Subgroups — C₃×C₅×#3013 #14276047

Order 1920.

1424 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×2₋¹⁺⁴	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#137	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#451	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#449	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#448	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×C₃×C₅×#103	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#408	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3013	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
14	C₃×C₅×2₋¹⁺⁴	—	2	4	no	—
15	C₂×C₃×C₅×#41	—	2	1	no	—
16	C₂×C₃×C₅×#41	—	2	2	no	—
17	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
18	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
21	C₂²×C₃×C₅×Q₈	—	2	1	no	—
22	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
23	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×#137	—	2	4	no	—
25	C₃×C₅×#135	—	2	4	no	—
26	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
28	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
29	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
33	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
35	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
36	C₃×C₅×#121	—	2	1	no	—
37	C₃×C₅×#121	—	2	2	no	—
38	C₃×C₅×#121	C₂²	1	2	yes	—
39	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
45	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
46	C₃×#3013	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
47	C₂×C₅×2₋¹⁺⁴	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#537	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#452	C₂×C₃	1	2	yes	complemented
52	C₅×#451	C₂×C₃	1	2	yes	complemented
53	C₅×#449	C₂×C₃	1	2	yes	complemented
54	C₅×#448	C₂×C₃	1	2	yes	complemented
55	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₅×#103	C₂×C₃	1	1	yes	characteristic, complemented
57	C₅×#408	C₂×C₃	1	1	yes	characteristic, complemented
58	C₃×C₅×#41	—	2	16	no	—
59	C₃×C₅×#41	—	2	8	no	—
60	C₃×C₅×#41	—	2	4	no	—
61	C₃×C₅×#41	—	2	4	no	—
62	C₃×C₅×#41	—	2	2	no	—
63	C₃×C₅×#41	—	2	2	no	—
64	C₃×C₅×#41	—	2	2	no	—
65	C₃×C₅×#41	—	2	2	no	—
66	C₃×C₅×#41	—	2	2	no	—
67	C₃×C₅×#41	D₄	1	4	yes	complemented
68	C₂×C₃×C₅×Q₈	—	2	8	no	—
69	C₂×C₃×C₅×Q₈	—	2	4	no	—
70	C₂×C₃×C₅×Q₈	—	2	4	no	—
71	C₂×C₃×C₅×Q₈	—	2	2	no	—
72	C₂×C₃×C₅×Q₈	—	2	1	no	—
73	C₂×C₃×C₅×Q₈	—	2	2	no	—
74	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
75	C₂×C₃×C₅×Q₈	D₄	1	4	yes	complemented
76	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
77	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
79	C₂×C₃×C₅×D₄	—	2	2	no	—
80	C₂×C₃×C₅×D₄	—	2	1	no	—
81	C₂×C₃×C₅×D₄	—	2	1	no	—
82	C₂×C₃×C₅×D₄	—	2	2	no	—
83	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
84	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
85	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
86	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
87	C₂²×C₃×C₄×C₅	—	2	2	no	—
88	C₂²×C₃×C₄×C₅	—	2	1	no	—
89	C₂²×C₃×C₄×C₅	—	2	2	no	—
90	C₂²×C₃×C₄×C₅	—	2	1	no	—
91	C₂²×C₃×C₄×C₅	—	2	1	no	—
92	C₂²×C₃×C₄×C₅	—	2	1	no	—
93	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
94	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
