Subgroups — C₃×C₅×#2699 #14275733

Order 1920.

1224 conjugacy classes of subgroups.

The subgroup lattice has 556 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#121	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#398	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#394	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#394	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#392	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#388	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#386	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#381	C₂	1	2	yes	maximal, complemented
10	C₅×#2699	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
12	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
16	C₃×C₅×#121	—	2	8	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
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	2	yes	—
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₃×C₅×#95	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	2	yes	—
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×#2699	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
34	C₂×C₅×#121	C₂×C₃	1	2	yes	complemented
35	C₅×#398	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#394	C₂×C₃	1	2	yes	complemented
37	C₅×#394	C₂×C₃	1	1	yes	characteristic, complemented
38	C₅×#392	C₂×C₃	1	2	yes	complemented
39	C₅×#390	C₂×C₃	1	1	yes	characteristic, complemented
40	C₅×#388	C₂×C₃	1	2	yes	complemented
41	C₅×#386	C₂×C₃	1	2	yes	complemented
42	C₅×#381	C₂×C₃	1	2	yes	complemented
43	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	2	4	no	—
47	C₂×C₃×C₅×D₄	—	2	4	no	—
48	C₂×C₃×C₅×D₄	—	4	1	no	—
49	C₂×C₃×C₅×D₄	—	4	1	no	—
50	C₂×C₃×C₅×D₄	—	4	2	no	—
51	C₂×C₃×C₅×D₄	—	4	2	no	—
52	C₂×C₃×C₅×D₄	—	4	2	no	—
53	C₂×C₃×C₅×D₄	—	4	2	no	—
54	C₂×C₃×C₅×D₄	—	4	1	no	—
55	C₂×C₃×C₅×D₄	D₄	1	4	yes	complemented
56	C₂²×C₃×C₄×C₅	—	2	4	no	—
57	C₂²×C₃×C₄×C₅	—	2	4	no	—
58	C₂²×C₃×C₄×C₅	—	4	2	no	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₃×C₅×C₄⋊C₄	—	2	4	no	—
67	C₃×C₅×C₄⋊C₄	—	4	1	no	—
68	C₃×C₅×C₄⋊C₄	—	4	1	no	—
69	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
70	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
71	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
72	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
73	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
74	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
75	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
76	C₃×C₄²×C₅	—	4	1	no	—
77	C₂×C₃×#121	C₂×C₅	1	2	yes	complemented
78	C₃×#398	C₂×C₅	1	1	yes	characteristic, complemented
79	C₃×#394	C₂×C₅	1	1	yes	characteristic, complemented
80	C₃×#394	C₂×C₅	1	2	yes	complemented
81	C₃×#392	C₂×C₅	1	2	yes	complemented
82	C₃×#390	C₂×C₅	1	1	yes	characteristic, complemented
83	C₃×#388	C₂×C₅	1	2	yes	complemented
84	C₃×#386	C₂×C₅	1	2	yes	complemented
85	C₃×#381	C₂×C₅	1	2	yes	complemented
86	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
87	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
