Subgroups — C₃×C₅×#3280 #14276314

Order 1920.

1052 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#546	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#450	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3280	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	complemented
14	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
15	C₃×C₅×#135	—	2	4	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
18	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×D₈	—	2	4	no	—
20	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
21	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
25	C₃×C₅×#124	C₂²	1	2	yes	complemented
26	C₃×C₅×#123	—	2	2	no	—
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃×C₅×#121	—	2	2	no	—
29	C₃×C₅×#121	C₂²	1	2	yes	complemented
30	C₃×C₅×#120	—	2	2	no	—
31	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₅×D₄	C₂²	1	2	yes	complemented
33	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
34	C₃×C₅×#107	C₂²	1	1	yes	characteristic, complemented
35	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×C₅×#103	C₂²	1	2	yes	complemented
37	C₃×C₅×#102	C₂²	1	2	yes	complemented
38	C₃×C₅×#102	C₂²	1	2	yes	complemented
39	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic, complemented
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
42	C₃×#3280	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#546	C₂×C₃	1	2	yes	complemented
46	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#463	C₂×C₃	1	2	yes	complemented
50	C₅×#450	C₂×C₃	1	2	yes	complemented
51	C₅×#449	C₂×C₃	1	2	yes	complemented
52	C₄×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂⁴×C₃×C₅	—	2	2	no	—
55	C₃×C₅×#41	—	2	4	no	—
56	C₃×C₅×#41	—	4	2	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
58	C₂×C₃×C₅×D₄	—	2	4	no	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	4	2	no	—
63	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	—	2	2	no	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₃×C₅×Q₁₆	—	2	2	no	—
71	C₃×C₅×SD₁₆	—	2	4	no	—
72	C₃×C₅×SD₁₆	—	4	2	no	—
73	C₃×C₅×D₈	—	2	4	no	—
74	C₃×C₅×D₈	—	2	2	no	—
75	C₃×C₅×D₈	D₄	1	4	yes	complemented
76	C₂×C₃×C₅×C₈	—	2	2	no	—
77	C₂×C₃×C₅×C₈	—	2	2	no	—
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	—	2	2	no	—
83	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
91	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#546	C₂×C₅	1	2	yes	complemented
96	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#463	C₂×C₅	1	2	yes	complemented
100	C₃×#450	C₂×C₅	1	2	yes	complemented
101	C₃×#449	C₂×C₅	1	2	yes	complemented
102	C₃×C₄×D₈	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×#41	C₂²×C₃	1	2	yes	complemented
105	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
106	C₅×#135	—	2	4	no	—
107	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
108	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
109	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
110	C₂×C₅×D₈	—	2	4	no	—
111	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
112	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
116	C₅×#124	C₂²×C₃	1	2	yes	complemented
117	C₅×#123	—	2	2	no	—
118	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
119	C₅×#121	—	2	2	no	—
120	C₅×#121	C₂²×C₃	1	2	yes	complemented
121	C₅×#120	—	2	2	no	—
122	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
123	C₄×C₅×D₄	C₂²×C₃	1	2	yes	complemented
124	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
125	C₅×#107	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₅×#103	C₂²×C₃	1	2	yes	complemented
128	C₅×#102	C₂²×C₃	1	2	yes	complemented
129	C₅×#102	C₂²×C₃	1	2	yes	complemented
130	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
131	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic, complemented