95	C₃×C₅×Q₁₆	—	2	2	no	—
96	C₃×C₅×Q₁₆	—	2	4	no	—
97	C₃×C₅×SD₁₆	—	2	2	no	—
98	C₃×C₅×SD₁₆	—	2	4	no	—
99	C₃×C₅×SD₁₆	—	2	2	no	—
100	C₃×C₅×D₈	—	2	2	no	—
101	C₃×C₅×M₁₆	—	2	2	no	—
102	C₂×C₃×C₅×C₈	—	2	2	no	—
103	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
104	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
105	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
106	C₃×C₅×C₄⋊C₄	—	2	1	no	—
107	C₃×C₅×C₄⋊C₄	—	2	2	no	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
109	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
110	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
111	C₂×C₃×2₋¹⁺⁴	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
113	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
114	C₃×#537	C₂×C₅	1	1	yes	characteristic, complemented
115	C₃×#452	C₂×C₅	1	2	yes	complemented
116	C₃×#451	C₂×C₅	1	2	yes	complemented
117	C₃×#449	C₂×C₅	1	2	yes	complemented
118	C₃×#448	C₂×C₅	1	2	yes	complemented
119	C₃×#417	C₂×C₅	1	1	yes	characteristic, complemented
120	C₂×C₃×#103	C₂×C₅	1	1	yes	characteristic, complemented
121	C₃×#408	C₂×C₅	1	1	yes	characteristic, complemented
122	C₅×2₋¹⁺⁴	—	2	4	no	—
123	C₅×2₋¹⁺⁴	—	2	4	no	—
124	C₂×C₅×#41	—	2	1	no	—
125	C₂×C₅×#41	—	2	2	no	—
126	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
127	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
128	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
129	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
130	C₂²×C₅×Q₈	—	2	1	no	—
131	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
132	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
133	C₅×#137	—	2	4	no	—
134	C₅×#135	—	2	4	no	—
135	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
136	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
137	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
138	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
139	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
140	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
141	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
142	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
143	C₅×C₂²⋊Q₈	—	2	1	no	—
144	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
145	C₅×#121	—	2	1	no	—
146	C₅×#121	—	2	2	no	—
147	C₅×#121	C₂²×C₃	1	2	yes	—
148	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
149	C₅×#103	C₂²×C₃	1	2	yes	—
150	C₅×#103	C₂²×C₃	1	2	yes	—
151	C₅×#103	C₂²×C₃	1	2	yes	—
152	C₅×#102	C₂²×C₃	1	2	yes	—
153	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
154	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
155	#3013	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
156	C₂³×C₃×C₅	—	2	1	no	—
157	C₂³×C₃×C₅	—	2	1	no	—
158	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
159	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
160	C₃×C₅×Q₈	—	2	8	no	—
161	C₃×C₅×Q₈	—	2	2	no	—
162	C₃×C₅×Q₈	—	2	4	no	—
163	C₃×C₅×Q₈	—	2	1	no	—
164	C₃×C₅×Q₈	—	2	2	no	—
165	C₃×C₅×Q₈	—	2	1	no	—
166	C₃×C₅×Q₈	—	2	1	no	—
167	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
168	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
169	C₃×C₅×D₄	—	2	8	no	—
170	C₃×C₅×D₄	—	2	4	no	—
171	C₃×C₅×D₄	—	2	4	no	—
