Subgroups — C₃×C₅×#3233 #14276267

Order 1920.

664 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#533	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#529	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#499	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#488	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#485	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#482	C₂	1	2	yes	maximal
7	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#474	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#431	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3233	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#126	—	2	1	no	—
16	C₃×C₅×#125	C₂²	1	2	yes	—
17	C₃×C₅×#125	C₂²	1	1	yes	characteristic
18	C₃×C₅×#124	C₂²	1	1	yes	characteristic
19	C₃×C₅×#123	—	2	1	no	—
20	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	1	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
23	C₃×C₅×#121	C₂²	1	1	yes	characteristic
24	C₃×C₄×C₅×Q₈	—	2	1	no	—
25	C₃×C₄×C₅×Q₈	—	2	1	no	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	—	2	1	no	—
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₃×C₅×#117	—	2	1	no	—
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₃×C₅×#107	C₂²	1	2	yes	—
33	C₃×C₅×#107	C₂²	1	2	yes	—
34	C₃×C₅×#106	C₂²	1	2	yes	—
35	C₃×C₅×#106	C₂²	1	2	yes	—
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#103	C₂²	1	2	yes	—
40	C₃×C₅×#102	C₂²	1	2	yes	—
41	C₃×C₅×#102	C₂²	1	2	yes	—
42	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
43	C₃×C₄×C₅×C₈	C₂²	1	2	yes	—
44	C₃×#3233	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₅×#533	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#529	C₂×C₃	1	1	yes	characteristic
47	C₅×#499	C₂×C₃	1	2	yes	complemented
48	C₅×#488	C₂×C₃	1	2	yes	complemented
49	C₅×#485	C₂×C₃	1	2	yes	complemented
50	C₅×#482	C₂×C₃	1	2	yes	—
51	C₅×#477	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#474	C₂×C₃	1	1	yes	characteristic, complemented
55	C₅×#431	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	—	2	1	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	1	no	—
60	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
67	C₃×C₅×C₄⋊C₄	—	2	1	no	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	—	2	1	no	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
77	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
80	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
81	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
85	C₃×C₄²×C₅	—	2	1	no	—
86	C₃×C₄²×C₅	—	2	2	no	—
87	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
88	C₃×C₄²×C₅	D₄	1	1	yes	characteristic
89	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
90	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
91	C₃×#533	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#529	C₂×C₅	1	1	yes	characteristic
93	C₃×#499	C₂×C₅	1	2	yes	complemented
94	C₃×#488	C₂×C₅	1	2	yes	complemented
95	C₃×#485	C₂×C₅	1	2	yes	complemented
96	C₃×#482	C₂×C₅	1	2	yes	—
97	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#474	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#431	C₂×C₅	1	1	yes	characteristic, complemented
102	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
103	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₅×#126	—	2	1	no	—
105	C₅×#125	C₂²×C₃	1	2	yes	—
106	C₅×#125	C₂²×C₃	1	1	yes	characteristic
107	C₅×#124	C₂²×C₃	1	1	yes	characteristic
108	C₅×#123	—	2	1	no	—
109	C₅×C₂²⋊Q₈	—	2	1	no	—
110	C₅×C₂²⋊Q₈	—	2	1	no	—
111	C₅×C₂²⋊Q₈	C₂²×C₃	1	1	yes	characteristic
112	C₅×#121	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×Q₈	—	2	1	no	—
114	C₄×C₅×Q₈	—	2	1	no	—
