Subgroups — C₃×C₅×#3046 #14276080

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#520	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#463	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#462	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#461	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#424	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3046	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#137	—	2	4	no	—
17	C₃×C₅×#135	—	2	4	no	—
18	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
22	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
25	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
26	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
27	C₃×C₅×#124	C₂²	1	2	yes	—
28	C₃×C₅×#123	—	2	2	no	—
29	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
30	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
31	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
32	C₃×C₄×C₅×D₄	—	2	2	no	—
33	C₃×C₄×C₅×D₄	C₂²	1	2	yes	—
34	C₃×C₅×#117	—	2	1	no	—
35	C₃×C₅×#117	C₂²	1	1	yes	characteristic
36	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
37	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
38	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
39	C₃×C₅×C₄⋊C₈	C₂²	1	2	yes	—
40	C₃×C₅×#103	C₂²	1	2	yes	—
41	C₃×C₅×#103	C₂²	1	2	yes	—
42	C₃×C₅×#103	C₂²	1	2	yes	—
43	C₃×C₅×#102	C₂²	1	2	yes	—
44	C₃×#3046	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic
47	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#520	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#464	C₂×C₃	1	2	yes	complemented
50	C₅×#463	C₂×C₃	1	2	yes	complemented
51	C₅×#462	C₂×C₃	1	2	yes	complemented
52	C₅×#461	C₂×C₃	1	2	yes	complemented
53	C₅×#424	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
55	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	D₄	1	4	yes	—
60	C₂×C₃×C₅×Q₈	—	2	1	no	—
61	C₂×C₃×C₅×Q₈	—	2	2	no	—
62	C₂×C₃×C₅×Q₈	—	2	2	no	—
63	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
64	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×D₄	—	2	1	no	—
67	C₂×C₃×C₅×D₄	—	2	1	no	—
68	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	—	2	1	no	—
71	C₂²×C₃×C₄×C₅	—	2	1	no	—
72	C₂²×C₃×C₄×C₅	—	2	1	no	—
73	C₂²×C₃×C₄×C₅	—	2	1	no	—
74	C₂²×C₃×C₄×C₅	—	2	2	no	—
75	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
76	C₃×C₅×Q₁₆	—	2	2	no	—
77	C₃×C₅×Q₁₆	—	2	4	no	—
78	C₃×C₅×SD₁₆	—	2	2	no	—
79	C₃×C₅×SD₁₆	—	2	2	no	—
80	C₃×C₅×SD₁₆	—	2	4	no	—
81	C₃×C₅×D₈	—	2	2	no	—
82	C₃×C₅×M₁₆	—	2	2	no	—
83	C₂×C₃×C₅×C₈	—	2	2	no	—
84	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
85	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
87	C₃×C₅×C₄⋊C₄	—	2	1	no	—
88	C₃×C₅×C₄⋊C₄	—	2	2	no	—
89	C₃×C₅×C₄⋊C₄	—	2	2	no	—
90	C₃×C₅×C₄⋊C₄	—	2	2	no	—
91	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
92	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
93	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
94	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
95	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
96	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
97	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
98	C₃×C₄²×C₅	—	2	2	no	—
99	C₃×C₄²×C₅	C₂³	1	2	yes	—
100	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
101	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic
102	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×#520	C₂×C₅	1	1	yes	characteristic, complemented
104	C₃×#464	C₂×C₅	1	2	yes	complemented
105	C₃×#463	C₂×C₅	1	2	yes	complemented
106	C₃×#462	C₂×C₅	1	2	yes	complemented