172	C₃×C₅×D₄	—	2	2	no	—
173	C₃×C₅×D₄	—	2	1	no	—
174	C₃×C₅×D₄	—	2	1	no	—
175	C₃×C₅×D₄	—	2	1	no	—
176	C₃×C₅×D₄	—	4	2	no	—
177	C₃×C₅×D₄	—	8	2	no	—
178	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
179	C₂×C₃×C₄×C₅	—	2	8	no	—
180	C₂×C₃×C₄×C₅	—	2	8	no	—
181	C₂×C₃×C₄×C₅	—	2	4	no	—
182	C₂×C₃×C₄×C₅	—	2	2	no	—
183	C₂×C₃×C₄×C₅	—	2	1	no	—
184	C₂×C₃×C₄×C₅	—	2	4	no	—
185	C₂×C₃×C₄×C₅	—	2	2	no	—
186	C₂×C₃×C₄×C₅	—	2	2	no	—
187	C₂×C₃×C₄×C₅	—	2	2	no	—
188	C₂×C₃×C₄×C₅	—	2	1	no	—
189	C₂×C₃×C₄×C₅	—	4	2	no	—
190	C₂×C₃×C₄×C₅	—	8	1	no	—
191	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
192	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
193	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
194	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
195	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
196	C₃×C₅×C₈	—	2	1	no	—
197	C₃×C₅×C₈	—	2	1	no	—
198	C₃×C₅×C₈	—	2	2	no	—
199	C₃×2₋¹⁺⁴	—	2	4	no	—
200	C₃×2₋¹⁺⁴	—	2	4	no	—
201	C₂×C₃×#41	—	2	1	no	—
202	C₂×C₃×#41	—	2	2	no	—
203	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
204	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
205	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
206	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
207	C₂²×C₃×Q₈	—	2	1	no	—
208	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
209	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
210	C₃×#137	—	2	4	no	—
211	C₃×#135	—	2	4	no	—
212	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
213	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
214	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
215	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
216	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
217	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
218	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
220	C₃×C₂²⋊Q₈	—	2	1	no	—
221	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
222	C₃×#121	—	2	1	no	—
223	C₃×#121	—	2	2	no	—
224	C₃×#121	C₂²×C₅	1	2	yes	—
225	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
226	C₃×#103	C₂²×C₅	1	2	yes	—
227	C₃×#103	C₂²×C₅	1	2	yes	—
228	C₃×#103	C₂²×C₅	1	2	yes	—
229	C₃×#102	C₂²×C₅	1	2	yes	—
230	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
231	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
232	C₅×#41	—	2	16	no	—
233	C₅×#41	—	2	8	no	—
234	C₅×#41	—	2	4	no	—
235	C₅×#41	—	2	4	no	—
236	C₅×#41	—	2	2	no	—
237	C₅×#41	—	2	2	no	—
238	C₅×#41	—	2	2	no	—
239	C₅×#41	—	2	2	no	—
240	C₅×#41	—	2	2	no	—
241	C₅×#41	C₃×D₄	1	4	yes	complemented
242	C₂×C₅×Q₈	—	2	8	no	—
243	C₂×C₅×Q₈	—	2	4	no	—
244	C₂×C₅×Q₈	—	2	4	no	—
245	C₂×C₅×Q₈	—	2	2	no	—
246	C₂×C₅×Q₈	—	2	1	no	—
247	C₂×C₅×Q₈	—	2	2	no	—
248	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
249	C₂×C₅×Q₈	C₃×D₄	1	4	yes	complemented
250	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
251	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
252	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
253	C₂×C₅×D₄	—	2	2	no	—
254	C₂×C₅×D₄	—	2	1	no	—
255	C₂×C₅×D₄	—	2	1	no	—
256	C₂×C₅×D₄	—	2	2	no	—
257	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
258	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
