Subgroups — C₃×C₅×#3276 #14276310

Order 1920.

944 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×D₄×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#547	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#494	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#470	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#462	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#461	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#451	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×#436	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3276	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
15	C₃×C₅×#137	—	2	8	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
19	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
20	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
22	C₃×C₅×C₄⋊Q₈	—	2	1	no	—
23	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
24	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#123	—	2	2	no	—
26	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
27	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₃×C₅×#121	—	2	1	no	—
30	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
31	C₃×C₄×C₅×D₄	—	2	1	no	—
32	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₂×C₃×C₅×C₄⋊C₄	—	2	1	no	—
35	C₃×C₅×#106	C₂²	1	1	yes	characteristic
36	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
37	C₃×C₅×#103	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	1	yes	characteristic
41	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
42	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
43	C₃×#3276	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
44	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
45	C₅×D₄×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#547	C₂×C₃	1	1	yes	characteristic
47	C₅×#494	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×#461	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	C₄×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
54	C₅×#436	C₂×C₃	1	1	yes	characteristic, complemented
55	C₃×C₅×#41	—	2	4	no	—
56	C₃×C₅×#41	—	4	2	no	—
57	C₂×C₃×C₅×Q₈	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	—	2	4	no	—
59	C₂×C₃×C₅×Q₈	—	4	2	no	—
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	—	2	1	no	—
68	C₂²×C₃×C₄×C₅	—	2	2	no	—
69	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
70	C₃×C₅×Q₁₆	—	2	4	no	—
71	C₃×C₅×Q₁₆	—	2	4	no	—
72	C₃×C₅×Q₁₆	—	4	2	no	—
73	C₃×C₅×SD₁₆	—	2	4	no	—
74	C₃×C₅×SD₁₆	D₄	1	4	yes	complemented
75	C₃×C₅×M₁₆	—	2	4	no	—
76	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
77	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	—	2	1	no	—
80	C₃×C₅×C₄⋊C₄	—	2	2	no	—
81	C₃×C₅×C₄⋊C₄	—	2	1	no	—
82	C₃×C₅×C₄⋊C₄	—	2	1	no	—
83	C₃×C₅×C₄⋊C₄	—	2	1	no	—
84	C₃×C₅×C₄⋊C₄	—	2	2	no	—
85	C₃×C₅×C₄⋊C₄	—	2	1	no	—
86	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
87	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
88	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
89	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
91	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
92	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
93	C₃×C₄²×C₅	—	2	1	no	—
94	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
95	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
96	C₃×D₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#547	C₂×C₅	1	1	yes	characteristic
98	C₃×#494	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#470	C₂×C₅	1	2	yes	complemented
100	C₃×#462	C₂×C₅	1	1	yes	characteristic, complemented
101	C₃×#461	C₂×C₅	1	1	yes	characteristic, complemented
102	C₃×#452	C₂×C₅	1	2	yes	complemented
103	C₃×#451	C₂×C₅	1	2	yes	complemented
104	C₃×C₄×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#436	C₂×C₅	1	1	yes	characteristic, complemented
106	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
107	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
108	C₅×#137	—	2	8	no	—
109	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
110	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
111	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
112	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
113	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic
114	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
115	C₅×C₄⋊Q₈	—	2	1	no	—
116	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
117	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
118	C₅×#123	—	2	2	no	—
119	C₅×C₂²⋊Q₈	—	2	2	no	—
120	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
121	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
122	C₅×#121	—	2	1	no	—
123	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
124	C₄×C₅×D₄	—	2	1	no	—
125	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
126	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
127	C₂×C₅×C₄⋊C₄	—	2	1	no	—
128	C₅×#106	C₂²×C₃	1	1	yes	characteristic
129	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