107	C₃×#461	C₂×C₅	1	2	yes	complemented
108	C₃×#424	C₂×C₅	1	1	yes	characteristic, complemented
109	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
110	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
111	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₅×#137	—	2	4	no	—
115	C₅×#135	—	2	4	no	—
116	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
118	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
119	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
120	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
122	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
123	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
124	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
125	C₅×#124	C₂²×C₃	1	2	yes	—
126	C₅×#123	—	2	2	no	—
127	C₅×C₂²⋊Q₈	—	2	1	no	—
128	C₅×C₂²⋊Q₈	—	2	1	no	—
129	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
130	C₄×C₅×D₄	—	2	2	no	—
131	C₄×C₅×D₄	C₂²×C₃	1	2	yes	—
132	C₅×#117	—	2	1	no	—
133	C₅×#117	C₂²×C₃	1	1	yes	characteristic
134	C₂×C₅×C₄⋊C₄	—	2	1	no	—
135	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
136	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
137	C₅×C₄⋊C₈	C₂²×C₃	1	2	yes	—
138	C₅×#103	C₂²×C₃	1	2	yes	—
139	C₅×#103	C₂²×C₃	1	2	yes	—
140	C₅×#103	C₂²×C₃	1	2	yes	—
141	C₅×#102	C₂²×C₃	1	2	yes	—
142	#3046	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
143	C₂³×C₃×C₅	—	2	1	no	—
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₃×C₅×Q₈	—	2	1	no	—
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	—	2	1	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	4	2	no	—
152	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
153	C₃×C₅×D₄	—	2	4	no	—
154	C₃×C₅×D₄	—	2	1	no	—
155	C₃×C₅×D₄	—	2	1	no	—
156	C₃×C₅×D₄	—	2	1	no	—
157	C₃×C₅×D₄	—	4	2	no	—
158	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	—	2	1	no	—
160	C₂×C₃×C₄×C₅	—	2	4	no	—
161	C₂×C₃×C₄×C₅	—	2	2	no	—
162	C₂×C₃×C₄×C₅	—	2	2	no	—
163	C₂×C₃×C₄×C₅	—	2	1	no	—
164	C₂×C₃×C₄×C₅	—	4	2	no	—
165	C₂×C₃×C₄×C₅	—	4	2	no	—
166	C₂×C₃×C₄×C₅	—	8	2	no	—
167	C₂×C₃×C₄×C₅	—	8	1	no	—
168	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
169	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
170	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
171	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
172	C₂×C₃×C₄×C₅	#41	1	2	yes	—
173	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
174	C₃×C₅×C₈	—	2	1	no	—
175	C₃×C₅×C₈	—	2	1	no	—
176	C₃×C₅×C₈	—	2	2	no	—
177	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
179	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
180	C₃×#137	—	2	4	no	—
181	C₃×#135	—	2	4	no	—
182	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
184	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
187	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
189	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
190	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	—
191	C₃×#124	C₂²×C₅	1	2	yes	—
192	C₃×#123	—	2	2	no	—
193	C₃×C₂²⋊Q₈	—	2	1	no	—
194	C₃×C₂²⋊Q₈	—	2	1	no	—
195	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
196	C₃×C₄×D₄	—	2	2	no	—
197	C₃×C₄×D₄	C₂²×C₅	1	2	yes	—
198	C₃×#117	—	2	1	no	—
199	C₃×#117	C₂²×C₅	1	1	yes	characteristic
200	C₂×C₃×C₄⋊C₄	—	2	1	no	—
201	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
202	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
203	C₃×C₄⋊C₈	C₂²×C₅	1	2	yes	—
204	C₃×#103	C₂²×C₅	1	2	yes	—
205	C₃×#103	C₂²×C₅	1	2	yes	—
206	C₃×#103	C₂²×C₅	1	2	yes	—
207	C₃×#102	C₂²×C₅	1	2	yes	—
208	C₅×#41	—	2	2	no	—
209	C₅×#41	—	2	2	no	—
