Subgroups — C₃×C₅×#3331 #14276365

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 508 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#554	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#483	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#476	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#470	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#417	C₂	1	2	yes	maximal, complemented
12	C₅×#3331	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
15	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#125	—	2	1	no	—
20	C₃×C₅×#123	—	2	2	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₅×#121	—	2	1	no	—
25	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₄×C₅×D₄	—	2	1	no	—
27	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×#106	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#103	C₂²	1	1	yes	characteristic
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×#3331	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#554	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#547	C₂×C₃	1	1	yes	characteristic
45	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#483	C₂×C₃	1	2	yes	complemented
47	C₅×#476	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#470	C₂×C₃	1	2	yes	complemented
49	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#452	C₂×C₃	1	2	yes	complemented
51	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×#436	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×#417	C₂×C₃	1	2	yes	complemented
54	C₃×C₅×#41	—	2	4	no	—
55	C₃×C₅×#41	—	4	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	1	no	—
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	—	2	2	no	—
63	C₂²×C₃×C₄×C₅	—	2	1	no	—
64	C₂²×C₃×C₄×C₅	—	2	2	no	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₃×C₅×Q₁₆	—	4	2	no	—
67	C₃×C₅×SD₁₆	—	2	2	no	—
68	C₃×C₅×M₁₆	—	4	2	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
70	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	—	2	1	no	—
73	C₃×C₅×C₄⋊C₄	—	2	2	no	—
74	C₃×C₅×C₄⋊C₄	—	2	2	no	—
75	C₃×C₅×C₄⋊C₄	—	2	1	no	—
76	C₃×C₅×C₄⋊C₄	—	2	1	no	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	1	no	—
79	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
82	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
83	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
84	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
85	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
86	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
87	C₃×C₄²×C₅	—	2	1	no	—
88	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
89	C₃×#554	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#547	C₂×C₅	1	1	yes	characteristic
91	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#483	C₂×C₅	1	2	yes	complemented
93	C₃×#476	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×#470	C₂×C₅	1	2	yes	complemented
95	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#452	C₂×C₅	1	2	yes	complemented
97	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#436	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#417	C₂×C₅	1	2	yes	complemented
100	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
101	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
102	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
104	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₅×#125	—	2	1	no	—
107	C₅×#123	—	2	2	no	—
108	C₅×C₂²⋊Q₈	—	2	2	no	—
109	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
110	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
111	C₅×#121	—	2	1	no	—
112	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×D₄	—	2	1	no	—
114	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₅×C₄⋊C₄	—	2	1	no	—
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
118	C₅×#106	C₂²×C₃	1	1	yes	characteristic
119	C₅×#106	C₂²×C₃	1	2	yes	—
120	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#103	C₂²×C₃	1	2	yes	—
122	C₅×#103	C₂²×C₃	1	2	yes	—
123	C₅×#103	C₂²×C₃	1	1	yes	characteristic
124	C₅×#103	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	1	yes	characteristic
126	C₅×#102	C₂²×C₃	1	2	yes	—
127	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
128	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
129	#3331	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³×C₃×C₅	—	2	1	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	1	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	8	1	no	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	1	no	—
139	C₃×C₅×D₄	—	4	4	no	—
140	C₃×C₅×D₄	#41	1	2	yes	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	4	4	no	—