115	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
116	C₄×C₅×D₄	—	2	1	no	—
117	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
118	C₅×#117	—	2	1	no	—
119	C₅×#117	C₂²×C₃	1	2	yes	—
120	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
121	C₅×#107	C₂²×C₃	1	2	yes	—
122	C₅×#107	C₂²×C₃	1	2	yes	—
123	C₅×#106	C₂²×C₃	1	2	yes	—
124	C₅×#106	C₂²×C₃	1	2	yes	—
125	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
126	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
127	C₅×#103	C₂²×C₃	1	2	yes	—
128	C₅×#103	C₂²×C₃	1	2	yes	—
129	C₅×#102	C₂²×C₃	1	2	yes	—
130	C₅×#102	C₂²×C₃	1	2	yes	—
131	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
132	C₄×C₅×C₈	C₂²×C₃	1	2	yes	—
133	#3233	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₃×C₅×Q₈	—	2	1	no	—
137	C₃×C₅×Q₈	—	2	1	no	—
138	C₃×C₅×Q₈	—	4	2	no	—
139	C₃×C₅×Q₈	—	4	2	no	—
140	C₃×C₅×D₄	—	2	1	no	—
141	C₃×C₅×D₄	—	2	1	no	—
142	C₃×C₅×D₄	—	4	2	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	1	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	4	1	no	—
152	C₂×C₃×C₄×C₅	—	4	2	no	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
156	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
157	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
158	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
159	C₃×C₅×C₈	—	2	2	no	—
160	C₃×C₅×C₈	—	2	2	no	—
161	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
162	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
163	C₃×#126	—	2	1	no	—
164	C₃×#125	C₂²×C₅	1	1	yes	characteristic
165	C₃×#125	C₂²×C₅	1	2	yes	—
166	C₃×#124	C₂²×C₅	1	1	yes	characteristic
167	C₃×#123	—	2	1	no	—
168	C₃×C₂²⋊Q₈	—	2	1	no	—
169	C₃×C₂²⋊Q₈	—	2	1	no	—
170	C₃×C₂²⋊Q₈	C₂²×C₅	1	1	yes	characteristic
171	C₃×#121	C₂²×C₅	1	1	yes	characteristic
172	C₃×C₄×Q₈	—	2	1	no	—
173	C₃×C₄×Q₈	—	2	1	no	—
174	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
175	C₃×C₄×D₄	—	2	1	no	—
176	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
177	C₃×#117	—	2	1	no	—
178	C₃×#117	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
180	C₃×#107	C₂²×C₅	1	2	yes	—
181	C₃×#107	C₂²×C₅	1	2	yes	—
182	C₃×#106	C₂²×C₅	1	2	yes	—
183	C₃×#106	C₂²×C₅	1	2	yes	—
184	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
185	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
186	C₃×#103	C₂²×C₅	1	2	yes	—
187	C₃×#103	C₂²×C₅	1	2	yes	—
188	C₃×#102	C₂²×C₅	1	2	yes	—
189	C₃×#102	C₂²×C₅	1	2	yes	—
190	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
191	C₃×C₄×C₈	C₂²×C₅	1	2	yes	—
192	C₂×C₅×Q₈	—	2	1	no	—
193	C₂×C₅×Q₈	—	2	1	no	—
194	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
195	C₂×C₅×D₄	—	2	1	no	—
196	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
197	C₂²×C₄×C₅	—	2	1	no	—
198	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
199	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
200	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
202	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	2	no	—
207	C₅×C₄⋊C₄	—	2	2	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	1	no	—
210	C₅×C₄⋊C₄	—	2	1	no	—
211	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
212	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
213	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	1	no	—
217	C₅×C₂²⋊C₄	—	2	1	no	—
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	—	2	1	no	—
220	C₅×C₂²⋊C₄	—	2	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	—	2	2	no	—
223	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
224	C₄²×C₅	C₃×D₄	1	1	yes	characteristic
225	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