132	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
133	#3280	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	—	2	2	no	—
136	C₂³×C₃×C₅	—	4	4	no	—
137	C₂³×C₃×C₅	—	4	4	no	—
138	C₂³×C₃×C₅	—	8	2	no	—
139	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	2	2	no	—
145	C₃×C₅×D₄	—	2	2	no	—
146	C₃×C₅×D₄	—	2	2	no	—
147	C₃×C₅×D₄	—	4	4	no	—
148	C₃×C₅×D₄	—	4	4	no	—
149	C₃×C₅×D₄	—	8	2	no	—
150	C₃×C₅×D₄	C₂×D₄	1	4	yes	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	1	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	4	4	no	—
158	C₂×C₃×C₄×C₅	—	8	2	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₃×C₅×C₈	—	2	1	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃×C₅×C₈	—	2	1	no	—
167	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
168	C₂×C₃×#41	C₂²×C₅	1	2	yes	complemented
169	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
170	C₃×#135	—	2	4	no	—
171	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
172	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
173	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
174	C₂×C₃×D₈	—	2	4	no	—
175	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
176	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
178	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
180	C₃×#124	C₂²×C₅	1	2	yes	complemented
181	C₃×#123	—	2	2	no	—
182	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
183	C₃×#121	—	2	2	no	—
184	C₃×#121	C₂²×C₅	1	2	yes	complemented
185	C₃×#120	—	2	2	no	—
186	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
187	C₃×C₄×D₄	C₂²×C₅	1	2	yes	complemented
188	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
189	C₃×#107	C₂²×C₅	1	1	yes	characteristic, complemented
190	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₃×#103	C₂²×C₅	1	2	yes	complemented
192	C₃×#102	C₂²×C₅	1	2	yes	complemented
193	C₃×#102	C₂²×C₅	1	2	yes	complemented
194	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
195	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic, complemented
197	C₂⁴×C₅	—	2	2	no	—
198	C₅×#41	—	2	4	no	—
199	C₅×#41	—	4	2	no	—
200	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
201	C₂×C₅×D₄	—	2	4	no	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	—	2	2	no	—
204	C₂×C₅×D₄	—	2	2	no	—
205	C₂×C₅×D₄	—	4	2	no	—
206	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
207	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
208	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
209	C₂²×C₄×C₅	—	2	2	no	—
210	C₂²×C₄×C₅	—	2	2	no	—
211	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
212	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
213	C₅×Q₁₆	—	2	2	no	—
214	C₅×SD₁₆	—	2	4	no	—
215	C₅×SD₁₆	—	4	2	no	—
216	C₅×D₈	—	2	4	no	—
217	C₅×D₈	—	2	2	no	—
218	C₅×D₈	C₃×D₄	1	4	yes	complemented
219	C₂×C₅×C₈	—	2	2	no	—
220	C₂×C₅×C₈	—	2	2	no	—
221	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
224	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
225	C₅×C₄⋊C₄	—	2	2	no	—
226	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
227	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	—	2	2	no	—
230	C₅×C₂²⋊C₄	—	2	2	no	—
231	C₅×C₂²⋊C₄	—	2	2	no	—
232	C₅×C₂²⋊C₄	—	2	2	no	—
233	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
234	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
235	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
236	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	#546	C₂×C₃×C₅	1	2	yes	complemented
239	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
240	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
242	#463	C₂×C₃×C₅	1	2	yes	complemented
243	#450	C₂×C₃×C₅	1	2	yes	complemented
244	#449	C₂×C₃×C₅	1	2	yes	complemented
245	C₄×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
