Subgroups — C₃×C₅×#3523 #14276557

Order 1920.

1984 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#557	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#557	C₂	1	3	yes	maximal, complemented
3	C₃×C₅×#556	C₂	1	3	yes	maximal, complemented
4	C₃×C₅×#552	C₂	1	6	yes	maximal, complemented
5	C₃×C₅×D₄×Q₈	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#541	C₂	1	6	yes	maximal, complemented
8	C₃×C₅×#533	C₂	1	3	yes	maximal, complemented
9	C₃×C₅×#529	C₂	1	3	yes	maximal
10	C₃×C₅×#519	C₂	1	2	yes	maximal, complemented
11	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3523	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	3	yes	—
16	C₃×C₅×C₄⋊Q₈	C₂²	1	3	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	6	yes	—
18	C₃×C₅×#126	C₂²	1	6	yes	—
19	C₃×C₅×#126	C₂²	1	12	yes	—
20	C₃×C₅×#125	C₂²	1	3	yes	—
21	C₃×C₅×#125	C₂²	1	6	yes	—
22	C₃×C₅×#125	C₂²	1	12	yes	—
23	C₃×C₅×#125	C₂²	1	6	yes	—
24	C₃×C₅×#124	C₂²	1	3	yes	—
25	C₃×C₅×#123	C₂²	1	6	yes	—
26	C₃×C₅×C₂²⋊Q₈	C₂²	1	3	yes	—
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	6	yes	—
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	6	yes	—
29	C₃×C₅×C₂²⋊Q₈	C₂²	1	6	yes	—
30	C₃×C₅×#121	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
32	C₃×C₄×C₅×Q₈	C₂²	1	3	yes	—
33	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
34	C₃×C₄×C₅×Q₈	C₂²	1	3	yes	—
35	C₃×C₄×C₅×Q₈	C₂²	1	6	yes	—
36	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
37	C₃×C₄×C₅×Q₈	C₂²	1	6	yes	—
38	C₃×C₄×C₅×Q₈	C₂²	1	3	yes	—
39	C₃×C₄×C₅×Q₈	C₂²	1	6	yes	—
40	C₃×C₄×C₅×D₄	C₂²	1	6	yes	—
41	C₃×C₄×C₅×D₄	C₂²	1	3	yes	—
42	C₃×C₅×#117	C₂²	1	6	yes	—
43	C₃×C₅×#117	C₂²	1	6	yes	—
44	C₃×C₅×#117	C₂²	1	6	yes	—
45	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	3	yes	—
46	C₂×C₃×C₄²×C₅	C₂²	1	3	yes	—
47	C₃×#3523	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
48	C₅×#557	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#557	C₂×C₃	1	3	yes	complemented
50	C₅×#556	C₂×C₃	1	3	yes	complemented
51	C₅×#552	C₂×C₃	1	6	yes	complemented
52	C₅×D₄×Q₈	C₂×C₃	1	2	yes	complemented
53	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#541	C₂×C₃	1	6	yes	complemented
55	C₅×#533	C₂×C₃	1	3	yes	complemented
56	C₅×#529	C₂×C₃	1	3	yes	—
57	C₅×#519	C₂×C₃	1	2	yes	complemented
58	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
59	C₂×C₃×C₅×Q₈	—	2	4	no	—
60	C₂×C₃×C₅×Q₈	—	2	8	no	—
61	C₂×C₃×C₅×Q₈	C₂³	1	3	yes	—
62	C₂×C₃×C₅×Q₈	C₂³	1	3	yes	—
63	C₂×C₃×C₅×Q₈	C₂³	1	6	yes	—
64	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
66	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
69	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
70	C₂²×C₃×C₄×C₅	C₂³	1	6	yes	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
72	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
73	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
74	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