226	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
227	#533	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#529	C₂×C₃×C₅	1	1	yes	characteristic
229	#499	C₂×C₃×C₅	1	2	yes	complemented
230	#488	C₂×C₃×C₅	1	2	yes	complemented
231	#485	C₂×C₃×C₅	1	2	yes	complemented
232	#482	C₂×C₃×C₅	1	2	yes	—
233	#477	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#474	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	#431	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	C₂²×C₃×C₅	—	2	1	no	—
239	C₂²×C₃×C₅	—	2	1	no	—
240	C₂²×C₃×C₅	—	2	1	no	—
241	C₂²×C₃×C₅	—	4	1	no	—
242	C₂²×C₃×C₅	—	4	1	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₃×C₄×C₅	—	2	1	no	—
246	C₃×C₄×C₅	—	2	1	no	—
247	C₃×C₄×C₅	—	2	1	no	—
248	C₃×C₄×C₅	—	2	1	no	—
249	C₃×C₄×C₅	—	4	1	no	—
250	C₃×C₄×C₅	—	4	1	no	—
251	C₃×C₄×C₅	—	4	2	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	—	4	2	no	—
254	C₃×C₄×C₅	#135	1	2	yes	—
255	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
256	C₃×C₄×C₅	2₋¹⁺⁴	1	1	yes	characteristic
257	C₂×C₃×Q₈	—	2	1	no	—
258	C₂×C₃×Q₈	—	2	1	no	—
259	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×D₄	—	2	1	no	—
261	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	2	1	no	—
263	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
264	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
265	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
267	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
268	C₃×C₄⋊C₄	—	2	1	no	—
269	C₃×C₄⋊C₄	—	2	1	no	—
270	C₃×C₄⋊C₄	—	2	1	no	—
271	C₃×C₄⋊C₄	—	2	2	no	—
272	C₃×C₄⋊C₄	—	2	2	no	—
273	C₃×C₄⋊C₄	—	2	1	no	—
274	C₃×C₄⋊C₄	—	2	1	no	—
275	C₃×C₄⋊C₄	—	2	1	no	—
276	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
277	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
278	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
280	C₃×C₂²⋊C₄	—	2	2	no	—
281	C₃×C₂²⋊C₄	—	2	1	no	—
282	C₃×C₂²⋊C₄	—	2	1	no	—
283	C₃×C₂²⋊C₄	—	2	1	no	—
284	C₃×C₂²⋊C₄	—	2	1	no	—
285	C₃×C₂²⋊C₄	—	2	1	no	—
286	C₃×C₄²	—	2	1	no	—
287	C₃×C₄²	—	2	2	no	—
288	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
289	C₃×C₄²	C₅×D₄	1	1	yes	characteristic
290	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
291	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
292	C₂³×C₅	—	2	1	no	—
293	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
294	C₅×Q₈	—	2	1	no	—
295	C₅×Q₈	—	2	1	no	—
296	C₅×Q₈	—	4	2	no	—
297	C₅×Q₈	—	4	2	no	—
298	C₅×D₄	—	2	1	no	—
299	C₅×D₄	—	2	1	no	—
300	C₅×D₄	—	4	2	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	2	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	4	1	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
312	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
313	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
315	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
316	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
317	C₅×C₈	—	2	2	no	—
318	C₅×C₈	—	2	2	no	—
319	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
320	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
321	#126	—	2	1	no	—
322	#125	C₂²×C₃×C₅	1	1	yes	characteristic
323	#125	C₂²×C₃×C₅	1	2	yes	—
324	#124	C₂²×C₃×C₅	1	1	yes	characteristic
325	#123	—	2	1	no	—
326	C₂²⋊Q₈	—	2	1	no	—
327	C₂²⋊Q₈	—	2	1	no	—
328	C₂²⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
329	#121	C₂²×C₃×C₅	1	1	yes	characteristic
330	C₄×Q₈	—	2	1	no	—
331	C₄×Q₈	—	2	1	no	—
332	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
333	C₄×D₄	—	2	1	no	—
334	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
335	#117	—	2	1	no	—
336	#117	C₂²×C₃×C₅	1	2	yes	—
337	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