246	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	—	2	1	no	—
250	C₂²×C₃×C₅	—	2	4	no	—
251	C₂²×C₃×C₅	—	2	1	no	—
252	C₂²×C₃×C₅	—	2	1	no	—
253	C₂²×C₃×C₅	—	4	2	no	—
254	C₂²×C₃×C₅	—	4	2	no	—
255	C₂²×C₃×C₅	—	4	2	no	—
256	C₂²×C₃×C₅	—	4	2	no	—
257	C₂²×C₃×C₅	—	4	2	no	—
258	C₂²×C₃×C₅	—	8	8	no	—
259	C₂²×C₃×C₅	#135	1	2	yes	complemented
260	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
261	C₃×C₄×C₅	—	2	1	no	—
262	C₃×C₄×C₅	—	2	1	no	—
263	C₃×C₄×C₅	—	2	1	no	—
264	C₃×C₄×C₅	—	2	1	no	—
265	C₃×C₄×C₅	—	4	2	no	—
266	C₃×C₄×C₅	—	4	2	no	—
267	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
268	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
269	C₂⁴×C₃	—	2	2	no	—
270	C₃×#41	—	2	4	no	—
271	C₃×#41	—	4	2	no	—
272	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
273	C₂×C₃×D₄	—	2	4	no	—
274	C₂×C₃×D₄	—	2	2	no	—
275	C₂×C₃×D₄	—	2	2	no	—
276	C₂×C₃×D₄	—	2	2	no	—
277	C₂×C₃×D₄	—	4	2	no	—
278	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
279	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
280	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
281	C₂²×C₃×C₄	—	2	2	no	—
282	C₂²×C₃×C₄	—	2	2	no	—
283	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
284	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
285	C₃×Q₁₆	—	2	2	no	—
286	C₃×SD₁₆	—	2	4	no	—
287	C₃×SD₁₆	—	4	2	no	—
288	C₃×D₈	—	2	4	no	—
289	C₃×D₈	—	2	2	no	—
290	C₃×D₈	C₅×D₄	1	4	yes	complemented
291	C₂×C₃×C₈	—	2	2	no	—
292	C₂×C₃×C₈	—	2	2	no	—
293	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
297	C₃×C₄⋊C₄	—	2	2	no	—
298	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
299	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
300	C₃×C₂²⋊C₄	—	2	2	no	—
301	C₃×C₂²⋊C₄	—	2	2	no	—
302	C₃×C₂²⋊C₄	—	2	2	no	—
303	C₃×C₂²⋊C₄	—	2	2	no	—
304	C₃×C₂²⋊C₄	—	2	2	no	—
305	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
306	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
307	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
308	C₂³×C₅	—	2	2	no	—
309	C₂³×C₅	—	2	2	no	—
310	C₂³×C₅	—	4	4	no	—
311	C₂³×C₅	—	4	4	no	—
312	C₂³×C₅	—	8	2	no	—
313	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
315	C₅×Q₈	—	2	2	no	—
316	C₅×Q₈	—	2	2	no	—
317	C₅×D₄	—	2	2	no	—
318	C₅×D₄	—	2	2	no	—
319	C₅×D₄	—	2	2	no	—
320	C₅×D₄	—	2	2	no	—
321	C₅×D₄	—	4	4	no	—
322	C₅×D₄	—	4	4	no	—
323	C₅×D₄	—	8	2	no	—
324	C₅×D₄	C₂×C₃×D₄	1	4	yes	—
325	C₂×C₄×C₅	—	2	1	no	—
326	C₂×C₄×C₅	—	2	1	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	1	no	—
329	C₂×C₄×C₅	—	2	2	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	4	4	no	—
332	C₂×C₄×C₅	—	8	2	no	—
333	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
334	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
335	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
336	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
337	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
338	C₅×C₈	—	2	1	no	—
339	C₅×C₈	—	2	1	no	—
340	C₅×C₈	—	2	1	no	—
341	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
342	C₂×#41	C₂²×C₃×C₅	1	2	yes	complemented
343	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
344	#135	—	2	4	no	—
345	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
346	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
347	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
348	C₂×D₈	—	2	4	no	—
349	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
350	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
351	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
352	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
353	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
354	#124	C₂²×C₃×C₅	1	2	yes	complemented
355	#123	—	2	2	no	—
356	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
357	#121	—	2	2	no	—
358	#121	C₂²×C₃×C₅	1	2	yes	complemented
359	#120	—	2	2	no	—