88	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
89	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
90	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
91	C₅×#121	—	2	8	no	—
92	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
98	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
99	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
103	C₅×#95	C₂²×C₃	1	1	yes	characteristic
104	C₅×#95	C₂²×C₃	1	2	yes	—
105	C₅×#95	C₂²×C₃	1	2	yes	—
106	C₅×#95	C₂²×C₃	1	2	yes	—
107	C₅×#95	C₂²×C₃	1	1	yes	characteristic
108	#2699	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	2	no	—
112	C₂³×C₃×C₅	—	2	2	no	—
113	C₂³×C₃×C₅	—	2	2	no	—
114	C₂³×C₃×C₅	—	2	2	no	—
115	C₂³×C₃×C₅	—	2	2	no	—
116	C₂³×C₃×C₅	—	2	2	no	—
117	C₂³×C₃×C₅	—	2	2	no	—
118	C₂³×C₃×C₅	—	2	2	no	—
119	C₂³×C₃×C₅	—	2	2	no	—
120	C₂³×C₃×C₅	—	2	2	no	—
121	C₂³×C₃×C₅	—	2	2	no	—
122	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
123	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
124	C₃×C₅×D₄	—	4	4	no	—
125	C₃×C₅×D₄	—	4	8	no	—
126	C₃×C₅×D₄	—	4	8	no	—
127	C₃×C₅×D₄	—	4	4	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	1	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	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	2	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	4	8	no	—
146	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×C₄×C₅	#41	1	4	yes	—
148	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
149	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
150	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
151	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
152	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
153	C₃×#121	—	2	8	no	—
154	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
155	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
157	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
158	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
160	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
161	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
162	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
165	C₃×#95	C₂²×C₅	1	1	yes	characteristic
166	C₃×#95	C₂²×C₅	1	2	yes	—
167	C₃×#95	C₂²×C₅	1	2	yes	—
168	C₃×#95	C₂²×C₅	1	2	yes	—
169	C₃×#95	C₂²×C₅	1	1	yes	characteristic
170	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
171	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
172	C₂×C₅×D₄	—	2	4	no	—
173	C₂×C₅×D₄	—	2	4	no	—
174	C₂×C₅×D₄	—	2	4	no	—
175	C₂×C₅×D₄	—	4	1	no	—
176	C₂×C₅×D₄	—	4	1	no	—
177	C₂×C₅×D₄	—	4	2	no	—
178	C₂×C₅×D₄	—	4	2	no	—
179	C₂×C₅×D₄	—	4	2	no	—
180	C₂×C₅×D₄	—	4	2	no	—
181	C₂×C₅×D₄	—	4	1	no	—
182	C₂×C₅×D₄	C₃×D₄	1	4	yes	complemented
183	C₂²×C₄×C₅	—	2	4	no	—
184	C₂²×C₄×C₅	—	2	4	no	—
185	C₂²×C₄×C₅	—	4	2	no	—
186	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
187	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
189	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
190	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