338	#107	C₂²×C₃×C₅	1	2	yes	—
339	#107	C₂²×C₃×C₅	1	2	yes	—
340	#106	C₂²×C₃×C₅	1	2	yes	—
341	#106	C₂²×C₃×C₅	1	2	yes	—
342	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
344	#103	C₂²×C₃×C₅	1	2	yes	—
345	#103	C₂²×C₃×C₅	1	2	yes	—
346	#102	C₂²×C₃×C₅	1	2	yes	—
347	#102	C₂²×C₃×C₅	1	2	yes	—
348	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
349	C₄×C₈	C₂²×C₃×C₅	1	2	yes	—
350	C₂×C₃×C₅	—	4	1	no	—
351	C₂×C₃×C₅	—	8	1	no	—
352	C₂×C₃×C₅	#536	1	1	yes	characteristic
353	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
354	C₂×C₃×C₅	#575	1	1	yes	characteristic
355	C₂³×C₃	—	2	1	no	—
356	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
357	C₃×Q₈	—	2	1	no	—
358	C₃×Q₈	—	2	1	no	—
359	C₃×Q₈	—	4	2	no	—
360	C₃×Q₈	—	4	2	no	—
361	C₃×D₄	—	2	1	no	—
362	C₃×D₄	—	2	1	no	—
363	C₃×D₄	—	4	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	1	no	—
369	C₂×C₃×C₄	—	2	2	no	—
370	C₂×C₃×C₄	—	2	2	no	—
371	C₂×C₃×C₄	—	2	1	no	—
372	C₂×C₃×C₄	—	4	1	no	—
373	C₂×C₃×C₄	—	4	2	no	—
374	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
375	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
376	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
378	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
380	C₃×C₈	—	2	2	no	—
381	C₃×C₈	—	2	2	no	—
382	C₂²×C₅	—	2	1	no	—
383	C₂²×C₅	—	2	1	no	—
384	C₂²×C₅	—	2	1	no	—
385	C₂²×C₅	—	4	1	no	—
386	C₂²×C₅	—	4	1	no	—
387	C₂²×C₅	—	4	1	no	—
388	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
389	C₄×C₅	—	2	1	no	—
390	C₄×C₅	—	2	1	no	—
391	C₄×C₅	—	2	1	no	—
392	C₄×C₅	—	2	1	no	—
393	C₄×C₅	—	4	1	no	—
394	C₄×C₅	—	4	2	no	—
395	C₄×C₅	—	4	1	no	—
396	C₄×C₅	—	4	2	no	—
397	C₄×C₅	—	4	1	no	—
398	C₄×C₅	C₃×#135	1	2	yes	—
399	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
400	C₄×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
401	C₂×Q₈	—	2	1	no	—
402	C₂×Q₈	—	2	1	no	—
403	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₂×D₄	—	2	1	no	—
405	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
406	C₂²×C₄	—	2	1	no	—
407	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
408	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
409	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
410	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
411	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
412	C₄⋊C₄	—	2	1	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	2	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
421	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
422	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
423	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	—	2	1	no	—
426	C₂²⋊C₄	—	2	1	no	—
427	C₂²⋊C₄	—	2	1	no	—
428	C₂²⋊C₄	—	2	1	no	—
429	C₂²⋊C₄	—	2	1	no	—
430	C₄²	—	2	1	no	—
431	C₄²	—	2	2	no	—
432	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
433	C₄²	C₃×C₅×D₄	1	1	yes	characteristic
434	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
435	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
436	C₃×C₅	#3233	1	1	yes	characteristic, direct product factor, Hall
437	C₂²×C₃	—	2	1	no	—
438	C₂²×C₃	—	2	1	no	—
439	C₂²×C₃	—	2	1	no	—
440	C₂²×C₃	—	4	1	no	—
441	C₂²×C₃	—	4	1	no	—
442	C₂²×C₃	—	4	1	no	—
443	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
444	C₃×C₄	—	2	1	no	—
445	C₃×C₄	—	2	1	no	—
446	C₃×C₄	—	2	1	no	—
447	C₃×C₄	—	2	1	no	—
448	C₃×C₄	—	4	1	no	—
449	C₃×C₄	—	4	1	no	—
450	C₃×C₄	—	4	2	no	—
451	C₃×C₄	—	4	1	no	—
452	C₃×C₄	—	4	2	no	—
453	C₃×C₄	C₅×#135	1	2	yes	—
454	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
455	C₃×C₄	C₅×2₋¹⁺⁴	1	1	yes	characteristic
456	C₂×C₅	—	4	1	no	—
457	C₂×C₅	—	8	1	no	—
458	C₂×C₅	C₃×#536	1	1	yes	characteristic
