Subgroups — C₃×C₅×#3299 #14276333

Order 1920.

776 conjugacy classes of subgroups.

The subgroup lattice has 492 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
2	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#487	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#484	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#477	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#467	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#451	C₂	1	2	yes	maximal, complemented
9	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic
11	C₂×C₃×C₅×#103	C₂	1	2	yes	maximal, complemented
12	C₅×#3299	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₅×#125	—	2	1	no	—
21	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
22	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
25	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×D₄	—	2	1	no	—
28	C₃×C₄×C₅×D₄	—	2	1	no	—
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
31	C₃×C₅×#107	C₂²	1	2	yes	—
32	C₃×C₅×#107	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	2	yes	—
37	C₃×C₅×#103	C₂²	1	1	yes	characteristic
38	C₃×C₅×#103	C₂²	1	2	yes	—
39	C₃×C₅×#103	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×#3299	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#554	C₂×C₃	1	1	yes	characteristic
44	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic
45	C₅×#487	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#484	C₂×C₃	1	2	yes	complemented
47	C₅×#477	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#467	C₂×C₃	1	2	yes	complemented
49	C₅×#462	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#451	C₂×C₃	1	2	yes	complemented
51	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
52	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic
53	C₂×C₅×#103	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	—	2	2	no	—
55	C₂×C₃×C₅×Q₈	—	2	1	no	—
56	C₂×C₃×C₅×Q₈	—	2	4	no	—
57	C₂×C₃×C₅×Q₈	—	4	2	no	—
58	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
61	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	—	2	2	no	—
63	C₂²×C₃×C₄×C₅	—	2	2	no	—
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₃×C₅×Q₁₆	—	2	2	no	—
66	C₃×C₅×Q₁₆	—	4	2	no	—
67	C₂×C₃×C₅×C₈	—	4	2	no	—
68	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
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	—	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	2	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	D₄	1	2	yes	—
86	C₃×C₄²×C₅	—	2	1	no	—
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
90	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic
91	C₃×#487	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#484	C₂×C₅	1	2	yes	complemented
93	C₃×#477	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×#467	C₂×C₅	1	2	yes	complemented
95	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#451	C₂×C₅	1	2	yes	complemented
97	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic
99	C₂×C₃×#103	C₂×C₅	1	2	yes	complemented
100	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
101	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
103	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
104	C₅×C₄⋊Q₈	—	2	1	no	—
105	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
106	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₅×#125	—	2	1	no	—
108	C₅×C₂²⋊Q₈	—	2	2	no	—
109	C₅×C₂²⋊Q₈	—	2	2	no	—
110	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
111	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
112	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