149	C₂×C₃×C₄×C₅	—	4	2	no	—
150	C₂×C₃×C₄×C₅	—	8	2	no	—
151	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
152	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
154	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
155	C₃×C₅×C₈	—	2	1	no	—
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	—	2	2	no	—
158	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
159	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
160	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
162	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
163	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₃×#125	—	2	1	no	—
165	C₃×#123	—	2	2	no	—
166	C₃×C₂²⋊Q₈	—	2	2	no	—
167	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
168	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
169	C₃×#121	—	2	1	no	—
170	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
171	C₃×C₄×D₄	—	2	1	no	—
172	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
173	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	—	2	1	no	—
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
176	C₃×#106	C₂²×C₅	1	1	yes	characteristic
177	C₃×#106	C₂²×C₅	1	2	yes	—
178	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
179	C₃×#103	C₂²×C₅	1	2	yes	—
180	C₃×#103	C₂²×C₅	1	2	yes	—
181	C₃×#103	C₂²×C₅	1	1	yes	characteristic
182	C₃×#103	C₂²×C₅	1	2	yes	—
183	C₃×#102	C₂²×C₅	1	1	yes	characteristic
184	C₃×#102	C₂²×C₅	1	2	yes	—
185	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
186	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
187	C₅×#41	—	2	4	no	—
188	C₅×#41	—	4	2	no	—
189	C₂×C₅×Q₈	—	2	1	no	—
190	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
192	C₂×C₅×D₄	—	2	2	no	—
193	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
194	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	—	2	1	no	—
197	C₂²×C₄×C₅	—	2	2	no	—
198	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
199	C₅×Q₁₆	—	4	2	no	—
200	C₅×SD₁₆	—	2	2	no	—
201	C₅×M₁₆	—	4	2	no	—
202	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
204	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	2	no	—
211	C₅×C₄⋊C₄	—	2	1	no	—
212	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
214	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
215	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
216	C₅×C₂²⋊C₄	—	2	2	no	—
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₅×C₂²⋊C₄	—	2	1	no	—
219	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
222	#554	C₂×C₃×C₅	1	1	yes	characteristic, complemented
223	#547	C₂×C₃×C₅	1	1	yes	characteristic
224	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
225	#483	C₂×C₃×C₅	1	2	yes	complemented
226	#476	C₂×C₃×C₅	1	1	yes	characteristic, complemented
227	#470	C₂×C₃×C₅	1	2	yes	complemented
228	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
229	#452	C₂×C₃×C₅	1	2	yes	complemented
230	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
231	#436	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	#417	C₂×C₃×C₅	1	2	yes	complemented
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	4	1	no	—
238	C₂²×C₃×C₅	—	4	1	no	—
239	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₃×C₄×C₅	—	2	2	no	—
241	C₃×C₄×C₅	—	2	1	no	—
242	C₃×C₄×C₅	—	4	2	no	—
243	C₃×C₄×C₅	—	4	1	no	—
244	C₃×C₄×C₅	—	4	1	no	—
245	C₃×C₄×C₅	—	4	1	no	—
246	C₃×C₄×C₅	—	4	2	no	—
247	C₃×C₄×C₅	#137	1	2	yes	—
248	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₃×#41	—	2	4	no	—
251	C₃×#41	—	4	2	no	—
252	C₂×C₃×Q₈	—	2	1	no	—
253	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
254	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₃×D₄	—	2	2	no	—
256	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
257	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
258	C₂²×C₃×C₄	—	2	2	no	—
259	C₂²×C₃×C₄	—	2	1	no	—
260	C₂²×C₃×C₄	—	2	2	no	—
261	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
262	C₃×Q₁₆	—	4	2	no	—
263	C₃×SD₁₆	—	2	2	no	—
264	C₃×M₁₆	—	4	2	no	—
265	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
267	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
268	C₃×C₄⋊C₄	—	2	1	no	—
269	C₃×C₄⋊C₄	—	2	2	no	—
270	C₃×C₄⋊C₄	—	2	2	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	—	2	1	no	—
273	C₃×C₄⋊C₄	—	2	2	no	—
274	C₃×C₄⋊C₄	—	2	1	no	—
275	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
278	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₂²⋊C₄	—	2	2	no	—
280	C₃×C₂²⋊C₄	—	2	2	no	—
281	C₃×C₂²⋊C₄	—	2	1	no	—
282	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
283	C₃×C₄²	—	2	1	no	—
284	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