259	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
260	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
261	C₂²×C₄×C₅	—	2	2	no	—
262	C₂²×C₄×C₅	—	2	1	no	—
263	C₂²×C₄×C₅	—	2	2	no	—
264	C₂²×C₄×C₅	—	2	1	no	—
265	C₂²×C₄×C₅	—	2	1	no	—
266	C₂²×C₄×C₅	—	2	1	no	—
267	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
268	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
269	C₅×Q₁₆	—	2	2	no	—
270	C₅×Q₁₆	—	2	4	no	—
271	C₅×SD₁₆	—	2	2	no	—
272	C₅×SD₁₆	—	2	4	no	—
273	C₅×SD₁₆	—	2	2	no	—
274	C₅×D₈	—	2	2	no	—
275	C₅×M₁₆	—	2	2	no	—
276	C₂×C₅×C₈	—	2	2	no	—
277	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
278	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
279	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
280	C₅×C₄⋊C₄	—	2	1	no	—
281	C₅×C₄⋊C₄	—	2	2	no	—
282	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
283	C₅×C₂²⋊C₄	—	2	2	no	—
284	C₅×C₂²⋊C₄	—	2	2	no	—
285	C₂×2₋¹⁺⁴	C₂×C₃×C₅	1	1	yes	characteristic, complemented
286	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
287	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
288	#537	C₂×C₃×C₅	1	1	yes	characteristic, complemented
289	#452	C₂×C₃×C₅	1	2	yes	complemented
290	#451	C₂×C₃×C₅	1	2	yes	complemented
291	#449	C₂×C₃×C₅	1	2	yes	complemented
292	#448	C₂×C₃×C₅	1	2	yes	complemented
293	#417	C₂×C₃×C₅	1	1	yes	characteristic, complemented
294	C₂×#103	C₂×C₃×C₅	1	1	yes	characteristic, complemented
295	#408	C₂×C₃×C₅	1	1	yes	characteristic, complemented
296	C₂²×C₃×C₅	—	2	1	no	—
297	C₂²×C₃×C₅	—	2	1	no	—
298	C₂²×C₃×C₅	—	2	2	no	—
299	C₂²×C₃×C₅	—	2	2	no	—
300	C₂²×C₃×C₅	—	2	2	no	—
301	C₂²×C₃×C₅	—	2	2	no	—
302	C₂²×C₃×C₅	—	4	1	no	—
303	C₂²×C₃×C₅	—	4	1	no	—
304	C₂²×C₃×C₅	—	4	1	no	—
305	C₂²×C₃×C₅	—	4	1	no	—
306	C₂²×C₃×C₅	—	4	1	no	—
307	C₂²×C₃×C₅	#120	1	2	yes	—
308	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
309	C₃×C₄×C₅	—	2	4	no	—
310	C₃×C₄×C₅	—	2	2	no	—
311	C₃×C₄×C₅	—	2	2	no	—
312	C₃×C₄×C₅	—	4	1	no	—
313	C₃×C₄×C₅	—	4	2	no	—
314	C₃×C₄×C₅	#120	1	2	yes	—
315	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
316	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
317	C₃×#41	—	2	16	no	—
318	C₃×#41	—	2	8	no	—
319	C₃×#41	—	2	4	no	—
320	C₃×#41	—	2	4	no	—
321	C₃×#41	—	2	2	no	—
322	C₃×#41	—	2	2	no	—
323	C₃×#41	—	2	2	no	—
324	C₃×#41	—	2	2	no	—
325	C₃×#41	—	2	2	no	—
326	C₃×#41	C₅×D₄	1	4	yes	complemented
327	C₂×C₃×Q₈	—	2	8	no	—
328	C₂×C₃×Q₈	—	2	4	no	—
329	C₂×C₃×Q₈	—	2	4	no	—
330	C₂×C₃×Q₈	—	2	2	no	—
331	C₂×C₃×Q₈	—	2	1	no	—
332	C₂×C₃×Q₈	—	2	2	no	—
333	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
334	C₂×C₃×Q₈	C₅×D₄	1	4	yes	complemented
335	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
336	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
337	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
338	C₂×C₃×D₄	—	2	2	no	—
339	C₂×C₃×D₄	—	2	1	no	—
340	C₂×C₃×D₄	—	2	1	no	—
341	C₂×C₃×D₄	—	2	2	no	—
342	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
343	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
344	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
345	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
346	C₂²×C₃×C₄	—	2	2	no	—
347	C₂²×C₃×C₄	—	2	1	no	—
348	C₂²×C₃×C₄	—	2	2	no	—
349	C₂²×C₃×C₄	—	2	1	no	—