78	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
79	C₃×C₅×C₄⋊C₄	C₂³	1	3	yes	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
81	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
82	C₃×C₅×C₄⋊C₄	C₂³	1	12	yes	—
83	C₃×C₅×C₄⋊C₄	C₂³	1	6	yes	—
84	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
85	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
86	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
87	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
88	C₃×C₅×C₂²⋊C₄	C₂³	1	6	yes	—
89	C₃×C₄²×C₅	C₂³	1	3	yes	—
90	C₃×C₄²×C₅	C₂³	1	3	yes	—
91	C₃×C₄²×C₅	C₂³	1	3	yes	—
92	C₃×C₄²×C₅	C₂³	1	3	yes	—
93	C₃×C₄²×C₅	C₂³	1	12	yes	—
94	C₃×C₄²×C₅	C₂³	1	6	yes	—
95	C₃×#557	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#557	C₂×C₅	1	3	yes	complemented
97	C₃×#556	C₂×C₅	1	3	yes	complemented
98	C₃×#552	C₂×C₅	1	6	yes	complemented
99	C₃×D₄×Q₈	C₂×C₅	1	2	yes	complemented
100	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#541	C₂×C₅	1	6	yes	complemented
102	C₃×#533	C₂×C₅	1	3	yes	complemented
103	C₃×#529	C₂×C₅	1	3	yes	—
104	C₃×#519	C₂×C₅	1	2	yes	complemented
105	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
108	C₅×C₄⋊Q₈	C₂²×C₃	1	3	yes	—
109	C₅×C₄⋊Q₈	C₂²×C₃	1	3	yes	—
110	C₅×C₄⋊Q₈	C₂²×C₃	1	6	yes	—
111	C₅×#126	C₂²×C₃	1	6	yes	—
112	C₅×#126	C₂²×C₃	1	12	yes	—
113	C₅×#125	C₂²×C₃	1	3	yes	—
114	C₅×#125	C₂²×C₃	1	6	yes	—
115	C₅×#125	C₂²×C₃	1	12	yes	—
116	C₅×#125	C₂²×C₃	1	6	yes	—
117	C₅×#124	C₂²×C₃	1	3	yes	—
118	C₅×#123	C₂²×C₃	1	6	yes	—
119	C₅×C₂²⋊Q₈	C₂²×C₃	1	3	yes	—
120	C₅×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
121	C₅×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
122	C₅×C₂²⋊Q₈	C₂²×C₃	1	6	yes	—
123	C₅×#121	C₂²×C₃	1	1	yes	characteristic
124	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
125	C₄×C₅×Q₈	C₂²×C₃	1	3	yes	—
126	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
127	C₄×C₅×Q₈	C₂²×C₃	1	3	yes	—
128	C₄×C₅×Q₈	C₂²×C₃	1	6	yes	—
129	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
130	C₄×C₅×Q₈	C₂²×C₃	1	6	yes	—
131	C₄×C₅×Q₈	C₂²×C₃	1	3	yes	—
132	C₄×C₅×Q₈	C₂²×C₃	1	6	yes	—
133	C₄×C₅×D₄	C₂²×C₃	1	6	yes	—
134	C₄×C₅×D₄	C₂²×C₃	1	3	yes	—
135	C₅×#117	C₂²×C₃	1	6	yes	—
136	C₅×#117	C₂²×C₃	1	6	yes	—
137	C₅×#117	C₂²×C₃	1	6	yes	—
138	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	3	yes	—
139	C₂×C₄²×C₅	C₂²×C₃	1	3	yes	—
140	#3523	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
141	C₂³×C₃×C₅	C₂⁴	1	2	yes	—
142	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
143	C₃×C₅×Q₈	—	2	6	no	—
144	C₃×C₅×Q₈	—	2	12	no	—
145	C₃×C₅×Q₈	—	2	6	no	—
146	C₃×C₅×Q₈	#41	1	4	yes	—
147	C₃×C₅×D₄	—	2	4	no	—
148	C₃×C₅×D₄	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	6	no	—
150	C₂×C₃×C₄×C₅	—	2	6	no	—
151	C₂×C₃×C₄×C₅	—	2	12	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
155	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