193	C₅×C₄⋊C₄	—	2	4	no	—
194	C₅×C₄⋊C₄	—	4	1	no	—
195	C₅×C₄⋊C₄	—	4	1	no	—
196	C₅×C₂²⋊C₄	—	2	4	no	—
197	C₅×C₂²⋊C₄	—	2	4	no	—
198	C₅×C₂²⋊C₄	—	2	4	no	—
199	C₅×C₂²⋊C₄	—	4	2	no	—
200	C₅×C₂²⋊C₄	—	4	2	no	—
201	C₅×C₂²⋊C₄	—	4	2	no	—
202	C₅×C₂²⋊C₄	—	4	2	no	—
203	C₄²×C₅	—	4	1	no	—
204	C₂×#121	C₂×C₃×C₅	1	2	yes	complemented
205	#398	C₂×C₃×C₅	1	1	yes	characteristic, complemented
206	#394	C₂×C₃×C₅	1	1	yes	characteristic, complemented
207	#394	C₂×C₃×C₅	1	2	yes	complemented
208	#392	C₂×C₃×C₅	1	2	yes	complemented
209	#390	C₂×C₃×C₅	1	1	yes	characteristic, complemented
210	#388	C₂×C₃×C₅	1	2	yes	complemented
211	#386	C₂×C₃×C₅	1	2	yes	complemented
212	#381	C₂×C₃×C₅	1	2	yes	complemented
213	C₂²×C₃×C₅	—	2	4	no	—
214	C₂²×C₃×C₅	—	2	4	no	—
215	C₂²×C₃×C₅	—	2	4	no	—
216	C₂²×C₃×C₅	—	4	2	no	—
217	C₂²×C₃×C₅	—	4	2	no	—
218	C₂²×C₃×C₅	—	4	2	no	—
219	C₂²×C₃×C₅	—	4	2	no	—
220	C₂²×C₃×C₅	—	4	2	no	—
221	C₂²×C₃×C₅	—	4	2	no	—
222	C₂²×C₃×C₅	—	4	2	no	—
223	C₂²×C₃×C₅	—	4	2	no	—
224	C₂²×C₃×C₅	—	4	2	no	—
225	C₂²×C₃×C₅	—	4	2	no	—
226	C₂²×C₃×C₅	—	4	2	no	—
227	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
228	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
229	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
230	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
231	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
232	C₃×C₄×C₅	—	2	2	no	—
233	C₃×C₄×C₅	—	2	4	no	—
234	C₃×C₄×C₅	—	4	2	no	—
235	C₃×C₄×C₅	—	4	2	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	—	4	1	no	—
238	C₃×C₄×C₅	—	4	1	no	—
239	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
240	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
241	C₂×C₃×D₄	—	2	4	no	—
242	C₂×C₃×D₄	—	2	4	no	—
243	C₂×C₃×D₄	—	2	4	no	—
244	C₂×C₃×D₄	—	4	1	no	—
245	C₂×C₃×D₄	—	4	1	no	—
246	C₂×C₃×D₄	—	4	2	no	—
247	C₂×C₃×D₄	—	4	2	no	—
248	C₂×C₃×D₄	—	4	2	no	—
249	C₂×C₃×D₄	—	4	2	no	—
250	C₂×C₃×D₄	—	4	1	no	—
251	C₂×C₃×D₄	C₅×D₄	1	4	yes	complemented
252	C₂²×C₃×C₄	—	2	4	no	—
253	C₂²×C₃×C₄	—	2	4	no	—
254	C₂²×C₃×C₄	—	4	2	no	—
255	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
256	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
258	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
259	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
260	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
261	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
262	C₃×C₄⋊C₄	—	2	4	no	—
263	C₃×C₄⋊C₄	—	4	1	no	—
264	C₃×C₄⋊C₄	—	4	1	no	—
265	C₃×C₂²⋊C₄	—	2	4	no	—
266	C₃×C₂²⋊C₄	—	2	4	no	—
267	C₃×C₂²⋊C₄	—	2	4	no	—
268	C₃×C₂²⋊C₄	—	4	2	no	—
269	C₃×C₂²⋊C₄	—	4	2	no	—
270	C₃×C₂²⋊C₄	—	4	2	no	—
271	C₃×C₂²⋊C₄	—	4	2	no	—
272	C₃×C₄²	—	4	1	no	—
273	C₂³×C₅	—	2	2	no	—
274	C₂³×C₅	—	2	2	no	—
275	C₂³×C₅	—	2	2	no	—
276	C₂³×C₅	—	2	2	no	—
277	C₂³×C₅	—	2	2	no	—
278	C₂³×C₅	—	2	2	no	—
279	C₂³×C₅	—	2	2	no	—
280	C₂³×C₅	—	2	2	no	—
281	C₂³×C₅	—	2	2	no	—
282	C₂³×C₅	—	2	2	no	—
283	C₂³×C₅	—	2	2	no	—
284	C₂³×C₅	—	2	2	no	—
285	C₂³×C₅	—	2	2	no	—
286	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
287	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