130	C₅×#103	C₂²×C₃	1	1	yes	characteristic
131	C₅×#103	C₂²×C₃	1	2	yes	—
132	C₅×#103	C₂²×C₃	1	2	yes	—
133	C₅×#102	C₂²×C₃	1	1	yes	characteristic
134	C₅×C₂²⋊C₈	C₂²×C₃	1	2	yes	—
135	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
136	#3276	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
139	C₃×C₅×Q₈	—	2	1	no	—
140	C₃×C₅×Q₈	—	2	2	no	—
141	C₃×C₅×Q₈	—	2	2	no	—
142	C₃×C₅×Q₈	—	2	2	no	—
143	C₃×C₅×Q₈	—	2	2	no	—
144	C₃×C₅×Q₈	—	4	4	no	—
145	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
146	C₃×C₅×D₄	—	2	2	no	—
147	C₃×C₅×D₄	—	2	1	no	—
148	C₃×C₅×D₄	—	4	4	no	—
149	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	2	1	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	2	no	—
157	C₂×C₃×C₄×C₅	—	4	4	no	—
158	C₂×C₃×C₄×C₅	—	4	4	no	—
159	C₂×C₃×C₄×C₅	—	4	2	no	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₃×C₅×C₈	—	2	2	no	—
165	C₃×C₅×C₈	—	2	1	no	—
166	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
167	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
168	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
169	C₃×#137	—	2	8	no	—
170	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
171	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
172	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
173	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
174	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
176	C₃×C₄⋊Q₈	—	2	1	no	—
177	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
178	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
179	C₃×#123	—	2	2	no	—
180	C₃×C₂²⋊Q₈	—	2	2	no	—
181	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
182	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
183	C₃×#121	—	2	1	no	—
184	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
185	C₃×C₄×D₄	—	2	1	no	—
186	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
187	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
188	C₂×C₃×C₄⋊C₄	—	2	1	no	—
189	C₃×#106	C₂²×C₅	1	1	yes	characteristic
190	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
191	C₃×#103	C₂²×C₅	1	1	yes	characteristic
192	C₃×#103	C₂²×C₅	1	2	yes	—
193	C₃×#103	C₂²×C₅	1	2	yes	—
194	C₃×#102	C₂²×C₅	1	1	yes	characteristic
195	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
196	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
197	C₅×#41	—	2	4	no	—
198	C₅×#41	—	4	2	no	—
199	C₂×C₅×Q₈	—	2	2	no	—
200	C₂×C₅×Q₈	—	2	4	no	—
201	C₂×C₅×Q₈	—	4	2	no	—
202	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
203	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
204	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₅×D₄	—	2	2	no	—
206	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
207	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	—	2	2	no	—
209	C₂²×C₄×C₅	—	2	1	no	—
210	C₂²×C₄×C₅	—	2	2	no	—
211	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
212	C₅×Q₁₆	—	2	4	no	—
213	C₅×Q₁₆	—	2	4	no	—
214	C₅×Q₁₆	—	4	2	no	—
215	C₅×SD₁₆	—	2	4	no	—
216	C₅×SD₁₆	C₃×D₄	1	4	yes	complemented
217	C₅×M₁₆	—	2	4	no	—
218	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
219	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
220	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
221	C₅×C₄⋊C₄	—	2	1	no	—
222	C₅×C₄⋊C₄	—	2	2	no	—
223	C₅×C₄⋊C₄	—	2	1	no	—
224	C₅×C₄⋊C₄	—	2	1	no	—
225	C₅×C₄⋊C₄	—	2	1	no	—
226	C₅×C₄⋊C₄	—	2	2	no	—
227	C₅×C₄⋊C₄	—	2	1	no	—
228	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
229	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
230	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
231	C₅×C₂²⋊C₄	—	2	2	no	—
232	C₅×C₂²⋊C₄	—	2	2	no	—
233	C₅×C₂²⋊C₄	—	2	1	no	—
234	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
235	C₄²×C₅	—	2	1	no	—
236	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
237	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
238	D₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
239	#547	C₂×C₃×C₅	1	1	yes	characteristic
240	#494	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	#470	C₂×C₃×C₅	1	2	yes	complemented
242	#462	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	#461	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	#452	C₂×C₃×C₅	1	2	yes	complemented
245	#451	C₂×C₃×C₅	1	2	yes	complemented
246	C₄×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
247	#436	C₂×C₃×C₅	1	1	yes	characteristic, complemented
248	C₂²×C₃×C₅	—	2	2	no	—
249	C₂²×C₃×C₅	—	2	2	no	—
250	C₂²×C₃×C₅	—	2	2	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	4	1	no	—
253	C₂²×C₃×C₅	—	4	1	no	—
254	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	1	no	—
258	C₃×C₄×C₅	—	4	2	no	—
259	C₃×C₄×C₅	—	4	2	no	—
260	C₃×C₄×C₅	—	4	1	no	—
261	C₃×C₄×C₅	—	4	1	no	—
262	C₃×C₄×C₅	#137	1	2	yes	complemented
263	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
264	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
265	C₃×#41	—	2	4	no	—
266	C₃×#41	—	4	2	no	—
267	C₂×C₃×Q₈	—	2	2	no	—
268	C₂×C₃×Q₈	—	2	4	no	—
269	C₂×C₃×Q₈	—	4	2	no	—