156	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
157	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
158	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
159	C₂×C₃×C₄×C₅	C₂⁴	1	6	yes	—
160	C₂×C₃×C₄×C₅	C₂⁴	1	3	yes	—
161	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
162	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
163	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
164	C₃×C₄⋊Q₈	C₂²×C₅	1	3	yes	—
165	C₃×C₄⋊Q₈	C₂²×C₅	1	3	yes	—
166	C₃×C₄⋊Q₈	C₂²×C₅	1	6	yes	—
167	C₃×#126	C₂²×C₅	1	6	yes	—
168	C₃×#126	C₂²×C₅	1	12	yes	—
169	C₃×#125	C₂²×C₅	1	3	yes	—
170	C₃×#125	C₂²×C₅	1	6	yes	—
171	C₃×#125	C₂²×C₅	1	12	yes	—
172	C₃×#125	C₂²×C₅	1	6	yes	—
173	C₃×#124	C₂²×C₅	1	3	yes	—
174	C₃×#123	C₂²×C₅	1	6	yes	—
175	C₃×C₂²⋊Q₈	C₂²×C₅	1	3	yes	—
176	C₃×C₂²⋊Q₈	C₂²×C₅	1	6	yes	—
177	C₃×C₂²⋊Q₈	C₂²×C₅	1	6	yes	—
178	C₃×C₂²⋊Q₈	C₂²×C₅	1	6	yes	—
179	C₃×#121	C₂²×C₅	1	1	yes	characteristic
180	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
181	C₃×C₄×Q₈	C₂²×C₅	1	3	yes	—
182	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
183	C₃×C₄×Q₈	C₂²×C₅	1	3	yes	—
184	C₃×C₄×Q₈	C₂²×C₅	1	6	yes	—
185	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
186	C₃×C₄×Q₈	C₂²×C₅	1	6	yes	—
187	C₃×C₄×Q₈	C₂²×C₅	1	3	yes	—
188	C₃×C₄×Q₈	C₂²×C₅	1	6	yes	—
189	C₃×C₄×D₄	C₂²×C₅	1	6	yes	—
190	C₃×C₄×D₄	C₂²×C₅	1	3	yes	—
191	C₃×#117	C₂²×C₅	1	6	yes	—
192	C₃×#117	C₂²×C₅	1	6	yes	—
193	C₃×#117	C₂²×C₅	1	6	yes	—
194	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	3	yes	—
195	C₂×C₃×C₄²	C₂²×C₅	1	3	yes	—
196	C₂×C₅×Q₈	—	2	4	no	—
197	C₂×C₅×Q₈	—	2	8	no	—
198	C₂×C₅×Q₈	C₂³×C₃	1	3	yes	—
199	C₂×C₅×Q₈	C₂³×C₃	1	3	yes	—
200	C₂×C₅×Q₈	C₂³×C₃	1	6	yes	—
201	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
203	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
206	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
207	C₂²×C₄×C₅	C₂³×C₃	1	6	yes	—
208	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
209	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
210	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
211	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
212	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
213	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
214	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
215	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
216	C₅×C₄⋊C₄	C₂³×C₃	1	3	yes	—
217	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
218	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
219	C₅×C₄⋊C₄	C₂³×C₃	1	12	yes	—
220	C₅×C₄⋊C₄	C₂³×C₃	1	6	yes	—
221	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
222	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
223	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
224	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
225	C₅×C₂²⋊C₄	C₂³×C₃	1	6	yes	—
226	C₄²×C₅	C₂³×C₃	1	3	yes	—
227	C₄²×C₅	C₂³×C₃	1	3	yes	—