288	C₅×D₄	—	4	4	no	—
289	C₅×D₄	—	4	8	no	—
290	C₅×D₄	—	4	8	no	—
291	C₅×D₄	—	4	4	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	1	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	2	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	2	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	4	8	no	—
310	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
311	C₂×C₄×C₅	C₃×#41	1	4	yes	—
312	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
313	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
314	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
315	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
317	#121	—	2	8	no	—
318	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
319	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
320	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
321	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
326	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
328	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
329	#95	C₂²×C₃×C₅	1	1	yes	characteristic
330	#95	C₂²×C₃×C₅	1	2	yes	—
331	#95	C₂²×C₃×C₅	1	2	yes	—
332	#95	C₂²×C₃×C₅	1	2	yes	—
333	#95	C₂²×C₃×C₅	1	1	yes	characteristic
334	C₂×C₃×C₅	—	4	4	no	—
335	C₂×C₃×C₅	—	8	2	no	—
336	C₂×C₃×C₅	#534	1	1	yes	characteristic
337	C₂×C₃×C₅	#540	1	2	yes	—
338	C₂×C₃×C₅	#546	1	2	yes	—
339	C₂×C₃×C₅	#555	1	1	yes	characteristic
340	C₂×C₃×C₅	#560	1	1	yes	characteristic
341	C₂³×C₃	—	2	2	no	—
342	C₂³×C₃	—	2	2	no	—
343	C₂³×C₃	—	2	2	no	—
344	C₂³×C₃	—	2	2	no	—
345	C₂³×C₃	—	2	2	no	—
346	C₂³×C₃	—	2	2	no	—
347	C₂³×C₃	—	2	2	no	—
348	C₂³×C₃	—	2	2	no	—
349	C₂³×C₃	—	2	2	no	—
350	C₂³×C₃	—	2	2	no	—
351	C₂³×C₃	—	2	2	no	—
352	C₂³×C₃	—	2	2	no	—
353	C₂³×C₃	—	2	2	no	—
354	C₂³×C₃	C₂×C₅×D₄	1	4	yes	—
355	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
356	C₃×D₄	—	4	4	no	—
357	C₃×D₄	—	4	8	no	—
358	C₃×D₄	—	4	8	no	—
359	C₃×D₄	—	4	4	no	—
360	C₂×C₃×C₄	—	2	2	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	2	no	—
372	C₂×C₃×C₄	—	2	2	no	—
373	C₂×C₃×C₄	—	2	2	no	—
374	C₂×C₃×C₄	—	2	1	no	—
375	C₂×C₃×C₄	—	2	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	4	8	no	—
378	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
379	C₂×C₃×C₄	C₅×#41	1	4	yes	—
380	C₂²×C₅	—	2	4	no	—
381	C₂²×C₅	—	2	4	no	—
382	C₂²×C₅	—	2	4	no	—
383	C₂²×C₅	—	4	2	no	—
384	C₂²×C₅	—	4	2	no	—
385	C₂²×C₅	—	4	2	no	—
386	C₂²×C₅	—	4	2	no	—
387	C₂²×C₅	—	4	2	no	—
388	C₂²×C₅	—	4	2	no	—
389	C₂²×C₅	—	4	2	no	—
390	C₂²×C₅	—	4	2	no	—
391	C₂²×C₅	—	4	2	no	—
392	C₂²×C₅	—	4	2	no	—
393	C₂²×C₅	—	4	2	no	—
394	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
395	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
396	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
398	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	2	4	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	—	4	1	no	—
403	C₄×C₅	—	4	2	no	—
404	C₄×C₅	—	4	2	no	—
405	C₄×C₅	—	4	2	no	—
406	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
407	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