350	C₂²×C₃×C₄	—	2	1	no	—
351	C₂²×C₃×C₄	—	2	1	no	—
352	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
353	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
354	C₃×Q₁₆	—	2	2	no	—
355	C₃×Q₁₆	—	2	4	no	—
356	C₃×SD₁₆	—	2	2	no	—
357	C₃×SD₁₆	—	2	4	no	—
358	C₃×SD₁₆	—	2	2	no	—
359	C₃×D₈	—	2	2	no	—
360	C₃×M₁₆	—	2	2	no	—
361	C₂×C₃×C₈	—	2	2	no	—
362	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
363	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
364	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
365	C₃×C₄⋊C₄	—	2	1	no	—
366	C₃×C₄⋊C₄	—	2	2	no	—
367	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
368	C₃×C₂²⋊C₄	—	2	2	no	—
369	C₃×C₂²⋊C₄	—	2	2	no	—
370	C₂³×C₅	—	2	1	no	—
371	C₂³×C₅	—	2	1	no	—
372	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
373	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
374	C₅×Q₈	—	2	8	no	—
375	C₅×Q₈	—	2	2	no	—
376	C₅×Q₈	—	2	4	no	—
377	C₅×Q₈	—	2	1	no	—
378	C₅×Q₈	—	2	2	no	—
379	C₅×Q₈	—	2	1	no	—
380	C₅×Q₈	—	2	1	no	—
381	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
382	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
383	C₅×D₄	—	2	8	no	—
384	C₅×D₄	—	2	4	no	—
385	C₅×D₄	—	2	4	no	—
386	C₅×D₄	—	2	2	no	—
387	C₅×D₄	—	2	1	no	—
388	C₅×D₄	—	2	1	no	—
389	C₅×D₄	—	2	1	no	—
390	C₅×D₄	—	4	2	no	—
391	C₅×D₄	—	8	2	no	—
392	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
393	C₂×C₄×C₅	—	2	8	no	—
394	C₂×C₄×C₅	—	2	8	no	—
395	C₂×C₄×C₅	—	2	4	no	—
396	C₂×C₄×C₅	—	2	2	no	—
397	C₂×C₄×C₅	—	2	1	no	—
398	C₂×C₄×C₅	—	2	4	no	—
399	C₂×C₄×C₅	—	2	2	no	—
400	C₂×C₄×C₅	—	2	2	no	—
401	C₂×C₄×C₅	—	2	2	no	—
402	C₂×C₄×C₅	—	2	1	no	—
403	C₂×C₄×C₅	—	4	2	no	—
404	C₂×C₄×C₅	—	8	1	no	—
405	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
406	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
407	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
408	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
409	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
410	C₅×C₈	—	2	1	no	—
411	C₅×C₈	—	2	1	no	—
412	C₅×C₈	—	2	2	no	—
413	2₋¹⁺⁴	—	2	4	no	—
414	2₋¹⁺⁴	—	2	4	no	—
415	C₂×#41	—	2	1	no	—
416	C₂×#41	—	2	2	no	—
417	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
418	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
419	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
420	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
421	C₂²×Q₈	—	2	1	no	—
422	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
423	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
424	#137	—	2	4	no	—
425	#135	—	2	4	no	—
426	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
427	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
428	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
429	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
430	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
431	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
432	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
433	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
434	C₂²⋊Q₈	—	2	1	no	—
435	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
436	#121	—	2	1	no	—
437	#121	—	2	2	no	—
438	#121	C₂²×C₃×C₅	1	2	yes	—
439	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