228	C₄²×C₅	C₂³×C₃	1	3	yes	—
229	C₄²×C₅	C₂³×C₃	1	3	yes	—
230	C₄²×C₅	C₂³×C₃	1	12	yes	—
231	C₄²×C₅	C₂³×C₃	1	6	yes	—
232	#557	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#557	C₂×C₃×C₅	1	3	yes	complemented
234	#556	C₂×C₃×C₅	1	3	yes	complemented
235	#552	C₂×C₃×C₅	1	6	yes	complemented
236	D₄×Q₈	C₂×C₃×C₅	1	2	yes	complemented
237	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	#541	C₂×C₃×C₅	1	6	yes	complemented
239	#533	C₂×C₃×C₅	1	3	yes	complemented
240	#529	C₂×C₃×C₅	1	3	yes	—
241	#519	C₂×C₃×C₅	1	2	yes	complemented
242	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	C₂²×C₃×C₅	—	2	1	no	—
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	2	2	no	—
246	C₂²×C₃×C₅	—	2	2	no	—
247	C₂²×C₃×C₅	—	2	2	no	—
248	C₂²×C₃×C₅	2₋¹⁺⁴	1	2	yes	—
249	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
250	C₃×C₄×C₅	—	2	3	no	—
251	C₃×C₄×C₅	—	2	6	no	—
252	C₃×C₄×C₅	—	2	3	no	—
253	C₃×C₄×C₅	—	2	3	no	—
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	—	2	6	no	—
257	C₃×C₄×C₅	C₂×#41	1	6	yes	—
258	C₃×C₄×C₅	2₋¹⁺⁴	1	2	yes	—
259	C₂×C₃×Q₈	—	2	4	no	—
260	C₂×C₃×Q₈	—	2	8	no	—
261	C₂×C₃×Q₈	C₂³×C₅	1	3	yes	—
262	C₂×C₃×Q₈	C₂³×C₅	1	3	yes	—
263	C₂×C₃×Q₈	C₂³×C₅	1	6	yes	—
264	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
265	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
266	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
267	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
268	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	3	yes	—
270	C₂²×C₃×C₄	C₂³×C₅	1	6	yes	—
271	C₃×C₄⋊C₄	C₂³×C₅	1	3	yes	—
272	C₃×C₄⋊C₄	C₂³×C₅	1	3	yes	—
273	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
274	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
275	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
276	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
277	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
278	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
279	C₃×C₄⋊C₄	C₂³×C₅	1	3	yes	—
280	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
281	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂³×C₅	1	12	yes	—
283	C₃×C₄⋊C₄	C₂³×C₅	1	6	yes	—
284	C₃×C₂²⋊C₄	C₂³×C₅	1	2	yes	—
285	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
286	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
287	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
288	C₃×C₂²⋊C₄	C₂³×C₅	1	6	yes	—
289	C₃×C₄²	C₂³×C₅	1	3	yes	—
290	C₃×C₄²	C₂³×C₅	1	3	yes	—
291	C₃×C₄²	C₂³×C₅	1	3	yes	—
292	C₃×C₄²	C₂³×C₅	1	3	yes	—
293	C₃×C₄²	C₂³×C₅	1	12	yes	—
294	C₃×C₄²	C₂³×C₅	1	6	yes	—
295	C₂³×C₅	C₂⁴×C₃	1	2	yes	—
296	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
297	C₅×Q₈	—	2	6	no	—
298	C₅×Q₈	—	2	12	no	—
299	C₅×Q₈	—	2	6	no	—
300	C₅×Q₈	C₃×#41	1	4	yes	—
301	C₅×D₄	—	2	4	no	—
302	C₅×D₄	—	2	2	no	—
303	C₂×C₄×C₅	—	2	6	no	—
304	C₂×C₄×C₅	—	2	6	no	—
305	C₂×C₄×C₅	—	2	12	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