285	C₂³×C₅	—	2	1	no	—
286	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
287	C₅×Q₈	—	2	1	no	—
288	C₅×Q₈	—	2	2	no	—
289	C₅×Q₈	—	2	1	no	—
290	C₅×Q₈	—	2	2	no	—
291	C₅×Q₈	—	8	1	no	—
292	C₅×D₄	—	2	2	no	—
293	C₅×D₄	—	2	1	no	—
294	C₅×D₄	—	4	4	no	—
295	C₅×D₄	C₃×#41	1	2	yes	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	—	2	2	no	—
298	C₂×C₄×C₅	—	2	1	no	—
299	C₂×C₄×C₅	—	2	1	no	—
300	C₂×C₄×C₅	—	2	1	no	—
301	C₂×C₄×C₅	—	2	2	no	—
302	C₂×C₄×C₅	—	2	2	no	—
303	C₂×C₄×C₅	—	4	4	no	—
304	C₂×C₄×C₅	—	4	2	no	—
305	C₂×C₄×C₅	—	8	2	no	—
306	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
307	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
308	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
309	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
310	C₅×C₈	—	2	1	no	—
311	C₅×C₈	—	2	1	no	—
312	C₅×C₈	—	2	2	no	—
313	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
314	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
315	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
317	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
318	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
319	#125	—	2	1	no	—
320	#123	—	2	2	no	—
321	C₂²⋊Q₈	—	2	2	no	—
322	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
323	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
324	#121	—	2	1	no	—
325	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
326	C₄×D₄	—	2	1	no	—
327	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
328	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
329	C₂×C₄⋊C₄	—	2	1	no	—
330	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
331	#106	C₂²×C₃×C₅	1	1	yes	characteristic
332	#106	C₂²×C₃×C₅	1	2	yes	—
333	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
334	#103	C₂²×C₃×C₅	1	2	yes	—
335	#103	C₂²×C₃×C₅	1	2	yes	—
336	#103	C₂²×C₃×C₅	1	1	yes	characteristic
337	#103	C₂²×C₃×C₅	1	2	yes	—
338	#102	C₂²×C₃×C₅	1	1	yes	characteristic
339	#102	C₂²×C₃×C₅	1	2	yes	—
340	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
341	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
342	C₂×C₃×C₅	—	4	2	no	—
343	C₂×C₃×C₅	—	4	2	no	—
344	C₂×C₃×C₅	#546	1	1	yes	characteristic
345	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
346	C₂×C₃×C₅	#577	1	1	yes	characteristic
347	C₂³×C₃	—	2	1	no	—
348	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
349	C₃×Q₈	—	2	1	no	—
350	C₃×Q₈	—	2	2	no	—
351	C₃×Q₈	—	2	1	no	—
352	C₃×Q₈	—	2	2	no	—
353	C₃×Q₈	—	8	1	no	—
354	C₃×D₄	—	2	2	no	—
355	C₃×D₄	—	2	1	no	—
356	C₃×D₄	—	4	4	no	—
357	C₃×D₄	C₅×#41	1	2	yes	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	1	no	—
362	C₂×C₃×C₄	—	2	1	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	4	4	no	—
366	C₂×C₃×C₄	—	4	2	no	—
367	C₂×C₃×C₄	—	8	2	no	—
368	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
369	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
370	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
371	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
372	C₃×C₈	—	2	1	no	—
373	C₃×C₈	—	2	1	no	—
374	C₃×C₈	—	2	2	no	—
375	C₂²×C₅	—	2	2	no	—
376	C₂²×C₅	—	2	2	no	—
377	C₂²×C₅	—	2	2	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	4	1	no	—
380	C₂²×C₅	—	4	1	no	—
381	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
382	C₄×C₅	—	2	1	no	—
383	C₄×C₅	—	2	2	no	—
384	C₄×C₅	—	4	1	no	—
385	C₄×C₅	—	4	1	no	—
386	C₄×C₅	—	4	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	C₃×#137	1	2	yes	—
390	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
391	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
392	#41	—	2	4	no	—
393	#41	—	4	2	no	—
394	C₂×Q₈	—	2	1	no	—
395	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
396	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
397	C₂×D₄	—	2	2	no	—
398	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
399	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
400	C₂²×C₄	—	2	2	no	—
401	C₂²×C₄	—	2	1	no	—
402	C₂²×C₄	—	2	2	no	—
403	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
404	Q₁₆	—	4	2	no	—
405	SD₁₆	—	2	2	no	—
406	M₁₆	—	4	2	no	—
407	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
408	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
409	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
410	C₄⋊C₄	—	2	1	no	—
411	C₄⋊C₄	—	2	2	no	—
412	C₄⋊C₄	—	2	2	no	—
413	C₄⋊C₄	—	2	1	no	—
414	C₄⋊C₄	—	2	1	no	—
415	C₄⋊C₄	—	2	2	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
418	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
419	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
420	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