210	C₅×#41	—	2	2	no	—
211	C₅×#41	C₃×D₄	1	4	yes	—
212	C₂×C₅×Q₈	—	2	1	no	—
213	C₂×C₅×Q₈	—	2	2	no	—
214	C₂×C₅×Q₈	—	2	2	no	—
215	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
216	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₅×D₄	—	2	1	no	—
219	C₂×C₅×D₄	—	2	1	no	—
220	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
222	C₂²×C₄×C₅	—	2	1	no	—
223	C₂²×C₄×C₅	—	2	1	no	—
224	C₂²×C₄×C₅	—	2	1	no	—
225	C₂²×C₄×C₅	—	2	1	no	—
226	C₂²×C₄×C₅	—	2	2	no	—
227	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
228	C₅×Q₁₆	—	2	2	no	—
229	C₅×Q₁₆	—	2	4	no	—
230	C₅×SD₁₆	—	2	2	no	—
231	C₅×SD₁₆	—	2	2	no	—
232	C₅×SD₁₆	—	2	4	no	—
233	C₅×D₈	—	2	2	no	—
234	C₅×M₁₆	—	2	2	no	—
235	C₂×C₅×C₈	—	2	2	no	—
236	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
237	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
238	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
239	C₅×C₄⋊C₄	—	2	1	no	—
240	C₅×C₄⋊C₄	—	2	2	no	—
241	C₅×C₄⋊C₄	—	2	2	no	—
242	C₅×C₄⋊C₄	—	2	2	no	—
243	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
244	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
245	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
246	C₅×C₂²⋊C₄	—	2	2	no	—
247	C₅×C₂²⋊C₄	—	2	2	no	—
248	C₅×C₂²⋊C₄	—	2	2	no	—
249	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
250	C₄²×C₅	—	2	2	no	—
251	C₄²×C₅	C₂³×C₃	1	2	yes	—
252	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
253	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic
254	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
255	#520	C₂×C₃×C₅	1	1	yes	characteristic, complemented
256	#464	C₂×C₃×C₅	1	2	yes	complemented
257	#463	C₂×C₃×C₅	1	2	yes	complemented
258	#462	C₂×C₃×C₅	1	2	yes	complemented
259	#461	C₂×C₃×C₅	1	2	yes	complemented
260	#424	C₂×C₃×C₅	1	1	yes	characteristic, complemented
261	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
263	C₂²×C₃×C₅	—	2	1	no	—
264	C₂²×C₃×C₅	—	2	1	no	—
265	C₂²×C₃×C₅	—	2	2	no	—
266	C₂²×C₃×C₅	—	4	1	no	—
267	C₂²×C₃×C₅	—	4	1	no	—
268	C₂²×C₃×C₅	—	4	1	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	—	4	1	no	—
271	C₂²×C₃×C₅	#121	1	2	yes	—
272	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
273	C₃×C₄×C₅	—	2	2	no	—
274	C₃×C₄×C₅	—	2	2	no	—
275	C₃×C₄×C₅	—	2	2	no	—
276	C₃×C₄×C₅	—	4	1	no	—
277	C₃×C₄×C₅	—	4	2	no	—
278	C₃×C₄×C₅	—	4	2	no	—
279	C₃×C₄×C₅	#121	1	2	yes	—
280	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
281	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
282	C₃×#41	—	2	2	no	—
283	C₃×#41	—	2	2	no	—
284	C₃×#41	—	2	2	no	—
285	C₃×#41	C₅×D₄	1	4	yes	—
286	C₂×C₃×Q₈	—	2	1	no	—
287	C₂×C₃×Q₈	—	2	2	no	—
288	C₂×C₃×Q₈	—	2	2	no	—
289	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
290	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
291	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
292	C₂×C₃×D₄	—	2	1	no	—
293	C₂×C₃×D₄	—	2	1	no	—
294	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
295	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
296	C₂²×C₃×C₄	—	2	1	no	—
297	C₂²×C₃×C₄	—	2	1	no	—
298	C₂²×C₃×C₄	—	2	1	no	—
299	C₂²×C₃×C₄	—	2	1	no	—
300	C₂²×C₃×C₄	—	2	2	no	—
301	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
302	C₃×Q₁₆	—	2	2	no	—
303	C₃×Q₁₆	—	2	4	no	—
304	C₃×SD₁₆	—	2	2	no	—
305	C₃×SD₁₆	—	2	2	no	—
306	C₃×SD₁₆	—	2	4	no	—
307	C₃×D₈	—	2	2	no	—
308	C₃×M₁₆	—	2	2	no	—
309	C₂×C₃×C₈	—	2	2	no	—
310	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
311	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
312	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
313	C₃×C₄⋊C₄	—	2	1	no	—
314	C₃×C₄⋊C₄	—	2	2	no	—