113	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₅×D₄	—	2	1	no	—
115	C₄×C₅×D₄	—	2	1	no	—
116	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
118	C₅×#107	C₂²×C₃	1	1	yes	characteristic
119	C₅×#107	C₂²×C₃	1	2	yes	—
120	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#103	C₂²×C₃	1	1	yes	characteristic
122	C₅×#103	C₂²×C₃	1	2	yes	—
123	C₅×#103	C₂²×C₃	1	2	yes	—
124	C₅×#103	C₂²×C₃	1	2	yes	—
125	C₅×#103	C₂²×C₃	1	1	yes	characteristic
126	C₅×#103	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	#3299	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
131	C₃×C₅×Q₈	—	2	1	no	—
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	—	4	4	no	—
137	C₃×C₅×Q₈	—	8	1	no	—
138	C₃×C₅×Q₈	#41	1	2	yes	—
139	C₃×C₅×D₄	Q₁₆	1	4	yes	complemented
140	C₂×C₃×C₄×C₅	—	2	1	no	—
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	—	8	2	no	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
153	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
154	C₃×C₅×C₈	—	2	1	no	—
155	C₃×C₅×C₈	—	2	1	no	—
156	C₃×C₅×C₈	—	2	2	no	—
157	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
158	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
159	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
160	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
161	C₃×C₄⋊Q₈	—	2	1	no	—
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×C₂²⋊Q₈	—	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×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
170	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
171	C₃×C₄×D₄	—	2	1	no	—
172	C₃×C₄×D₄	—	2	1	no	—
173	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
175	C₃×#107	C₂²×C₅	1	1	yes	characteristic
176	C₃×#107	C₂²×C₅	1	2	yes	—
177	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
178	C₃×#103	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	2	yes	—
182	C₃×#103	C₂²×C₅	1	1	yes	characteristic
183	C₃×#103	C₂²×C₅	1	2	yes	—
184	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
185	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
186	C₂×C₅×Q₈	—	2	2	no	—
187	C₂×C₅×Q₈	—	2	1	no	—
188	C₂×C₅×Q₈	—	2	4	no	—
189	C₂×C₅×Q₈	—	4	2	no	—
190	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
192	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
194	C₂²×C₄×C₅	—	2	2	no	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
197	C₅×Q₁₆	—	2	2	no	—
198	C₅×Q₁₆	—	4	2	no	—
199	C₂×C₅×C₈	—	4	2	no	—
200	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
201	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
202	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
203	C₅×C₄⋊C₄	—	2	2	no	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	—	2	1	no	—
207	C₅×C₄⋊C₄	—	2	1	no	—
208	C₅×C₄⋊C₄	—	2	1	no	—
209	C₅×C₄⋊C₄	—	2	2	no	—
210	C₅×C₄⋊C₄	—	2	2	no	—
211	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
212	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
213	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
214	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
215	C₅×C₂²⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	2	no	—
217	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
218	C₄²×C₅	—	2	1	no	—
219	C₄²×C₅	—	2	1	no	—
220	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
221	#554	C₂×C₃×C₅	1	1	yes	characteristic
222	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
223	#487	C₂×C₃×C₅	1	1	yes	characteristic, complemented
224	#484	C₂×C₃×C₅	1	2	yes	complemented
225	#477	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#467	C₂×C₃×C₅	1	2	yes	complemented