421	C₂²⋊C₄	—	2	2	no	—
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	1	no	—
424	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
425	C₄²	—	2	1	no	—
426	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
427	C₃×C₅	#3331	1	1	yes	characteristic, direct product factor, Hall
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	2	2	no	—
430	C₂²×C₃	—	2	2	no	—
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	4	1	no	—
433	C₂²×C₃	—	4	1	no	—
434	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
435	C₃×C₄	—	2	2	no	—
436	C₃×C₄	—	2	1	no	—
437	C₃×C₄	—	4	2	no	—
438	C₃×C₄	—	4	1	no	—
439	C₃×C₄	—	4	1	no	—
440	C₃×C₄	—	4	1	no	—
441	C₃×C₄	—	4	2	no	—
442	C₃×C₄	C₅×#137	1	2	yes	—
443	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
444	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
445	C₂×C₅	—	4	2	no	—
446	C₂×C₅	—	4	2	no	—
447	C₂×C₅	C₃×#546	1	1	yes	characteristic
448	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
449	C₂×C₅	C₃×#577	1	1	yes	characteristic
450	C₂³	—	2	1	no	—
451	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
452	Q₈	—	2	1	no	—
453	Q₈	—	2	2	no	—
454	Q₈	—	2	1	no	—
455	Q₈	—	2	2	no	—
456	Q₈	—	8	1	no	—
457	D₄	—	2	1	no	—
458	D₄	—	2	2	no	—
459	D₄	—	4	4	no	—
460	D₄	C₃×C₅×#41	1	2	yes	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	2	no	—
463	C₂×C₄	—	2	1	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	1	no	—
466	C₂×C₄	—	2	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	4	4	no	—
469	C₂×C₄	—	4	2	no	—
470	C₂×C₄	—	8	2	no	—
471	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
472	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
473	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
474	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
475	C₈	—	2	1	no	—
476	C₈	—	2	1	no	—
477	C₈	—	2	2	no	—
478	C₂×C₃	—	4	2	no	—
479	C₂×C₃	—	4	2	no	—
480	C₂×C₃	C₅×#546	1	1	yes	characteristic
481	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
482	C₂×C₃	C₅×#577	1	1	yes	characteristic
483	C₅	C₃×#3331	1	1	yes	characteristic, direct product factor, Sylow
484	C₂²	—	2	2	no	—
485	C₂²	—	2	2	no	—
486	C₂²	—	2	2	no	—
487	C₂²	—	2	2	no	—
488	C₂²	—	4	1	no	—
489	C₂²	—	4	1	no	—
490	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
491	C₄	—	2	2	no	—
492	C₄	—	2	1	no	—
493	C₄	—	4	2	no	—
494	C₄	—	4	1	no	—
495	C₄	—	4	1	no	—
496	C₄	—	4	1	no	—
497	C₄	—	4	2	no	—
498	C₄	C₃×C₅×#137	1	2	yes	—
499	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
500	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
501	C₃	C₅×#3331	1	1	yes	characteristic, direct product factor, Sylow
502	C₂	—	4	2	no	—
503	C₂	—	4	2	no	—
504	C₂	C₃×C₅×#546	1	1	yes	characteristic
505	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
506	C₂	C₃×C₅×#577	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×#547	C₂
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. C₃×C₅×#554	C₂	semidirect
3. C₃×C₅×#487	C₂	semidirect
4. C₃×C₅×#483	C₂	semidirect
5. C₃×C₅×#476	C₂	semidirect
6. C₃×C₅×#470	C₂	semidirect
7. C₃×C₅×#462	C₂	semidirect
8. C₃×C₅×#452	C₂	semidirect
9. C₃×C₄×C₅×SD₁₆	C₂	semidirect
10. C₃×C₅×#436	C₂	semidirect
11. C₃×C₅×#417	C₂	semidirect
12. C₅×#3331	C₃	direct (N × H)
42. C₃×#3331	C₅	direct (N × H)
43. C₅×#554	C₂×C₃	semidirect
45. C₅×#487	C₂×C₃	semidirect
46. C₅×#483	C₂×C₃	semidirect
47. C₅×#476	C₂×C₃	semidirect
48. C₅×#470	C₂×C₃	semidirect
49. C₅×#462	C₂×C₃	semidirect
50. C₅×#452	C₂×C₃	semidirect
51. C₄×C₅×SD₁₆	C₂×C₃	semidirect
52. C₅×#436	C₂×C₃	semidirect
53. C₅×#417	C₂×C₃	semidirect
89. C₃×#554	C₂×C₅	semidirect
91. C₃×#487	C₂×C₅	semidirect
92. C₃×#483	C₂×C₅	semidirect
93. C₃×#476	C₂×C₅	semidirect
94. C₃×#470	C₂×C₅	semidirect
95. C₃×#462	C₂×C₅	semidirect
96. C₃×#452	C₂×C₅	semidirect
97. C₃×C₄×SD₁₆	C₂×C₅	semidirect
98. C₃×#436	C₂×C₅	semidirect
99. C₃×#417	C₂×C₅	semidirect
129. #3331	C₃×C₅	direct (N × H)
222. #554	C₂×C₃×C₅	semidirect
224. #487	C₂×C₃×C₅	semidirect
225. #483	C₂×C₃×C₅	semidirect
226. #476	C₂×C₃×C₅	semidirect
227. #470	C₂×C₃×C₅	semidirect
228. #462	C₂×C₃×C₅	semidirect
229. #452	C₂×C₃×C₅	semidirect
230. C₄×SD₁₆	C₂×C₃×C₅	semidirect
231. #436	C₂×C₃×C₅	semidirect
232. #417	C₂×C₃×C₅	semidirect
427. C₃×C₅	#3331	direct (N × H)
483. C₅	C₃×#3331	direct (N × H)
501. C₃	C₅×#3331	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×#554	2
C₃×C₅×#547	2
C₃×C₅×#487	2
C₃×C₅×#483	2
C₃×C₅×#476	2
C₃×C₅×#470	2
C₃×C₅×#462	2
C₃×C₅×#452	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#436	2
C₃×C₅×#417	2
C₅×#3331	3
C₃×#3331	5

Subgroups — C3×C5×#3331 #14276365

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3331 #14276365