408	C₂×D₄	—	2	4	no	—
409	C₂×D₄	—	2	4	no	—
410	C₂×D₄	—	2	4	no	—
411	C₂×D₄	—	4	1	no	—
412	C₂×D₄	—	4	1	no	—
413	C₂×D₄	—	4	2	no	—
414	C₂×D₄	—	4	2	no	—
415	C₂×D₄	—	4	2	no	—
416	C₂×D₄	—	4	2	no	—
417	C₂×D₄	—	4	1	no	—
418	C₂×D₄	C₃×C₅×D₄	1	4	yes	complemented
419	C₂²×C₄	—	2	4	no	—
420	C₂²×C₄	—	2	4	no	—
421	C₂²×C₄	—	4	2	no	—
422	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
423	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
424	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
425	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
426	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
427	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
428	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
429	C₄⋊C₄	—	2	4	no	—
430	C₄⋊C₄	—	4	1	no	—
431	C₄⋊C₄	—	4	1	no	—
432	C₂²⋊C₄	—	2	4	no	—
433	C₂²⋊C₄	—	2	4	no	—
434	C₂²⋊C₄	—	2	4	no	—
435	C₂²⋊C₄	—	4	2	no	—
436	C₂²⋊C₄	—	4	2	no	—
437	C₂²⋊C₄	—	4	2	no	—
438	C₂²⋊C₄	—	4	2	no	—
439	C₄²	—	4	1	no	—
440	C₃×C₅	#2699	1	1	yes	characteristic, direct product factor, Hall
441	C₂²×C₃	—	2	4	no	—
442	C₂²×C₃	—	2	4	no	—
443	C₂²×C₃	—	2	4	no	—
444	C₂²×C₃	—	4	2	no	—
445	C₂²×C₃	—	4	2	no	—
446	C₂²×C₃	—	4	2	no	—
447	C₂²×C₃	—	4	2	no	—
448	C₂²×C₃	—	4	2	no	—
449	C₂²×C₃	—	4	2	no	—
450	C₂²×C₃	—	4	2	no	—
451	C₂²×C₃	—	4	2	no	—
452	C₂²×C₃	—	4	2	no	—
453	C₂²×C₃	—	4	2	no	—
454	C₂²×C₃	—	4	2	no	—
455	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
456	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
457	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
458	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
459	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
460	C₃×C₄	—	2	2	no	—
461	C₃×C₄	—	2	4	no	—
462	C₃×C₄	—	4	2	no	—
463	C₃×C₄	—	4	2	no	—
464	C₃×C₄	—	4	2	no	—
465	C₃×C₄	—	4	1	no	—
466	C₃×C₄	—	4	1	no	—
467	C₂×C₅	—	4	4	no	—
468	C₂×C₅	—	8	2	no	—
469	C₂×C₅	C₃×#534	1	1	yes	characteristic
470	C₂×C₅	C₃×#540	1	2	yes	—
471	C₂×C₅	C₃×#546	1	2	yes	—
472	C₂×C₅	C₃×#555	1	1	yes	characteristic
473	C₂×C₅	C₃×#560	1	1	yes	characteristic
474	C₂³	—	2	2	no	—
475	C₂³	—	2	2	no	—
476	C₂³	—	2	2	no	—
477	C₂³	—	2	2	no	—
478	C₂³	—	2	2	no	—
479	C₂³	—	2	2	no	—
480	C₂³	—	2	2	no	—
481	C₂³	—	2	2	no	—
482	C₂³	—	2	2	no	—
483	C₂³	—	2	2	no	—
484	C₂³	—	2	2	no	—
485	C₂³	—	2	2	no	—
486	C₂³	—	2	2	no	—
487	C₂³	C₂×C₃×C₅×D₄	1	4	yes	—
488	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
489	D₄	—	4	4	no	—
490	D₄	—	4	8	no	—
491	D₄	—	4	8	no	—
492	D₄	—	4	4	no	—
493	C₂×C₄	—	2	2	no	—
494	C₂×C₄	—	2	1	no	—
495	C₂×C₄	—	2	1	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	2	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	2	2	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	2	2	no	—
504	C₂×C₄	—	2	2	no	—
505	C₂×C₄	—	2	2	no	—
506	C₂×C₄	—	2	2	no	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	2	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	4	8	no	—
511	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
512	C₂×C₄	C₃×C₅×#41	1	4	yes	—
513	C₂×C₃	—	4	4	no	—
514	C₂×C₃	—	8	2	no	—