315	C₃×C₄⋊C₄	—	2	2	no	—
316	C₃×C₄⋊C₄	—	2	2	no	—
317	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
318	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
319	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
320	C₃×C₂²⋊C₄	—	2	2	no	—
321	C₃×C₂²⋊C₄	—	2	2	no	—
322	C₃×C₂²⋊C₄	—	2	2	no	—
323	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
324	C₃×C₄²	—	2	2	no	—
325	C₃×C₄²	C₂³×C₅	1	2	yes	—
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	—	2	1	no	—
328	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
329	C₅×Q₈	—	2	1	no	—
330	C₅×Q₈	—	2	2	no	—
331	C₅×Q₈	—	2	1	no	—
332	C₅×Q₈	—	2	2	no	—
333	C₅×Q₈	—	2	1	no	—
334	C₅×Q₈	—	4	2	no	—
335	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
336	C₅×D₄	—	2	4	no	—
337	C₅×D₄	—	2	1	no	—
338	C₅×D₄	—	2	1	no	—
339	C₅×D₄	—	2	1	no	—
340	C₅×D₄	—	4	2	no	—
341	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
342	C₂×C₄×C₅	—	2	1	no	—
343	C₂×C₄×C₅	—	2	4	no	—
344	C₂×C₄×C₅	—	2	2	no	—
345	C₂×C₄×C₅	—	2	2	no	—
346	C₂×C₄×C₅	—	2	1	no	—
347	C₂×C₄×C₅	—	4	2	no	—
348	C₂×C₄×C₅	—	4	2	no	—
349	C₂×C₄×C₅	—	8	2	no	—
350	C₂×C₄×C₅	—	8	1	no	—
351	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
352	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
353	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
354	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
355	C₂×C₄×C₅	C₃×#41	1	2	yes	—
356	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
357	C₅×C₈	—	2	1	no	—
358	C₅×C₈	—	2	1	no	—
359	C₅×C₈	—	2	2	no	—
360	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
361	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
362	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
363	#137	—	2	4	no	—
364	#135	—	2	4	no	—
365	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
366	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
367	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
368	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
369	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
370	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
371	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
372	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
373	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
374	#124	C₂²×C₃×C₅	1	2	yes	—
375	#123	—	2	2	no	—
376	C₂²⋊Q₈	—	2	1	no	—
377	C₂²⋊Q₈	—	2	1	no	—
378	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
379	C₄×D₄	—	2	2	no	—
380	C₄×D₄	C₂²×C₃×C₅	1	2	yes	—
381	#117	—	2	1	no	—
382	#117	C₂²×C₃×C₅	1	1	yes	characteristic
383	C₂×C₄⋊C₄	—	2	1	no	—
384	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
385	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
386	C₄⋊C₈	C₂²×C₃×C₅	1	2	yes	—
387	#103	C₂²×C₃×C₅	1	2	yes	—
388	#103	C₂²×C₃×C₅	1	2	yes	—
389	#103	C₂²×C₃×C₅	1	2	yes	—
390	#102	C₂²×C₃×C₅	1	2	yes	—
391	C₂×C₃×C₅	—	2	2	no	—
392	C₂×C₃×C₅	—	4	2	no	—
393	C₂×C₃×C₅	—	8	1	no	—
394	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
395	C₂×C₃×C₅	#577	1	1	yes	characteristic
396	C₂×C₃×C₅	#578	1	1	yes	characteristic
397	C₂³×C₃	—	2	1	no	—
398	C₂³×C₃	—	2	1	no	—
399	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
400	C₃×Q₈	—	2	1	no	—
401	C₃×Q₈	—	2	2	no	—
402	C₃×Q₈	—	2	1	no	—
403	C₃×Q₈	—	2	2	no	—
404	C₃×Q₈	—	2	1	no	—
405	C₃×Q₈	—	4	2	no	—
406	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
407	C₃×D₄	—	2	4	no	—
408	C₃×D₄	—	2	1	no	—
409	C₃×D₄	—	2	1	no	—
410	C₃×D₄	—	2	1	no	—
411	C₃×D₄	—	4	2	no	—
412	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
413	C₂×C₃×C₄	—	2	1	no	—
414	C₂×C₃×C₄	—	2	4	no	—
