	C₃×C₄²	—	4	2	no	—
239	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	—	2	2	no	—
242	C₂³×C₅	—	2	2	no	—
243	C₂³×C₅	—	2	2	no	—
244	C₂³×C₅	—	2	2	no	—
245	C₂³×C₅	—	2	2	no	—
246	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
247	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
248	C₅×Q₈	—	4	4	no	—
249	C₅×D₄	—	4	4	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	1	no	—
252	C₂×C₄×C₅	—	2	2	no	—
253	C₂×C₄×C₅	—	2	2	no	—
254	C₂×C₄×C₅	—	2	2	no	—
255	C₂×C₄×C₅	—	2	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	1	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	2	2	no	—
260	C₂×C₄×C₅	—	2	2	no	—
261	C₂×C₄×C₅	—	2	2	no	—
262	C₂×C₄×C₅	—	2	2	no	—
263	C₂×C₄×C₅	—	2	2	no	—
264	C₂×C₄×C₅	—	2	2	no	—
265	C₂×C₄×C₅	—	2	2	no	—
266	C₂×C₄×C₅	—	2	2	no	—
267	C₂×C₄×C₅	—	4	8	no	—
268	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
269	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
270	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
271	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
272	C₂×C₄×C₅	C₃×#41	1	4	yes	—
273	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
274	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
275	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
276	#124	C₃×C₄×C₅	1	8	yes	complemented
277	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
278	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
279	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
280	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
281	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
282	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
283	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
284	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
285	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
286	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
287	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
288	#95	C₂²×C₃×C₅	1	2	yes	—
289	#95	C₂²×C₃×C₅	1	2	yes	—
290	#95	C₂²×C₃×C₅	1	2	yes	—
291	#95	C₂²×C₃×C₅	1	1	yes	characteristic
292	#95	C₂²×C₃×C₅	1	2	yes	—
293	#95	C₂²×C₃×C₅	1	1	yes	characteristic
294	#95	C₂²×C₃×C₅	1	2	yes	—
295	C₂×C₃×C₅	—	4	4	no	—
296	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
297	C₂×C₃×C₅	#518	1	1	yes	characteristic
298	C₂×C₃×C₅	#520	1	1	yes	characteristic
299	C₂×C₃×C₅	#538	1	2	yes	—
300	C₂×C₃×C₅	#542	1	2	yes	—
301	C₂³×C₃	—	2	2	no	—
302	C₂³×C₃	—	2	2	no	—
303	C₂³×C₃	—	2	2	no	—
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	2	2	no	—
306	C₂³×C₃	—	2	2	no	—
307	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
308	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
309	C₃×Q₈	—	4	4	no	—
310	C₃×D₄	—	4	4	no	—
311	C₂×C₃×C₄	—	2	2	no	—
312	C₂×C₃×C₄	—	2	1	no	—
313	C₂×C₃×C₄	—	2	2	no	—
314	C₂×C₃×C₄	—	2	2	no	—
315	C₂×C₃×C₄	—	2	2	no	—
316	C₂×C₃×C₄	—	2	2	no	—
317	C₂×C₃×C₄	—	2	2	no	—
318	C₂×C₃×C₄	—	2	1	no	—
319	C₂×C₃×C₄	—	2	2	no	—
320	C₂×C₃×C₄	—	2	2	no	—
321	C₂×C₃×C₄	—	2	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	2	2	no	—
326	C₂×C₃×C₄	—	2	2	no	—
327	C₂×C₃×C₄	—	2	2	no	—
328	C₂×C₃×C₄	—	4	8	no	—
329	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
330	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
331	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
332	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
333	C₂×C₃×C₄	C₅×#41	1	4	yes	—
334	C₂²×C₅	—	2	4	no	—
335	C₂²×C₅	—	2	4	no	—
336	C₂²×C₅	—	2	4	no	—
337	C₂²×C₅	—	4	2	no	—
338	C₂²×C₅	—	4	2	no	—
339	C₂²×C₅	—	4	2	no	—
340	C₂²×C₅	—	4	2	no	—
341	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
342	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
343	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
344	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
345	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
346	C₄×C₅	—	2	2	no	—
347	C₄×C₅	—	2	2	no	—
348	C₄×C₅	—	2	4	no	—
349	C₄×C₅	—	2	2	no	—
350	C₄×C₅	—	2	4	no	—
351	C₄×C₅	—	4	2	no	—
352	C₄×C₅	—	4	2	no	—
353	C₄×C₅	—	4	2	no	—
354	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
355	C₂×Q₈	—	4	2	no	—
356	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
357	C₂×D₄	—	4	2	no	—
358	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
359	C₂²×C₄	—	2	4	no	—
360	C₂²×C₄	—	4	2	no	—
361	C₂²×C₄	—	4	2	no	—
362	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
363	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
364	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
365	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
366	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
367	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
368	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
369	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
370	C₄⋊C₄	—	2	4	no	—
371	C₄⋊C₄	—	4	2	no	—
372	C₂²⋊C₄	—	2	4	no	—
373	C₂²⋊C₄	—	4	2	no	—
374	C₂²⋊C₄	—	4	2	no	—
375	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
376	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
377	C₄²	—	4	1	no	—
378	C₄²	—	4	1	no	—
379	C₄²	—	4	2	no	—
380	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
381	C₃×C₅	#2337	1	1	yes	characteristic, direct product factor, Hall
382	C₂²×C₃	—	2	4	no	—
383	C₂²×C₃	—	2	4	no	—
384	C₂²×C₃	—	2	4	no	—
385	C₂²×C₃	—	4	2	no	—
386	C₂²×C₃	—	4	2	no	—
387	C₂²×C₃	—	4	2	no	—
388	C₂²×C₃	—	4	2	no	—