459	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
460	C₂×C₅	C₃×#575	1	1	yes	characteristic
461	C₂³	—	2	1	no	—
462	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
463	Q₈	—	2	1	no	—
464	Q₈	—	2	1	no	—
465	Q₈	—	4	2	no	—
466	Q₈	—	4	2	no	—
467	D₄	—	2	1	no	—
468	D₄	—	2	1	no	—
469	D₄	—	4	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	2	1	no	—
475	C₂×C₄	—	2	2	no	—
476	C₂×C₄	—	2	2	no	—
477	C₂×C₄	—	2	1	no	—
478	C₂×C₄	—	4	1	no	—
479	C₂×C₄	—	4	2	no	—
480	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
481	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
482	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
483	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
484	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
485	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
486	C₈	—	2	2	no	—
487	C₈	—	2	2	no	—
488	C₂×C₃	—	4	1	no	—
489	C₂×C₃	—	8	1	no	—
490	C₂×C₃	C₅×#536	1	1	yes	characteristic
491	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
492	C₂×C₃	C₅×#575	1	1	yes	characteristic
493	C₅	C₃×#3233	1	1	yes	characteristic, direct product factor, Sylow
494	C₂²	—	2	1	no	—
495	C₂²	—	2	1	no	—
496	C₂²	—	2	1	no	—
497	C₂²	—	4	1	no	—
498	C₂²	—	4	1	no	—
499	C₂²	—	4	1	no	—
500	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
501	C₄	—	2	1	no	—
502	C₄	—	2	1	no	—
503	C₄	—	2	1	no	—
504	C₄	—	2	1	no	—
505	C₄	—	4	1	no	—
506	C₄	—	4	1	no	—
507	C₄	—	4	2	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	2	no	—
510	C₄	C₃×C₅×#135	1	2	yes	—
511	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
512	C₄	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
513	C₃	C₅×#3233	1	1	yes	characteristic, direct product factor, Sylow
514	C₂	—	4	1	no	—
515	C₂	—	8	1	no	—
516	C₂	C₃×C₅×#536	1	1	yes	characteristic
517	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
518	C₂	C₃×C₅×#575	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
prime radical	C₃×C₅×#121	C₂²
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂×C₃×C₄²×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#533	C₂	semidirect
3. C₃×C₅×#499	C₂	semidirect
4. C₃×C₅×#488	C₂	semidirect
5. C₃×C₅×#485	C₂	semidirect
7. C₃×C₅×#477	C₂	semidirect
8. C₃×C₅×#476	C₂	semidirect
9. C₃×C₅×#475	C₂	semidirect
10. C₃×C₅×#474	C₂	semidirect
11. C₃×C₅×#431	C₂	semidirect
12. C₅×#3233	C₃	direct (N × H)
44. C₃×#3233	C₅	direct (N × H)
45. C₅×#533	C₂×C₃	semidirect
47. C₅×#499	C₂×C₃	semidirect
48. C₅×#488	C₂×C₃	semidirect
49. C₅×#485	C₂×C₃	semidirect
51. C₅×#477	C₂×C₃	semidirect
52. C₅×#476	C₂×C₃	semidirect
53. C₅×#475	C₂×C₃	semidirect
54. C₅×#474	C₂×C₃	semidirect
55. C₅×#431	C₂×C₃	semidirect
91. C₃×#533	C₂×C₅	semidirect
93. C₃×#499	C₂×C₅	semidirect
94. C₃×#488	C₂×C₅	semidirect
95. C₃×#485	C₂×C₅	semidirect
97. C₃×#477	C₂×C₅	semidirect
98. C₃×#476	C₂×C₅	semidirect
99. C₃×#475	C₂×C₅	semidirect
100. C₃×#474	C₂×C₅	semidirect
101. C₃×#431	C₂×C₅	semidirect
133. #3233	C₃×C₅	direct (N × H)
227. #533	C₂×C₃×C₅	semidirect
229. #499	C₂×C₃×C₅	semidirect
230. #488	C₂×C₃×C₅	semidirect
231. #485	C₂×C₃×C₅	semidirect
233. #477	C₂×C₃×C₅	semidirect
234. #476	C₂×C₃×C₅	semidirect
235. #475	C₂×C₃×C₅	semidirect
236. #474	C₂×C₃×C₅	semidirect
237. #431	C₂×C₃×C₅	semidirect
436. C₃×C₅	#3233	direct (N × H)
493. C₅	C₃×#3233	direct (N × H)
513. C₃	C₅×#3233	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×#533	2
C₃×C₅×#529	2
C₃×C₅×#499	2
C₃×C₅×#488	2
C₃×C₅×#485	2
C₃×C₅×#482	2
C₃×C₅×#477	2
C₃×C₅×#476	2
C₃×C₅×#475	2
C₃×C₅×#474	2
C₃×C₅×#431	2
C₅×#3233	3
C₃×#3233	5

Subgroups — C3×C5×#3233 #14276267

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3233 #14276267