227	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#451	C₂×C₃×C₅	1	2	yes	complemented
229	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic
231	C₂×#103	C₂×C₃×C₅	1	2	yes	complemented
232	C₂²×C₃×C₅	—	2	2	no	—
233	C₂²×C₃×C₅	—	2	2	no	—
234	C₂²×C₃×C₅	C₂×Q₁₆	1	4	yes	—
235	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
236	C₃×C₄×C₅	—	2	2	no	—
237	C₃×C₄×C₅	—	2	2	no	—
238	C₃×C₄×C₅	—	2	1	no	—
239	C₃×C₄×C₅	—	4	2	no	—
240	C₃×C₄×C₅	—	4	1	no	—
241	C₃×C₄×C₅	—	4	1	no	—
242	C₃×C₄×C₅	—	4	1	no	—
243	C₃×C₄×C₅	—	4	2	no	—
244	C₃×C₄×C₅	C₂×Q₁₆	1	2	yes	—
245	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
246	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
247	C₂×C₃×Q₈	—	2	2	no	—
248	C₂×C₃×Q₈	—	2	1	no	—
249	C₂×C₃×Q₈	—	2	4	no	—
250	C₂×C₃×Q₈	—	4	2	no	—
251	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
252	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
253	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
254	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
255	C₂²×C₃×C₄	—	2	2	no	—
256	C₂²×C₃×C₄	—	2	2	no	—
257	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
258	C₃×Q₁₆	—	2	2	no	—
259	C₃×Q₁₆	—	4	2	no	—
260	C₂×C₃×C₈	—	4	2	no	—
261	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
263	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
264	C₃×C₄⋊C₄	—	2	2	no	—
265	C₃×C₄⋊C₄	—	2	1	no	—
266	C₃×C₄⋊C₄	—	2	1	no	—
267	C₃×C₄⋊C₄	—	2	1	no	—
268	C₃×C₄⋊C₄	—	2	1	no	—
269	C₃×C₄⋊C₄	—	2	1	no	—
270	C₃×C₄⋊C₄	—	2	2	no	—
271	C₃×C₄⋊C₄	—	2	2	no	—
272	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
273	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
274	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
275	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
276	C₃×C₂²⋊C₄	—	2	2	no	—
277	C₃×C₂²⋊C₄	—	2	2	no	—
278	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
279	C₃×C₄²	—	2	1	no	—
280	C₃×C₄²	—	2	1	no	—
281	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
282	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
283	C₅×Q₈	—	2	1	no	—
284	C₅×Q₈	—	2	1	no	—
285	C₅×Q₈	—	2	2	no	—
286	C₅×Q₈	—	2	1	no	—
287	C₅×Q₈	—	2	2	no	—
288	C₅×Q₈	—	4	4	no	—
289	C₅×Q₈	—	8	1	no	—
290	C₅×Q₈	C₃×#41	1	2	yes	—
291	C₅×D₄	C₃×Q₁₆	1	4	yes	complemented
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	2	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	—	2	1	no	—
298	C₂×C₄×C₅	—	2	2	no	—
299	C₂×C₄×C₅	—	2	2	no	—
300	C₂×C₄×C₅	—	4	4	no	—
301	C₂×C₄×C₅	—	8	2	no	—
302	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
303	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
304	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
306	C₅×C₈	—	2	1	no	—
307	C₅×C₈	—	2	1	no	—
308	C₅×C₈	—	2	2	no	—
309	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
310	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
311	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
312	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
313	C₄⋊Q₈	—	2	1	no	—
314	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
315	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
316	#125	—	2	1	no	—
317	C₂²⋊Q₈	—	2	2	no	—
318	C₂²⋊Q₈	—	2	2	no	—
319	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
320	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
321	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
322	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
323	C₄×D₄	—	2	1	no	—
324	C₄×D₄	—	2	1	no	—
325	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
326	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