308	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
309	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
310	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
311	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
312	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
313	C₂×C₄×C₅	C₂⁴×C₃	1	6	yes	—
314	C₂×C₄×C₅	C₂⁴×C₃	1	3	yes	—
315	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
316	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
318	C₄⋊Q₈	C₂²×C₃×C₅	1	3	yes	—
319	C₄⋊Q₈	C₂²×C₃×C₅	1	3	yes	—
320	C₄⋊Q₈	C₂²×C₃×C₅	1	6	yes	—
321	#126	C₂²×C₃×C₅	1	6	yes	—
322	#126	C₂²×C₃×C₅	1	12	yes	—
323	#125	C₂²×C₃×C₅	1	3	yes	—
324	#125	C₂²×C₃×C₅	1	6	yes	—
325	#125	C₂²×C₃×C₅	1	12	yes	—
326	#125	C₂²×C₃×C₅	1	6	yes	—
327	#124	C₂²×C₃×C₅	1	3	yes	—
328	#123	C₂²×C₃×C₅	1	6	yes	—
329	C₂²⋊Q₈	C₂²×C₃×C₅	1	3	yes	—
330	C₂²⋊Q₈	C₂²×C₃×C₅	1	6	yes	—
331	C₂²⋊Q₈	C₂²×C₃×C₅	1	6	yes	—
332	C₂²⋊Q₈	C₂²×C₃×C₅	1	6	yes	—
333	#121	C₂²×C₃×C₅	1	1	yes	characteristic
334	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
335	C₄×Q₈	C₂²×C₃×C₅	1	3	yes	—
336	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
337	C₄×Q₈	C₂²×C₃×C₅	1	3	yes	—
338	C₄×Q₈	C₂²×C₃×C₅	1	6	yes	—
339	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
340	C₄×Q₈	C₂²×C₃×C₅	1	6	yes	—
341	C₄×Q₈	C₂²×C₃×C₅	1	3	yes	—
342	C₄×Q₈	C₂²×C₃×C₅	1	6	yes	—
343	C₄×D₄	C₂²×C₃×C₅	1	6	yes	—
344	C₄×D₄	C₂²×C₃×C₅	1	3	yes	—
345	#117	C₂²×C₃×C₅	1	6	yes	—
346	#117	C₂²×C₃×C₅	1	6	yes	—
347	#117	C₂²×C₃×C₅	1	6	yes	—
348	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	3	yes	—
349	C₂×C₄²	C₂²×C₃×C₅	1	3	yes	—
350	C₂×C₃×C₅	—	2	2	no	—
351	C₂×C₃×C₅	—	4	2	no	—
352	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
353	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
354	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	1	yes	characteristic
355	C₂³×C₃	C₂⁴×C₅	1	2	yes	—
356	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
357	C₃×Q₈	—	2	6	no	—
358	C₃×Q₈	—	2	12	no	—
359	C₃×Q₈	—	2	6	no	—
360	C₃×Q₈	C₅×#41	1	4	yes	—
361	C₃×D₄	—	2	4	no	—
362	C₃×D₄	—	2	2	no	—
363	C₂×C₃×C₄	—	2	6	no	—
364	C₂×C₃×C₄	—	2	6	no	—
365	C₂×C₃×C₄	—	2	12	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
368	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
369	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
370	C₂×C₃×C₄	C₂⁴×C₅	1	2	yes	—
371	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
372	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
373	C₂×C₃×C₄	C₂⁴×C₅	1	6	yes	—
374	C₂×C₃×C₄	C₂⁴×C₅	1	3	yes	—
375	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
376	C₂²×C₅	—	2	1	no	—
377	C₂²×C₅	—	2	1	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	2	2	no	—
380	C₂²×C₅	—	2	2	no	—
381	C₂²×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
382	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
383	C₄×C₅	—	2	3	no	—
384	C₄×C₅	—	2	6	no	—