360	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
361	C₄×D₄	C₂²×C₃×C₅	1	2	yes	complemented
362	C₂×C₂²⋊C₄	—	2	2	no	—
363	#107	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
364	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
365	#103	C₂²×C₃×C₅	1	2	yes	complemented
366	#102	C₂²×C₃×C₅	1	2	yes	complemented
367	#102	C₂²×C₃×C₅	1	2	yes	complemented
368	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
369	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
370	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
371	C₂×C₃×C₅	—	2	2	no	—
372	C₂×C₃×C₅	—	4	1	no	—
373	C₂×C₃×C₅	—	4	4	no	—
374	C₂×C₃×C₅	—	8	2	no	—
375	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
376	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
377	C₂×C₃×C₅	#576	1	1	yes	characteristic
378	C₂³×C₃	—	2	2	no	—
379	C₂³×C₃	—	2	2	no	—
380	C₂³×C₃	—	4	4	no	—
381	C₂³×C₃	—	4	4	no	—
382	C₂³×C₃	—	8	2	no	—
383	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
384	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
385	C₃×Q₈	—	2	2	no	—
386	C₃×Q₈	—	2	2	no	—
387	C₃×D₄	—	2	2	no	—
388	C₃×D₄	—	2	2	no	—
389	C₃×D₄	—	2	2	no	—
390	C₃×D₄	—	2	2	no	—
391	C₃×D₄	—	4	4	no	—
392	C₃×D₄	—	4	4	no	—
393	C₃×D₄	—	8	2	no	—
394	C₃×D₄	C₂×C₅×D₄	1	4	yes	—
395	C₂×C₃×C₄	—	2	1	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	1	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	4	4	no	—
402	C₂×C₃×C₄	—	8	2	no	—
403	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
404	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
405	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
406	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
407	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
408	C₃×C₈	—	2	1	no	—
409	C₃×C₈	—	2	1	no	—
410	C₃×C₈	—	2	1	no	—
411	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
412	C₂²×C₅	—	2	1	no	—
413	C₂²×C₅	—	2	1	no	—
414	C₂²×C₅	—	2	1	no	—
415	C₂²×C₅	—	2	1	no	—
416	C₂²×C₅	—	2	1	no	—
417	C₂²×C₅	—	2	4	no	—
418	C₂²×C₅	—	4	2	no	—
419	C₂²×C₅	—	4	2	no	—
420	C₂²×C₅	—	4	2	no	—
421	C₂²×C₅	—	4	2	no	—
422	C₂²×C₅	—	4	2	no	—
423	C₂²×C₅	—	8	8	no	—
424	C₂²×C₅	C₃×#135	1	2	yes	complemented
425	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
426	C₄×C₅	—	2	1	no	—
427	C₄×C₅	—	2	1	no	—
428	C₄×C₅	—	2	1	no	—
429	C₄×C₅	—	2	1	no	—
430	C₄×C₅	—	4	2	no	—
431	C₄×C₅	—	4	2	no	—
432	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
433	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
434	C₂⁴	—	2	2	no	—
435	#41	—	2	4	no	—
436	#41	—	4	2	no	—
437	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
438	C₂×D₄	—	2	4	no	—
439	C₂×D₄	—	2	2	no	—
440	C₂×D₄	—	2	2	no	—
441	C₂×D₄	—	2	2	no	—
442	C₂×D₄	—	4	2	no	—
443	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
444	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
445	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
446	C₂²×C₄	—	2	2	no	—
447	C₂²×C₄	—	2	2	no	—
448	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
449	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
450	Q₁₆	—	2	2	no	—
451	SD₁₆	—	2	4	no	—
452	SD₁₆	—	4	2	no	—
453	D₈	—	2	4	no	—
454	D₈	—	2	2	no	—
455	D₈	C₃×C₅×D₄	1	4	yes	complemented
456	C₂×C₈	—	2	2	no	—
457	C₂×C₈	—	2	2	no	—
458	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
459	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
460	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
461	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
464	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
465	C₂²⋊C₄	—	2	2	no	—
466	C₂²⋊C₄	—	2	2	no	—
467	C₂²⋊C₄	—	2	2	no	—
468	C₂²⋊C₄	—	2	2	no	—
469	C₂²⋊C₄	—	2	2	no	—
470	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
471	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
472	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