440	#103	C₂²×C₃×C₅	1	2	yes	—
441	#103	C₂²×C₃×C₅	1	2	yes	—
442	#103	C₂²×C₃×C₅	1	2	yes	—
443	#102	C₂²×C₃×C₅	1	2	yes	—
444	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
445	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
446	C₂×C₃×C₅	—	2	2	no	—
447	C₂×C₃×C₅	—	4	2	no	—
448	C₂×C₃×C₅	—	4	2	no	—
449	C₂×C₃×C₅	—	8	1	no	—
450	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
451	C₂×C₃×C₅	#577	1	1	yes	characteristic
452	C₂×C₃×C₅	#578	1	1	yes	characteristic
453	C₂³×C₃	—	2	1	no	—
454	C₂³×C₃	—	2	1	no	—
455	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
456	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
457	C₃×Q₈	—	2	8	no	—
458	C₃×Q₈	—	2	2	no	—
459	C₃×Q₈	—	2	4	no	—
460	C₃×Q₈	—	2	1	no	—
461	C₃×Q₈	—	2	2	no	—
462	C₃×Q₈	—	2	1	no	—
463	C₃×Q₈	—	2	1	no	—
464	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
465	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
466	C₃×D₄	—	2	8	no	—
467	C₃×D₄	—	2	4	no	—
468	C₃×D₄	—	2	4	no	—
469	C₃×D₄	—	2	2	no	—
470	C₃×D₄	—	2	1	no	—
471	C₃×D₄	—	2	1	no	—
472	C₃×D₄	—	2	1	no	—
473	C₃×D₄	—	4	2	no	—
474	C₃×D₄	—	8	2	no	—
475	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
476	C₂×C₃×C₄	—	2	8	no	—
477	C₂×C₃×C₄	—	2	8	no	—
478	C₂×C₃×C₄	—	2	4	no	—
479	C₂×C₃×C₄	—	2	2	no	—
480	C₂×C₃×C₄	—	2	1	no	—
481	C₂×C₃×C₄	—	2	4	no	—
482	C₂×C₃×C₄	—	2	2	no	—
483	C₂×C₃×C₄	—	2	2	no	—
484	C₂×C₃×C₄	—	2	2	no	—
485	C₂×C₃×C₄	—	2	1	no	—
486	C₂×C₃×C₄	—	4	2	no	—
487	C₂×C₃×C₄	—	8	1	no	—
488	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
489	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
490	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
491	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
492	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
493	C₃×C₈	—	2	1	no	—
494	C₃×C₈	—	2	1	no	—
495	C₃×C₈	—	2	2	no	—
496	C₂²×C₅	—	2	1	no	—
497	C₂²×C₅	—	2	1	no	—
498	C₂²×C₅	—	2	2	no	—
499	C₂²×C₅	—	2	2	no	—
500	C₂²×C₅	—	2	2	no	—
501	C₂²×C₅	—	2	2	no	—
502	C₂²×C₅	—	4	1	no	—
503	C₂²×C₅	—	4	1	no	—
504	C₂²×C₅	—	4	1	no	—
505	C₂²×C₅	—	4	1	no	—
506	C₂²×C₅	—	4	1	no	—
507	C₂²×C₅	C₃×#120	1	2	yes	—
508	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
509	C₄×C₅	—	2	4	no	—
510	C₄×C₅	—	2	2	no	—
511	C₄×C₅	—	2	2	no	—
512	C₄×C₅	—	4	2	no	—
513	C₄×C₅	—	4	1	no	—
514	C₄×C₅	C₃×#120	1	2	yes	—
515	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
516	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
517	#41	—	2	16	no	—
518	#41	—	2	8	no	—
519	#41	—	2	4	no	—
520	#41	—	2	4	no	—
521	#41	—	2	2	no	—
522	#41	—	2	2	no	—
523	#41	—	2	2	no	—
524	#41	—	2	2	no	—
525	#41	—	2	2	no	—
526	#41	C₃×C₅×D₄	1	4	yes	complemented
527	C₂×Q₈	—	2	8	no	—
528	C₂×Q₈	—	2	4	no	—
529	C₂×Q₈	—	2	4	no	—
530	C₂×Q₈	—	2	2	no	—
531	C₂×Q₈	—	2	1	no	—
532	C₂×Q₈	—	2	2	no	—
533	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
534	C₂×Q₈	C₃×C₅×D₄	1	4	yes	complemented
535	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
536	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
537	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
538	C₂×D₄	—	2	2	no	—
539	C₂×D₄	—	2	1	no	—
540	C₂×D₄	—	2	1	no	—
541	C₂×D₄	—	2	2	no	—
542	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