515	C₂×C₃	C₅×#534	1	1	yes	characteristic
516	C₂×C₃	C₅×#540	1	2	yes	—
517	C₂×C₃	C₅×#546	1	2	yes	—
518	C₂×C₃	C₅×#555	1	1	yes	characteristic
519	C₂×C₃	C₅×#560	1	1	yes	characteristic
520	C₅	C₃×#2699	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²	—	2	4	no	—
522	C₂²	—	2	4	no	—
523	C₂²	—	2	4	no	—
524	C₂²	—	4	2	no	—
525	C₂²	—	4	2	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	—	4	2	no	—
530	C₂²	—	4	2	no	—
531	C₂²	—	4	2	no	—
532	C₂²	—	4	2	no	—
533	C₂²	—	4	2	no	—
534	C₂²	—	4	2	no	—
535	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
536	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
537	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
538	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
539	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
540	C₄	—	2	2	no	—
541	C₄	—	2	4	no	—
542	C₄	—	4	2	no	—
543	C₄	—	4	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	4	1	no	—
546	C₄	—	4	1	no	—
547	C₃	C₅×#2699	1	1	yes	characteristic, direct product factor, Sylow
548	C₂	—	4	4	no	—
549	C₂	—	8	2	no	—
550	C₂	C₃×C₅×#534	1	1	yes	characteristic
551	C₂	C₃×C₅×#540	1	2	yes	—
552	C₂	C₃×C₅×#546	1	2	yes	—
553	C₂	C₃×C₅×#555	1	1	yes	characteristic
554	C₂	C₃×C₅×#560	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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
1. C₂×C₃×C₅×#121	C₂	semidirect
2. C₃×C₅×#398	C₂	semidirect
3. C₃×C₅×#394	C₂	semidirect
4. C₃×C₅×#394	C₂	semidirect
5. C₃×C₅×#392	C₂	semidirect
6. C₃×C₅×#390	C₂	semidirect
7. C₃×C₅×#388	C₂	semidirect
8. C₃×C₅×#386	C₂	semidirect
9. C₃×C₅×#381	C₂	semidirect
10. C₅×#2699	C₃	direct (N × H)
33. C₃×#2699	C₅	direct (N × H)
34. C₂×C₅×#121	C₂×C₃	semidirect
35. C₅×#398	C₂×C₃	semidirect
36. C₅×#394	C₂×C₃	semidirect
37. C₅×#394	C₂×C₃	semidirect
38. C₅×#392	C₂×C₃	semidirect
39. C₅×#390	C₂×C₃	semidirect
40. C₅×#388	C₂×C₃	semidirect
41. C₅×#386	C₂×C₃	semidirect
42. C₅×#381	C₂×C₃	semidirect
55. C₂×C₃×C₅×D₄	D₄	semidirect
77. C₂×C₃×#121	C₂×C₅	semidirect
78. C₃×#398	C₂×C₅	semidirect
79. C₃×#394	C₂×C₅	semidirect
80. C₃×#394	C₂×C₅	semidirect
81. C₃×#392	C₂×C₅	semidirect
82. C₃×#390	C₂×C₅	semidirect
83. C₃×#388	C₂×C₅	semidirect
84. C₃×#386	C₂×C₅	semidirect
85. C₃×#381	C₂×C₅	semidirect
108. #2699	C₃×C₅	direct (N × H)
182. C₂×C₅×D₄	C₃×D₄	semidirect
204. C₂×#121	C₂×C₃×C₅	semidirect
205. #398	C₂×C₃×C₅	semidirect
206. #394	C₂×C₃×C₅	semidirect
207. #394	C₂×C₃×C₅	semidirect
208. #392	C₂×C₃×C₅	semidirect
209. #390	C₂×C₃×C₅	semidirect
210. #388	C₂×C₃×C₅	semidirect
211. #386	C₂×C₃×C₅	semidirect
212. #381	C₂×C₃×C₅	semidirect
251. C₂×C₃×D₄	C₅×D₄	semidirect
418. C₂×D₄	C₃×C₅×D₄	semidirect
440. C₃×C₅	#2699	direct (N × H)
520. C₅	C₃×#2699	direct (N × H)
547. C₃	C₅×#2699	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×#121	2
C₃×C₅×#398	2
C₃×C₅×#394	2
C₃×C₅×#392	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#386	2
C₃×C₅×#381	2
C₅×#2699	3
C₃×#2699	5

Subgroups — C3×C5×#2699 #14275733

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2699 #14275733