473	C₃×C₅	#3280	1	1	yes	characteristic, direct product factor, Hall
474	C₂²×C₃	—	2	1	no	—
475	C₂²×C₃	—	2	1	no	—
476	C₂²×C₃	—	2	1	no	—
477	C₂²×C₃	—	2	4	no	—
478	C₂²×C₃	—	2	1	no	—
479	C₂²×C₃	—	2	1	no	—
480	C₂²×C₃	—	4	2	no	—
481	C₂²×C₃	—	4	2	no	—
482	C₂²×C₃	—	4	2	no	—
483	C₂²×C₃	—	4	2	no	—
484	C₂²×C₃	—	4	2	no	—
485	C₂²×C₃	—	8	8	no	—
486	C₂²×C₃	C₅×#135	1	2	yes	complemented
487	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
488	C₃×C₄	—	2	1	no	—
489	C₃×C₄	—	2	1	no	—
490	C₃×C₄	—	2	1	no	—
491	C₃×C₄	—	2	1	no	—
492	C₃×C₄	—	4	2	no	—
493	C₃×C₄	—	4	2	no	—
494	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
495	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
496	C₂×C₅	—	2	2	no	—
497	C₂×C₅	—	4	1	no	—
498	C₂×C₅	—	4	4	no	—
499	C₂×C₅	—	8	2	no	—
500	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
501	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
502	C₂×C₅	C₃×#576	1	1	yes	characteristic
503	C₂³	—	2	2	no	—
504	C₂³	—	2	2	no	—
505	C₂³	—	4	4	no	—
506	C₂³	—	4	4	no	—
507	C₂³	—	8	2	no	—
508	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
509	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
510	Q₈	—	2	2	no	—
511	Q₈	—	2	2	no	—
512	D₄	—	2	2	no	—
513	D₄	—	2	2	no	—
514	D₄	—	2	2	no	—
515	D₄	—	2	2	no	—
516	D₄	—	4	4	no	—
517	D₄	—	4	4	no	—
518	D₄	—	8	2	no	—
519	D₄	C₂×C₃×C₅×D₄	1	4	yes	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	1	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	2	no	—
525	C₂×C₄	—	2	2	no	—
526	C₂×C₄	—	4	4	no	—
527	C₂×C₄	—	8	2	no	—
528	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
529	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
530	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
531	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
532	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
533	C₈	—	2	1	no	—
534	C₈	—	2	1	no	—
535	C₈	—	2	1	no	—
536	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
537	C₂×C₃	—	2	2	no	—
538	C₂×C₃	—	4	1	no	—
539	C₂×C₃	—	4	4	no	—
540	C₂×C₃	—	8	2	no	—
541	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
542	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
543	C₂×C₃	C₅×#576	1	1	yes	characteristic
544	C₅	C₃×#3280	1	1	yes	characteristic, direct product factor, Sylow
545	C₂²	—	2	1	no	—
546	C₂²	—	2	1	no	—
547	C₂²	—	2	1	no	—
548	C₂²	—	2	4	no	—
549	C₂²	—	2	1	no	—
550	C₂²	—	2	1	no	—
551	C₂²	—	4	2	no	—
552	C₂²	—	4	2	no	—
553	C₂²	—	4	2	no	—
554	C₂²	—	4	2	no	—
555	C₂²	—	4	2	no	—
556	C₂²	—	8	8	no	—
557	C₂²	C₃×C₅×#135	1	2	yes	complemented
558	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
559	C₄	—	2	1	no	—
560	C₄	—	2	1	no	—
561	C₄	—	2	1	no	—
562	C₄	—	2	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	4	2	no	—
565	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
566	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
567	C₃	C₅×#3280	1	1	yes	characteristic, direct product factor, Sylow
568	C₂	—	2	2	no	—
569	C₂	—	4	1	no	—
570	C₂	—	4	4	no	—
571	C₂	—	8	2	no	—
572	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
573	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
574	C₂	C₃×C₅×#576	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₄×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#135	C₂	semidirect
2. C₂²×C₃×C₅×D₈	C₂	semidirect
3. C₃×C₅×#546	C₂	semidirect
4. C₃×C₅×#495	C₂	semidirect
5. C₃×C₅×#467	C₂	semidirect
6. C₃×C₅×#466	C₂	semidirect
7. C₃×C₅×#463	C₂	semidirect
8. C₃×C₅×#450	C₂	semidirect
9. C₃×C₅×#449	C₂	semidirect
10. C₃×C₄×C₅×D₈	C₂	semidirect
11. C₃×C₅×C₈×D₄	C₂	semidirect
12. C₅×#3280	C₃	direct (N × H)
13. C₂×C₃×C₅×#41	C₂²	semidirect
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
17. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
18. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