543	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
544	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
545	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
546	C₂²×C₄	—	2	2	no	—
547	C₂²×C₄	—	2	1	no	—
548	C₂²×C₄	—	2	2	no	—
549	C₂²×C₄	—	2	1	no	—
550	C₂²×C₄	—	2	1	no	—
551	C₂²×C₄	—	2	1	no	—
552	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
553	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
554	Q₁₆	—	2	2	no	—
555	Q₁₆	—	2	4	no	—
556	SD₁₆	—	2	2	no	—
557	SD₁₆	—	2	4	no	—
558	SD₁₆	—	2	2	no	—
559	D₈	—	2	2	no	—
560	M₁₆	—	2	2	no	—
561	C₂×C₈	—	2	2	no	—
562	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
563	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
564	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
565	C₄⋊C₄	—	2	1	no	—
566	C₄⋊C₄	—	2	2	no	—
567	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
568	C₂²⋊C₄	—	2	2	no	—
569	C₂²⋊C₄	—	2	2	no	—
570	C₃×C₅	#3013	1	1	yes	characteristic, direct product factor, Hall
571	C₂²×C₃	—	2	1	no	—
572	C₂²×C₃	—	2	1	no	—
573	C₂²×C₃	—	2	2	no	—
574	C₂²×C₃	—	2	2	no	—
575	C₂²×C₃	—	2	2	no	—
576	C₂²×C₃	—	2	2	no	—
577	C₂²×C₃	—	4	1	no	—
578	C₂²×C₃	—	4	1	no	—
579	C₂²×C₃	—	4	1	no	—
580	C₂²×C₃	—	4	1	no	—
581	C₂²×C₃	—	4	1	no	—
582	C₂²×C₃	C₅×#120	1	2	yes	—
583	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
584	C₃×C₄	—	2	4	no	—
585	C₃×C₄	—	2	2	no	—
586	C₃×C₄	—	2	2	no	—
587	C₃×C₄	—	4	1	no	—
588	C₃×C₄	—	4	2	no	—
589	C₃×C₄	C₅×#120	1	2	yes	—
590	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
591	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
592	C₂×C₅	—	2	2	no	—
593	C₂×C₅	—	4	2	no	—
594	C₂×C₅	—	4	2	no	—
595	C₂×C₅	—	8	1	no	—
596	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
597	C₂×C₅	C₃×#577	1	1	yes	characteristic
598	C₂×C₅	C₃×#578	1	1	yes	characteristic
599	C₂³	—	2	1	no	—
600	C₂³	—	2	1	no	—
601	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
602	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
603	Q₈	—	2	8	no	—
604	Q₈	—	2	2	no	—
605	Q₈	—	2	4	no	—
606	Q₈	—	2	1	no	—
607	Q₈	—	2	2	no	—
608	Q₈	—	2	1	no	—
609	Q₈	—	2	1	no	—
610	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
611	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
612	D₄	—	2	8	no	—
613	D₄	—	2	4	no	—
614	D₄	—	2	4	no	—
615	D₄	—	2	2	no	—
616	D₄	—	2	1	no	—
617	D₄	—	2	1	no	—
618	D₄	—	2	1	no	—
619	D₄	—	4	2	no	—
620	D₄	—	8	2	no	—
621	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
622	C₂×C₄	—	2	8	no	—
623	C₂×C₄	—	2	8	no	—
624	C₂×C₄	—	2	4	no	—
625	C₂×C₄	—	2	2	no	—
626	C₂×C₄	—	2	1	no	—
627	C₂×C₄	—	2	4	no	—
628	C₂×C₄	—	2	2	no	—
629	C₂×C₄	—	2	2	no	—
630	C₂×C₄	—	2	2	no	—
631	C₂×C₄	—	2	1	no	—
632	C₂×C₄	—	4	2	no	—
633	C₂×C₄	—	8	1	no	—
634	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
635	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
636	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
637	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
638	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
639	C₈	—	2	1	no	—
640	C₈	—	2	1	no	—
641	C₈	—	2	2	no	—
642	C₂×C₃	—	2	2	no	—
643	C₂×C₃	—	4	2	no	—
644	C₂×C₃	—	4	2	no	—
645	C₂×C₃	—	8	1	no	—
646	C₂×C₃	C₂×C₅×#120	1	1	yes	characteristic
647	C₂×C₃	C₅×#577	1	1	yes	characteristic