385	C₄×C₅	—	2	3	no	—
386	C₄×C₅	—	2	3	no	—
387	C₄×C₅	—	2	1	no	—
388	C₄×C₅	—	2	2	no	—
389	C₄×C₅	—	2	6	no	—
390	C₄×C₅	C₂×C₃×#41	1	6	yes	—
391	C₄×C₅	C₃×2₋¹⁺⁴	1	2	yes	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	2	8	no	—
394	C₂×Q₈	C₂³×C₃×C₅	1	3	yes	—
395	C₂×Q₈	C₂³×C₃×C₅	1	3	yes	—
396	C₂×Q₈	C₂³×C₃×C₅	1	6	yes	—
397	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
398	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
399	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
400	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
402	C₂²×C₄	C₂³×C₃×C₅	1	3	yes	—
403	C₂²×C₄	C₂³×C₃×C₅	1	6	yes	—
404	C₄⋊C₄	C₂³×C₃×C₅	1	3	yes	—
405	C₄⋊C₄	C₂³×C₃×C₅	1	3	yes	—
406	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
407	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
408	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
409	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
410	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
411	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
412	C₄⋊C₄	C₂³×C₃×C₅	1	3	yes	—
413	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
414	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
415	C₄⋊C₄	C₂³×C₃×C₅	1	12	yes	—
416	C₄⋊C₄	C₂³×C₃×C₅	1	6	yes	—
417	C₂²⋊C₄	C₂³×C₃×C₅	1	2	yes	—
418	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	—
419	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	—
420	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	—
421	C₂²⋊C₄	C₂³×C₃×C₅	1	6	yes	—
422	C₄²	C₂³×C₃×C₅	1	3	yes	—
423	C₄²	C₂³×C₃×C₅	1	3	yes	—
424	C₄²	C₂³×C₃×C₅	1	3	yes	—
425	C₄²	C₂³×C₃×C₅	1	3	yes	—
426	C₄²	C₂³×C₃×C₅	1	12	yes	—
427	C₄²	C₂³×C₃×C₅	1	6	yes	—
428	C₃×C₅	#3523	1	1	yes	characteristic, direct product factor, Hall
429	C₂²×C₃	—	2	1	no	—
430	C₂²×C₃	—	2	1	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	C₅×2₋¹⁺⁴	1	2	yes	—
435	C₂²×C₃	C₂⁵×C₅	1	1	yes	characteristic
436	C₃×C₄	—	2	3	no	—
437	C₃×C₄	—	2	6	no	—
438	C₃×C₄	—	2	3	no	—
439	C₃×C₄	—	2	3	no	—
440	C₃×C₄	—	2	1	no	—
441	C₃×C₄	—	2	2	no	—
442	C₃×C₄	—	2	6	no	—
443	C₃×C₄	C₂×C₅×#41	1	6	yes	—
444	C₃×C₄	C₅×2₋¹⁺⁴	1	2	yes	—
445	C₂×C₅	—	2	2	no	—
446	C₂×C₅	—	4	2	no	—
447	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
448	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
449	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂³	C₂⁴×C₃×C₅	1	2	yes	—
451	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
452	Q₈	—	2	6	no	—
453	Q₈	—	2	12	no	—
454	Q₈	—	2	6	no	—
455	Q₈	C₃×C₅×#41	1	4	yes	—
456	D₄	—	2	4	no	—
457	D₄	—	2	2	no	—
458	C₂×C₄	—	2	6	no	—
459	C₂×C₄	—	2	6	no	—
460	C₂×C₄	—	2	12	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
463	C₂×C₄	C₂⁴×C₃×C₅	1	3	yes	—
464	C₂×C₄	C₂⁴×C₃×C₅	1	6	yes	—
465	C₂×C₄	C₂⁴×C₃×C₅	1	2	yes	—
466	C₂×C₄	C₂⁴×C₃×C₅	1	3	yes	—
467	C₂×C₄	C₂⁴×C₃×C₅	1	3	yes	—
468	C₂×C₄	C₂⁴×C₃×C₅	1	6	yes	—
469	C₂×C₄	C₂⁴×C₃×C₅	1	3	yes	—