24. C₂²×C₃×C₅×C₈	C₂²	semidirect
25. C₃×C₅×#124	C₂²	semidirect
29. C₃×C₅×#121	C₂²	semidirect
32. C₃×C₄×C₅×D₄	C₂²	semidirect
34. C₃×C₅×#107	C₂²	semidirect
35. C₃×C₅×C₄⋊C₈	C₂²	semidirect
36. C₃×C₅×#103	C₂²	semidirect
37. C₃×C₅×#102	C₂²	semidirect
38. C₃×C₅×#102	C₂²	semidirect
40. C₃×C₅×C₂²⋊C₈	C₂²	semidirect
41. C₃×C₄×C₅×C₈	C₂²	semidirect
42. C₃×#3280	C₅	direct (N × H)
43. C₂×C₅×#135	C₂×C₃	semidirect
44. C₂²×C₅×D₈	C₂×C₃	semidirect
45. C₅×#546	C₂×C₃	semidirect
46. C₅×#495	C₂×C₃	semidirect
47. C₅×#467	C₂×C₃	semidirect
48. C₅×#466	C₂×C₃	semidirect
49. C₅×#463	C₂×C₃	semidirect
50. C₅×#450	C₂×C₃	semidirect
51. C₅×#449	C₂×C₃	semidirect
52. C₄×C₅×D₈	C₂×C₃	semidirect
53. C₅×C₈×D₄	C₂×C₃	semidirect
75. C₃×C₅×D₈	D₄	semidirect
93. C₂×C₃×#135	C₂×C₅	semidirect
94. C₂²×C₃×D₈	C₂×C₅	semidirect
95. C₃×#546	C₂×C₅	semidirect
96. C₃×#495	C₂×C₅	semidirect
97. C₃×#467	C₂×C₅	semidirect
98. C₃×#466	C₂×C₅	semidirect
99. C₃×#463	C₂×C₅	semidirect
100. C₃×#450	C₂×C₅	semidirect
101. C₃×#449	C₂×C₅	semidirect
102. C₃×C₄×D₈	C₂×C₅	semidirect
103. C₃×C₈×D₄	C₂×C₅	semidirect
104. C₂×C₅×#41	C₂²×C₃	semidirect
107. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
108. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
109. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
115. C₂²×C₅×C₈	C₂²×C₃	semidirect
116. C₅×#124	C₂²×C₃	semidirect
120. C₅×#121	C₂²×C₃	semidirect
123. C₄×C₅×D₄	C₂²×C₃	semidirect
125. C₅×#107	C₂²×C₃	semidirect
126. C₅×C₄⋊C₈	C₂²×C₃	semidirect
127. C₅×#103	C₂²×C₃	semidirect
128. C₅×#102	C₂²×C₃	semidirect
129. C₅×#102	C₂²×C₃	semidirect
131. C₅×C₂²⋊C₈	C₂²×C₃	semidirect
132. C₄×C₅×C₈	C₂²×C₃	semidirect
133. #3280	C₃×C₅	direct (N × H)
168. C₂×C₃×#41	C₂²×C₅	semidirect
171. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
172. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
173. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
179. C₂²×C₃×C₈	C₂²×C₅	semidirect
180. C₃×#124	C₂²×C₅	semidirect
184. C₃×#121	C₂²×C₅	semidirect
187. C₃×C₄×D₄	C₂²×C₅	semidirect
189. C₃×#107	C₂²×C₅	semidirect
190. C₃×C₄⋊C₈	C₂²×C₅	semidirect
191. C₃×#103	C₂²×C₅	semidirect
192. C₃×#102	C₂²×C₅	semidirect
193. C₃×#102	C₂²×C₅	semidirect
195. C₃×C₂²⋊C₈	C₂²×C₅	semidirect
196. C₃×C₄×C₈	C₂²×C₅	semidirect
218. C₅×D₈	C₃×D₄	semidirect
236. C₂×#135	C₂×C₃×C₅	semidirect
237. C₂²×D₈	C₂×C₃×C₅	semidirect
238. #546	C₂×C₃×C₅	semidirect
239. #495	C₂×C₃×C₅	semidirect
240. #467	C₂×C₃×C₅	semidirect
241. #466	C₂×C₃×C₅	semidirect
242. #463	C₂×C₃×C₅	semidirect
243. #450	C₂×C₃×C₅	semidirect
244. #449	C₂×C₃×C₅	semidirect
245. C₄×D₈	C₂×C₃×C₅	semidirect
246. C₈×D₄	C₂×C₃×C₅	semidirect
259. C₂²×C₃×C₅	#135	semidirect
290. C₃×D₈	C₅×D₄	semidirect
342. C₂×#41	C₂²×C₃×C₅	semidirect
345. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
346. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
347. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
353. C₂²×C₈	C₂²×C₃×C₅	semidirect
354. #124	C₂²×C₃×C₅	semidirect
358. #121	C₂²×C₃×C₅	semidirect
361. C₄×D₄	C₂²×C₃×C₅	semidirect
363. #107	C₂²×C₃×C₅	semidirect
364. C₄⋊C₈	C₂²×C₃×C₅	semidirect
365. #103	C₂²×C₃×C₅	semidirect
366. #102	C₂²×C₃×C₅	semidirect
367. #102	C₂²×C₃×C₅	semidirect
369. C₂²⋊C₈	C₂²×C₃×C₅	semidirect
370. C₄×C₈	C₂²×C₃×C₅	semidirect
424. C₂²×C₅	C₃×#135	semidirect
455. D₈	C₃×C₅×D₄	semidirect
473. C₃×C₅	#3280	direct (N × H)
486. C₂²×C₃	C₅×#135	semidirect
544. C₅	C₃×#3280	direct (N × H)
557. C₂²	C₃×C₅×#135	semidirect
567. C₃	C₅×#3280	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×#135	2
C₂²×C₃×C₅×D₈	2
C₃×C₅×#546	2
C₃×C₅×#495	2
C₃×C₅×#467	2
C₃×C₅×#466	2
C₃×C₅×#463	2
C₃×C₅×#450	2
C₃×C₅×#449	2
C₃×C₄×C₅×D₈	2
C₃×C₅×C₈×D₄	2
C₅×#3280	3
C₃×#3280	5

Subgroups — C3×C5×#3280 #14276314

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3280 #14276314