648	C₂×C₃	C₅×#578	1	1	yes	characteristic
649	C₅	C₃×#3013	1	1	yes	characteristic, direct product factor, Sylow
650	C₂²	—	2	1	no	—
651	C₂²	—	2	1	no	—
652	C₂²	—	2	2	no	—
653	C₂²	—	2	2	no	—
654	C₂²	—	2	2	no	—
655	C₂²	—	2	2	no	—
656	C₂²	—	4	1	no	—
657	C₂²	—	4	1	no	—
658	C₂²	—	4	1	no	—
659	C₂²	—	4	1	no	—
660	C₂²	—	4	1	no	—
661	C₂²	C₃×C₅×#120	1	2	yes	—
662	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
663	C₄	—	2	4	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	—	4	1	no	—
667	C₄	—	4	2	no	—
668	C₄	C₃×C₅×#120	1	2	yes	—
669	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
670	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
671	C₃	C₅×#3013	1	1	yes	characteristic, direct product factor, Sylow
672	C₂	—	2	2	no	—
673	C₂	—	4	2	no	—
674	C₂	—	4	2	no	—
675	C₂	—	8	1	no	—
676	C₂	C₂×C₃×C₅×#120	1	1	yes	characteristic
677	C₂	C₃×C₅×#577	1	1	yes	characteristic
678	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
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₅×#41 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×2₋¹⁺⁴	C₂	semidirect
2. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₃×C₅×#135	C₂	semidirect
4. C₃×C₅×#537	C₂	semidirect
5. C₃×C₅×#452	C₂	semidirect
6. C₃×C₅×#451	C₂	semidirect
7. C₃×C₅×#449	C₂	semidirect
8. C₃×C₅×#448	C₂	semidirect
9. C₃×C₅×#417	C₂	semidirect
10. C₂×C₃×C₅×#103	C₂	semidirect
11. C₃×C₅×#408	C₂	semidirect
12. C₅×#3013	C₃	direct (N × H)
46. C₃×#3013	C₅	direct (N × H)
47. C₂×C₅×2₋¹⁺⁴	C₂×C₃	semidirect
48. C₂×C₅×#137	C₂×C₃	semidirect
49. C₂×C₅×#135	C₂×C₃	semidirect
50. C₅×#537	C₂×C₃	semidirect
51. C₅×#452	C₂×C₃	semidirect
52. C₅×#451	C₂×C₃	semidirect
53. C₅×#449	C₂×C₃	semidirect
54. C₅×#448	C₂×C₃	semidirect
55. C₅×#417	C₂×C₃	semidirect
56. C₂×C₅×#103	C₂×C₃	semidirect
57. C₅×#408	C₂×C₃	semidirect
67. C₃×C₅×#41	D₄	semidirect
75. C₂×C₃×C₅×Q₈	D₄	semidirect
111. C₂×C₃×2₋¹⁺⁴	C₂×C₅	semidirect
112. C₂×C₃×#137	C₂×C₅	semidirect
113. C₂×C₃×#135	C₂×C₅	semidirect
114. C₃×#537	C₂×C₅	semidirect
115. C₃×#452	C₂×C₅	semidirect
116. C₃×#451	C₂×C₅	semidirect
117. C₃×#449	C₂×C₅	semidirect
118. C₃×#448	C₂×C₅	semidirect
119. C₃×#417	C₂×C₅	semidirect
120. C₂×C₃×#103	C₂×C₅	semidirect
121. C₃×#408	C₂×C₅	semidirect
155. #3013	C₃×C₅	direct (N × H)
241. C₅×#41	C₃×D₄	semidirect
249. C₂×C₅×Q₈	C₃×D₄	semidirect
285. C₂×2₋¹⁺⁴	C₂×C₃×C₅	semidirect
286. C₂×#137	C₂×C₃×C₅	semidirect
287. C₂×#135	C₂×C₃×C₅	semidirect
288. #537	C₂×C₃×C₅	semidirect
289. #452	C₂×C₃×C₅	semidirect
290. #451	C₂×C₃×C₅	semidirect
291. #449	C₂×C₃×C₅	semidirect
292. #448	C₂×C₃×C₅	semidirect
293. #417	C₂×C₃×C₅	semidirect
294. C₂×#103	C₂×C₃×C₅	semidirect
295. #408	C₂×C₃×C₅	semidirect
326. C₃×#41	C₅×D₄	semidirect
334. C₂×C₃×Q₈	C₅×D₄	semidirect
526. #41	C₃×C₅×D₄	semidirect
534. C₂×Q₈	C₃×C₅×D₄	semidirect
570. C₃×C₅	#3013	direct (N × H)
649. C₅	C₃×#3013	direct (N × H)
671. C₃	C₅×#3013	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×C₅×2₋¹⁺⁴	2
C₂×C₃×C₅×#137	2
C₂×C₃×C₅×#135	2
C₃×C₅×#537	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₅×#449	2
C₃×C₅×#448	2
C₃×C₅×#417	2
C₂×C₃×C₅×#103	2
C₃×C₅×#408	2
C₅×#3013	3
C₃×#3013	5

Subgroups — C3×C5×#3013 #14276047

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3013 #14276047