389	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
390	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
391	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
392	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
393	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
394	C₃×C₄	—	2	2	no	—
395	C₃×C₄	—	2	2	no	—
396	C₃×C₄	—	2	4	no	—
397	C₃×C₄	—	2	2	no	—
398	C₃×C₄	—	2	4	no	—
399	C₃×C₄	—	4	2	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	—	4	2	no	—
402	C₂×C₅	—	4	4	no	—
403	C₂×C₅	C₃×C₄×#41	1	1	yes	characteristic
404	C₂×C₅	C₃×#518	1	1	yes	characteristic
405	C₂×C₅	C₃×#520	1	1	yes	characteristic
406	C₂×C₅	C₃×#538	1	2	yes	—
407	C₂×C₅	C₃×#542	1	2	yes	—
408	C₂³	—	2	2	no	—
409	C₂³	—	2	2	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	2	2	no	—
412	C₂³	—	2	2	no	—
413	C₂³	—	2	2	no	—
414	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
415	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
416	Q₈	—	4	4	no	—
417	D₄	—	4	4	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	1	no	—
420	C₂×C₄	—	2	2	no	—
421	C₂×C₄	—	2	2	no	—
422	C₂×C₄	—	2	2	no	—
423	C₂×C₄	—	2	2	no	—
424	C₂×C₄	—	2	2	no	—
425	C₂×C₄	—	2	1	no	—
426	C₂×C₄	—	2	2	no	—
427	C₂×C₄	—	2	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	2	2	no	—
432	C₂×C₄	—	2	2	no	—
433	C₂×C₄	—	2	2	no	—
434	C₂×C₄	—	2	2	no	—
435	C₂×C₄	—	4	8	no	—
436	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
437	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
438	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
439	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
440	C₂×C₄	C₃×C₅×#41	1	4	yes	—
441	C₂×C₃	—	4	4	no	—
442	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
443	C₂×C₃	C₅×#518	1	1	yes	characteristic
444	C₂×C₃	C₅×#520	1	1	yes	characteristic
445	C₂×C₃	C₅×#538	1	2	yes	—
446	C₂×C₃	C₅×#542	1	2	yes	—
447	C₅	C₃×#2337	1	1	yes	characteristic, direct product factor, Sylow
448	C₂²	—	2	4	no	—
449	C₂²	—	2	4	no	—
450	C₂²	—	2	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	4	2	no	—
453	C₂²	—	4	2	no	—
454	C₂²	—	4	2	no	—
455	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
456	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
457	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
458	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
460	C₄	—	2	2	no	—
461	C₄	—	2	2	no	—
462	C₄	—	2	4	no	—
463	C₄	—	2	2	no	—
464	C₄	—	2	4	no	—
465	C₄	—	4	2	no	—
466	C₄	—	4	2	no	—
467	C₄	—	4	2	no	—
468	C₃	C₅×#2337	1	1	yes	characteristic, direct product factor, Sylow
469	C₂	—	4	4	no	—
470	C₂	C₃×C₄×C₅×#41	1	1	yes	characteristic
471	C₂	C₃×C₅×#518	1	1	yes	characteristic
472	C₂	C₃×C₅×#520	1	1	yes	characteristic
473	C₂	C₃×C₅×#538	1	2	yes	—
474	C₂	C₃×C₅×#542	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂²×C₃×C₅×D₄	C₂²
LCS	G ▷ C₂² ▷ 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×#391	C₂	semidirect
3. C₃×C₅×#388	C₂	semidirect
4. C₃×C₅×#388	C₂	semidirect
6. C₃×C₅×#385	C₂	semidirect
7. C₃×C₅×#383	C₂	semidirect
8. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
9. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
10. C₅×#2337	C₃	direct (N × H)
14. C₃×C₅×#124	C₄	semidirect
33. C₃×#2337	C₅	direct (N × H)
35. C₅×#391	C₂×C₃	semidirect
36. C₅×#388	C₂×C₃	semidirect
37. C₅×#388	C₂×C₃	semidirect
39. C₅×#385	C₂×C₃	semidirect
40. C₅×#383	C₂×C₃	semidirect
41. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
42. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
45. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
64. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
65. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
69. C₃×C₄²×C₅	C₂×C₄	semidirect
71. C₃×#391	C₂×C₅	semidirect
72. C₃×#388	C₂×C₅	semidirect
73. C₃×#388	C₂×C₅	semidirect
75. C₃×#385	C₂×C₅	semidirect
76. C₃×#383	C₂×C₅	semidirect
77. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
78. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
82. C₅×#124	C₃×C₄	semidirect
101. #2337	C₃×C₅	direct (N × H)
138. C₃×#124	C₄×C₅	semidirect
159. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
178. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
179. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
183. C₄²×C₅	C₂×C₃×C₄	semidirect
185. #391	C₂×C₃×C₅	semidirect
186. #388	C₂×C₃×C₅	semidirect
187. #388	C₂×C₃×C₅	semidirect
189. #385	C₂×C₃×C₅	semidirect
190. #383	C₂×C₃×C₅	semidirect
191. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
192. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
215. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
234. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
235. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
239. C₃×C₄²	C₂×C₄×C₅	semidirect
276. #124	C₃×C₄×C₅	semidirect
356. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
375. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
376. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
380. C₄²	C₂×C₃×C₄×C₅	semidirect
381. C₃×C₅	#2337	direct (N × H)
447. C₅	C₃×#2337	direct (N × H)
468. C₃	C₅×#2337	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×#124	2
C₃×C₅×#391	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#385	2
C₃×C₅×#383	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2337	3
C₃×#2337	5

Subgroups — C3×C5×#2337 #14275371

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2337 #14275371