327	#107	C₂²×C₃×C₅	1	1	yes	characteristic
328	#107	C₂²×C₃×C₅	1	2	yes	—
329	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
330	#103	C₂²×C₃×C₅	1	1	yes	characteristic
331	#103	C₂²×C₃×C₅	1	2	yes	—
332	#103	C₂²×C₃×C₅	1	2	yes	—
333	#103	C₂²×C₃×C₅	1	2	yes	—
334	#103	C₂²×C₃×C₅	1	1	yes	characteristic
335	#103	C₂²×C₃×C₅	1	2	yes	—
336	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
337	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
338	C₂×C₃×C₅	—	2	4	no	—
339	C₂×C₃×C₅	#546	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂²×Q₁₆	1	1	yes	characteristic
341	C₂×C₃×C₅	#577	1	1	yes	characteristic
342	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
343	C₃×Q₈	—	2	1	no	—
344	C₃×Q₈	—	2	1	no	—
345	C₃×Q₈	—	2	2	no	—
346	C₃×Q₈	—	2	1	no	—
347	C₃×Q₈	—	2	2	no	—
348	C₃×Q₈	—	4	4	no	—
349	C₃×Q₈	—	8	1	no	—
350	C₃×Q₈	C₅×#41	1	2	yes	—
351	C₃×D₄	C₅×Q₁₆	1	4	yes	complemented
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	2	no	—
355	C₂×C₃×C₄	—	2	1	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	1	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	4	4	no	—
361	C₂×C₃×C₄	—	8	2	no	—
362	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
363	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
365	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
366	C₃×C₈	—	2	1	no	—
367	C₃×C₈	—	2	1	no	—
368	C₃×C₈	—	2	2	no	—
369	C₂²×C₅	—	2	2	no	—
370	C₂²×C₅	—	2	2	no	—
371	C₂²×C₅	C₂×C₃×Q₁₆	1	4	yes	—
372	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
373	C₄×C₅	—	2	1	no	—
374	C₄×C₅	—	2	2	no	—
375	C₄×C₅	—	2	2	no	—
376	C₄×C₅	—	4	1	no	—
377	C₄×C₅	—	4	1	no	—
378	C₄×C₅	—	4	2	no	—
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	C₂×C₃×Q₁₆	1	2	yes	—
382	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
383	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
384	C₂×Q₈	—	2	2	no	—
385	C₂×Q₈	—	2	1	no	—
386	C₂×Q₈	—	2	4	no	—
387	C₂×Q₈	—	4	2	no	—
388	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
389	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
390	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
391	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
392	C₂²×C₄	—	2	2	no	—
393	C₂²×C₄	—	2	2	no	—
394	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
395	Q₁₆	—	2	2	no	—
396	Q₁₆	—	4	2	no	—
397	C₂×C₈	—	4	2	no	—
398	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
399	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
400	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
401	C₄⋊C₄	—	2	2	no	—
402	C₄⋊C₄	—	2	1	no	—
403	C₄⋊C₄	—	2	1	no	—
404	C₄⋊C₄	—	2	1	no	—
405	C₄⋊C₄	—	2	1	no	—
406	C₄⋊C₄	—	2	1	no	—
407	C₄⋊C₄	—	2	2	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
410	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
411	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
412	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
413	C₂²⋊C₄	—	2	2	no	—
414	C₂²⋊C₄	—	2	2	no	—
415	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
416	C₄²	—	2	1	no	—
417	C₄²	—	2	1	no	—
418	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
419	C₃×C₅	#3299	1	1	yes	characteristic, direct product factor, Hall
420	C₂²×C₃	—	2	2	no	—
421	C₂²×C₃	—	2	2	no	—
422	C₂²×C₃	C₂×C₅×Q₁₆	1	4	yes	—
423	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
424	C₃×C₄	—	2	2	no	—
425	C₃×C₄	—	2	2	no	—
426	C₃×C₄	—	2	1	no	—
427	C₃×C₄	—	4	2	no	—
428	C₃×C₄	—	4	1	no	—
429	C₃×C₄	—	4	1	no	—
430	C₃×C₄	—	4	1	no	—
431	C₃×C₄	—	4	2	no	—
432	C₃×C₄	C₂×C₅×Q₁₆	1	2	yes	—
433	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