415	C₂×C₃×C₄	—	2	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	4	2	no	—
419	C₂×C₃×C₄	—	4	2	no	—
420	C₂×C₃×C₄	—	8	2	no	—
421	C₂×C₃×C₄	—	8	1	no	—
422	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
423	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
424	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
425	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
426	C₂×C₃×C₄	C₅×#41	1	2	yes	—
427	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
428	C₃×C₈	—	2	1	no	—
429	C₃×C₈	—	2	1	no	—
430	C₃×C₈	—	2	2	no	—
431	C₂²×C₅	—	2	1	no	—
432	C₂²×C₅	—	2	1	no	—
433	C₂²×C₅	—	2	2	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	—	4	1	no	—
436	C₂²×C₅	—	4	1	no	—
437	C₂²×C₅	—	4	1	no	—
438	C₂²×C₅	—	4	1	no	—
439	C₂²×C₅	C₃×#121	1	2	yes	—
440	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
441	C₄×C₅	—	2	2	no	—
442	C₄×C₅	—	2	2	no	—
443	C₄×C₅	—	2	2	no	—
444	C₄×C₅	—	4	2	no	—
445	C₄×C₅	—	4	1	no	—
446	C₄×C₅	—	4	2	no	—
447	C₄×C₅	C₃×#121	1	2	yes	—
448	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
449	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
450	#41	—	2	2	no	—
451	#41	—	2	2	no	—
452	#41	—	2	2	no	—
453	#41	C₃×C₅×D₄	1	4	yes	—
454	C₂×Q₈	—	2	1	no	—
455	C₂×Q₈	—	2	2	no	—
456	C₂×Q₈	—	2	2	no	—
457	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
458	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
459	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
460	C₂×D₄	—	2	1	no	—
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
463	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
464	C₂²×C₄	—	2	1	no	—
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	2	1	no	—
468	C₂²×C₄	—	2	2	no	—
469	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
470	Q₁₆	—	2	2	no	—
471	Q₁₆	—	2	4	no	—
472	SD₁₆	—	2	2	no	—
473	SD₁₆	—	2	2	no	—
474	SD₁₆	—	2	4	no	—
475	D₈	—	2	2	no	—
476	M₁₆	—	2	2	no	—
477	C₂×C₈	—	2	2	no	—
478	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
479	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
480	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
481	C₄⋊C₄	—	2	1	no	—
482	C₄⋊C₄	—	2	2	no	—
483	C₄⋊C₄	—	2	2	no	—
484	C₄⋊C₄	—	2	2	no	—
485	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
486	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
487	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
488	C₂²⋊C₄	—	2	2	no	—
489	C₂²⋊C₄	—	2	2	no	—
490	C₂²⋊C₄	—	2	2	no	—
491	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
492	C₄²	—	2	2	no	—
493	C₄²	C₂³×C₃×C₅	1	2	yes	—
494	C₃×C₅	#3046	1	1	yes	characteristic, direct product factor, Hall
495	C₂²×C₃	—	2	1	no	—
496	C₂²×C₃	—	2	1	no	—
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	4	1	no	—
499	C₂²×C₃	—	4	1	no	—
500	C₂²×C₃	—	4	1	no	—
501	C₂²×C₃	—	4	1	no	—
502	C₂²×C₃	—	4	1	no	—
503	C₂²×C₃	C₅×#121	1	2	yes	—
504	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
505	C₃×C₄	—	2	2	no	—
506	C₃×C₄	—	2	2	no	—
507	C₃×C₄	—	2	2	no	—
508	C₃×C₄	—	4	1	no	—
509	C₃×C₄	—	4	2	no	—
510	C₃×C₄	—	4	2	no	—
511	C₃×C₄	C₅×#121	1	2	yes	—
512	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
513	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
514	C₂×C₅	—	2	2	no	—
515	C₂×C₅	—	4	2	no	—
516	C₂×C₅	—	8	1	no	—
517	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
518	C₂×C₅	C₃×#577	1	1	yes	characteristic
519	C₂×C₅	C₃×#578	1	1	yes	characteristic
520	C₂³	—	2	1	no	—
521	C₂³	—	2	1	no	—
522	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
523	Q₈	—	2	1	no	—
524	Q₈	—	2	2	no	—
525	Q₈	—	2	1	no	—
526	Q₈	—	2	2	no	—
527	Q₈	—	2	1	no	—
528	Q₈	—	4	2	no	—
529	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