470	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
471	C₂×C₃	—	2	2	no	—
472	C₂×C₃	—	4	2	no	—
473	C₂×C₃	C₂²×C₅×#41	1	1	yes	characteristic
474	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
475	C₂×C₃	C₂×C₅×2₋¹⁺⁴	1	1	yes	characteristic
476	C₅	C₃×#3523	1	1	yes	characteristic, direct product factor, Sylow
477	C₂²	—	2	1	no	—
478	C₂²	—	2	1	no	—
479	C₂²	—	2	2	no	—
480	C₂²	—	2	2	no	—
481	C₂²	—	2	2	no	—
482	C₂²	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
483	C₂²	C₂⁵×C₃×C₅	1	1	yes	characteristic
484	C₄	—	2	3	no	—
485	C₄	—	2	6	no	—
486	C₄	—	2	3	no	—
487	C₄	—	2	3	no	—
488	C₄	—	2	1	no	—
489	C₄	—	2	2	no	—
490	C₄	—	2	6	no	—
491	C₄	C₂×C₃×C₅×#41	1	6	yes	—
492	C₄	C₃×C₅×2₋¹⁺⁴	1	2	yes	—
493	C₃	C₅×#3523	1	1	yes	characteristic, direct product factor, Sylow
494	C₂	—	2	2	no	—
495	C₂	—	4	2	no	—
496	C₂	C₂²×C₃×C₅×#41	1	1	yes	characteristic
497	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
498	C₂	C₂×C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁵×C₃×C₅
prime radical	C₃×C₅×#121	C₂²
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#557	C₂	semidirect
2. C₃×C₅×#557	C₂	semidirect
3. C₃×C₅×#556	C₂	semidirect
4. C₃×C₅×#552	C₂	semidirect
5. C₃×C₅×D₄×Q₈	C₂	semidirect
6. C₃×C₅×D₄×Q₈	C₂	semidirect
7. C₃×C₅×#541	C₂	semidirect
8. C₃×C₅×#533	C₂	semidirect
10. C₃×C₅×#519	C₂	semidirect
11. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
12. C₅×#3523	C₃	direct (N × H)
47. C₃×#3523	C₅	direct (N × H)
48. C₅×#557	C₂×C₃	semidirect
49. C₅×#557	C₂×C₃	semidirect
50. C₅×#556	C₂×C₃	semidirect
51. C₅×#552	C₂×C₃	semidirect
52. C₅×D₄×Q₈	C₂×C₃	semidirect
53. C₅×D₄×Q₈	C₂×C₃	semidirect
54. C₅×#541	C₂×C₃	semidirect
55. C₅×#533	C₂×C₃	semidirect
57. C₅×#519	C₂×C₃	semidirect
58. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
95. C₃×#557	C₂×C₅	semidirect
96. C₃×#557	C₂×C₅	semidirect
97. C₃×#556	C₂×C₅	semidirect
98. C₃×#552	C₂×C₅	semidirect
99. C₃×D₄×Q₈	C₂×C₅	semidirect
100. C₃×D₄×Q₈	C₂×C₅	semidirect
101. C₃×#541	C₂×C₅	semidirect
102. C₃×#533	C₂×C₅	semidirect
104. C₃×#519	C₂×C₅	semidirect
105. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
140. #3523	C₃×C₅	direct (N × H)
232. #557	C₂×C₃×C₅	semidirect
233. #557	C₂×C₃×C₅	semidirect
234. #556	C₂×C₃×C₅	semidirect
235. #552	C₂×C₃×C₅	semidirect
236. D₄×Q₈	C₂×C₃×C₅	semidirect
237. D₄×Q₈	C₂×C₃×C₅	semidirect
238. #541	C₂×C₃×C₅	semidirect
239. #533	C₂×C₃×C₅	semidirect
241. #519	C₂×C₃×C₅	semidirect
242. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
428. C₃×C₅	#3523	direct (N × H)
476. C₅	C₃×#3523	direct (N × H)
493. C₃	C₅×#3523	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₃×C₅×#557	2
C₃×C₅×#556	2
C₃×C₅×#552	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#541	2
C₃×C₅×#533	2
C₃×C₅×#529	2
C₃×C₅×#519	2
C₂×C₃×C₄×C₅×Q₈	2
C₅×#3523	3
C₃×#3523	5

Subgroups — C3×C5×#3523 #14276557

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3523 #14276557