434	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
435	C₂×C₅	—	2	4	no	—
436	C₂×C₅	C₃×#546	1	1	yes	characteristic
437	C₂×C₅	C₂²×C₃×Q₁₆	1	1	yes	characteristic
438	C₂×C₅	C₃×#577	1	1	yes	characteristic
439	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
440	Q₈	—	2	1	no	—
441	Q₈	—	2	1	no	—
442	Q₈	—	2	2	no	—
443	Q₈	—	2	1	no	—
444	Q₈	—	2	2	no	—
445	Q₈	—	4	4	no	—
446	Q₈	—	8	1	no	—
447	Q₈	C₃×C₅×#41	1	2	yes	—
448	D₄	C₃×C₅×Q₁₆	1	4	yes	complemented
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	2	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	1	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	4	4	no	—
458	C₂×C₄	—	8	2	no	—
459	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
460	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
461	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
462	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
463	C₈	—	2	1	no	—
464	C₈	—	2	1	no	—
465	C₈	—	2	2	no	—
466	C₂×C₃	—	2	4	no	—
467	C₂×C₃	C₅×#546	1	1	yes	characteristic
468	C₂×C₃	C₂²×C₅×Q₁₆	1	1	yes	characteristic
469	C₂×C₃	C₅×#577	1	1	yes	characteristic
470	C₅	C₃×#3299	1	1	yes	characteristic, direct product factor, Sylow
471	C₂²	—	2	2	no	—
472	C₂²	—	2	2	no	—
473	C₂²	C₂×C₃×C₅×Q₁₆	1	4	yes	—
474	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
475	C₄	—	2	2	no	—
476	C₄	—	2	2	no	—
477	C₄	—	2	1	no	—
478	C₄	—	4	2	no	—
479	C₄	—	4	1	no	—
480	C₄	—	4	1	no	—
481	C₄	—	4	2	no	—
482	C₄	—	4	1	no	—
483	C₄	C₂×C₃×C₅×Q₁₆	1	2	yes	—
484	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
485	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
486	C₃	C₅×#3299	1	1	yes	characteristic, direct product factor, Sylow
487	C₂	—	2	4	no	—
488	C₂	C₃×C₅×#546	1	1	yes	characteristic
489	C₂	C₂²×C₃×C₅×Q₁₆	1	1	yes	characteristic
490	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	C₂×C₃×C₅×D₄	D₄
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
3. C₃×C₅×#487	C₂	semidirect
4. C₃×C₅×#484	C₂	semidirect
5. C₃×C₅×#477	C₂	semidirect
6. C₃×C₅×#467	C₂	semidirect
7. C₃×C₅×#462	C₂	semidirect
8. C₃×C₅×#451	C₂	semidirect
9. C₃×C₄×C₅×Q₁₆	C₂	semidirect
11. C₂×C₃×C₅×#103	C₂	semidirect
12. C₅×#3299	C₃	direct (N × H)
42. C₃×#3299	C₅	direct (N × H)
45. C₅×#487	C₂×C₃	semidirect
46. C₅×#484	C₂×C₃	semidirect
47. C₅×#477	C₂×C₃	semidirect
48. C₅×#467	C₂×C₃	semidirect
49. C₅×#462	C₂×C₃	semidirect
50. C₅×#451	C₂×C₃	semidirect
51. C₄×C₅×Q₁₆	C₂×C₃	semidirect
53. C₂×C₅×#103	C₂×C₃	semidirect
91. C₃×#487	C₂×C₅	semidirect
92. C₃×#484	C₂×C₅	semidirect
93. C₃×#477	C₂×C₅	semidirect
94. C₃×#467	C₂×C₅	semidirect
95. C₃×#462	C₂×C₅	semidirect
96. C₃×#451	C₂×C₅	semidirect
97. C₃×C₄×Q₁₆	C₂×C₅	semidirect
99. C₂×C₃×#103	C₂×C₅	semidirect
129. #3299	C₃×C₅	direct (N × H)
139. C₃×C₅×D₄	Q₁₆	semidirect
223. #487	C₂×C₃×C₅	semidirect
224. #484	C₂×C₃×C₅	semidirect
225. #477	C₂×C₃×C₅	semidirect
226. #467	C₂×C₃×C₅	semidirect
227. #462	C₂×C₃×C₅	semidirect
228. #451	C₂×C₃×C₅	semidirect
229. C₄×Q₁₆	C₂×C₃×C₅	semidirect
231. C₂×#103	C₂×C₃×C₅	semidirect
291. C₅×D₄	C₃×Q₁₆	semidirect
351. C₃×D₄	C₅×Q₁₆	semidirect
419. C₃×C₅	#3299	direct (N × H)
448. D₄	C₃×C₅×Q₁₆	semidirect
470. C₅	C₃×#3299	direct (N × H)
486. C₃	C₅×#3299	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×D₄×Q₈	2
C₃×C₅×#487	2
C₃×C₅×#484	2
C₃×C₅×#477	2
C₃×C₅×#467	2
C₃×C₅×#462	2
C₃×C₅×#451	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×C₈×D₄	2
C₂×C₃×C₅×#103	2
C₅×#3299	3
C₃×#3299	5

Subgroups — C3×C5×#3299 #14276333

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3299 #14276333