530	D₄	—	2	4	no	—
531	D₄	—	2	1	no	—
532	D₄	—	2	1	no	—
533	D₄	—	2	1	no	—
534	D₄	—	4	2	no	—
535	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
536	C₂×C₄	—	2	1	no	—
537	C₂×C₄	—	2	4	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	2	no	—
540	C₂×C₄	—	2	1	no	—
541	C₂×C₄	—	4	2	no	—
542	C₂×C₄	—	4	2	no	—
543	C₂×C₄	—	8	2	no	—
544	C₂×C₄	—	8	1	no	—
545	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
546	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
547	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
548	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
549	C₂×C₄	C₃×C₅×#41	1	2	yes	—
550	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
551	C₈	—	2	1	no	—
552	C₈	—	2	1	no	—
553	C₈	—	2	2	no	—
554	C₂×C₃	—	2	2	no	—
555	C₂×C₃	—	4	2	no	—
556	C₂×C₃	—	8	1	no	—
557	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
558	C₂×C₃	C₅×#577	1	1	yes	characteristic
559	C₂×C₃	C₅×#578	1	1	yes	characteristic
560	C₅	C₃×#3046	1	1	yes	characteristic, direct product factor, Sylow
561	C₂²	—	2	1	no	—
562	C₂²	—	2	1	no	—
563	C₂²	—	2	2	no	—
564	C₂²	—	4	1	no	—
565	C₂²	—	4	1	no	—
566	C₂²	—	4	1	no	—
567	C₂²	—	4	1	no	—
568	C₂²	—	4	1	no	—
569	C₂²	C₃×C₅×#121	1	2	yes	—
570	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	1	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	C₃×C₅×#121	1	2	yes	—
578	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
579	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
580	C₃	C₅×#3046	1	1	yes	characteristic, direct product factor, Sylow
581	C₂	—	2	2	no	—
582	C₂	—	4	2	no	—
583	C₂	—	8	1	no	—
584	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic
585	C₂	C₃×C₅×#577	1	1	yes	characteristic
586	C₂	C₃×C₅×#578	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₂×C₃×C₅×#135	C₂
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
3. C₃×C₅×#536	C₂	semidirect
4. C₃×C₅×#520	C₂	semidirect
5. C₃×C₅×#464	C₂	semidirect
6. C₃×C₅×#463	C₂	semidirect
7. C₃×C₅×#462	C₂	semidirect
8. C₃×C₅×#461	C₂	semidirect
9. C₃×C₅×#424	C₂	semidirect
10. C₃×C₅×#417	C₂	semidirect
11. C₂×C₃×C₅×#103	C₂	semidirect
12. C₅×#3046	C₃	direct (N × H)
44. C₃×#3046	C₅	direct (N × H)
45. C₂×C₅×#137	C₂×C₃	semidirect
47. C₅×#536	C₂×C₃	semidirect
48. C₅×#520	C₂×C₃	semidirect
49. C₅×#464	C₂×C₃	semidirect
50. C₅×#463	C₂×C₃	semidirect
51. C₅×#462	C₂×C₃	semidirect
52. C₅×#461	C₂×C₃	semidirect
53. C₅×#424	C₂×C₃	semidirect
54. C₅×#417	C₂×C₃	semidirect
55. C₂×C₅×#103	C₂×C₃	semidirect
100. C₂×C₃×#137	C₂×C₅	semidirect
102. C₃×#536	C₂×C₅	semidirect
103. C₃×#520	C₂×C₅	semidirect
104. C₃×#464	C₂×C₅	semidirect
105. C₃×#463	C₂×C₅	semidirect
106. C₃×#462	C₂×C₅	semidirect
107. C₃×#461	C₂×C₅	semidirect
108. C₃×#424	C₂×C₅	semidirect
109. C₃×#417	C₂×C₅	semidirect
110. C₂×C₃×#103	C₂×C₅	semidirect
142. #3046	C₃×C₅	direct (N × H)
252. C₂×#137	C₂×C₃×C₅	semidirect
254. #536	C₂×C₃×C₅	semidirect
255. #520	C₂×C₃×C₅	semidirect
256. #464	C₂×C₃×C₅	semidirect
257. #463	C₂×C₃×C₅	semidirect
258. #462	C₂×C₃×C₅	semidirect
259. #461	C₂×C₃×C₅	semidirect
260. #424	C₂×C₃×C₅	semidirect
261. #417	C₂×C₃×C₅	semidirect
262. C₂×#103	C₂×C₃×C₅	semidirect
494. C₃×C₅	#3046	direct (N × H)
560. C₅	C₃×#3046	direct (N × H)
580. C₃	C₅×#3046	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×#137	2
C₂×C₃×C₅×#135	2
C₃×C₅×#536	2
C₃×C₅×#520	2
C₃×C₅×#464	2
C₃×C₅×#463	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#424	2
C₃×C₅×#417	2
C₂×C₃×C₅×#103	2
C₅×#3046	3
C₃×#3046	5

Subgroups — C3×C5×#3046 #14276080

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3046 #14276080