270	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
271	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
272	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
273	C₂×C₃×D₄	—	2	2	no	—
274	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
275	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	2	1	no	—
278	C₂²×C₃×C₄	—	2	2	no	—
279	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
280	C₃×Q₁₆	—	2	4	no	—
281	C₃×Q₁₆	—	2	4	no	—
282	C₃×Q₁₆	—	4	2	no	—
283	C₃×SD₁₆	—	2	4	no	—
284	C₃×SD₁₆	C₅×D₄	1	4	yes	complemented
285	C₃×M₁₆	—	2	4	no	—
286	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
288	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
289	C₃×C₄⋊C₄	—	2	1	no	—
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	2	1	no	—
292	C₃×C₄⋊C₄	—	2	1	no	—
293	C₃×C₄⋊C₄	—	2	1	no	—
294	C₃×C₄⋊C₄	—	2	2	no	—
295	C₃×C₄⋊C₄	—	2	1	no	—
296	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
297	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
298	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
299	C₃×C₂²⋊C₄	—	2	2	no	—
300	C₃×C₂²⋊C₄	—	2	2	no	—
301	C₃×C₂²⋊C₄	—	2	1	no	—
302	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
303	C₃×C₄²	—	2	1	no	—
304	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
305	C₂³×C₅	—	2	1	no	—
306	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
307	C₅×Q₈	—	2	1	no	—
308	C₅×Q₈	—	2	2	no	—
309	C₅×Q₈	—	2	2	no	—
310	C₅×Q₈	—	2	2	no	—
311	C₅×Q₈	—	2	2	no	—
312	C₅×Q₈	—	4	4	no	—
313	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
314	C₅×D₄	—	2	2	no	—
315	C₅×D₄	—	2	1	no	—
316	C₅×D₄	—	4	4	no	—
317	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	1	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	4	4	no	—
326	C₂×C₄×C₅	—	4	4	no	—
327	C₂×C₄×C₅	—	4	2	no	—
328	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
329	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
330	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
331	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
332	C₅×C₈	—	2	2	no	—
333	C₅×C₈	—	2	1	no	—
334	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
335	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
336	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
337	#137	—	2	8	no	—
338	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
339	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
340	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
341	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
342	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
344	C₄⋊Q₈	—	2	1	no	—
345	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
346	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
347	#123	—	2	2	no	—
348	C₂²⋊Q₈	—	2	2	no	—
349	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
350	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
351	#121	—	2	1	no	—
352	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
353	C₄×D₄	—	2	1	no	—
354	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
356	C₂×C₄⋊C₄	—	2	1	no	—
357	#106	C₂²×C₃×C₅	1	1	yes	characteristic
358	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
359	#103	C₂²×C₃×C₅	1	1	yes	characteristic
360	#103	C₂²×C₃×C₅	1	2	yes	—
361	#103	C₂²×C₃×C₅	1	2	yes	—
362	#102	C₂²×C₃×C₅	1	1	yes	characteristic
363	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
364	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
365	C₂×C₃×C₅	—	4	2	no	—
366	C₂×C₃×C₅	—	4	2	no	—
367	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
368	C₂×C₃×C₅	C₂×#137	1	1	yes	characteristic
369	C₂×C₃×C₅	#578	1	1	yes	characteristic
370	C₂³×C₃	—	2	1	no	—
371	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
372	C₃×Q₈	—	2	1	no	—
373	C₃×Q₈	—	2	2	no	—
374	C₃×Q₈	—	2	2	no	—
375	C₃×Q₈	—	2	2	no	—
376	C₃×Q₈	—	2	2	no	—
377	C₃×Q₈	—	4	4	no	—
378	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
379	C₃×D₄	—	2	2	no	—
380	C₃×D₄	—	2	1	no	—
381	C₃×D₄	—	4	4	no	—
382	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	2	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	2	no	—
390	C₂×C₃×C₄	—	4	4	no	—
391	C₂×C₃×C₄	—	4	4	no	—
392	C₂×C₃×C₄	—	4	2	no	—
393	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
395	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
396	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
397	C₃×C₈	—	2	2	no	—
398	C₃×C₈	—	2	1	no	—
399	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
400	C₂²×C₅	—	2	2	no	—
401	C₂²×C₅	—	2	2	no	—
402	C₂²×C₅	—	2	2	no	—
403	C₂²×C₅	—	2	2	no	—
404	C₂²×C₅	—	4	1	no	—
405	C₂²×C₅	—	4	1	no	—
406	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
407	C₄×C₅	—	2	1	no	—
408	C₄×C₅	—	2	2	no	—
409	C₄×C₅	—	2	2	no	—
410	C₄×C₅	—	4	1	no	—
411	C₄×C₅	—	4	1	no	—
412	C₄×C₅	—	4	2	no	—
413	C₄×C₅	—	4	2	no	—
414	C₄×C₅	C₃×#137	1	2	yes	complemented
415	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
416	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
417	#41	—	2	4	no	—
418	#41	—	4	2	no	—
419	C₂×Q₈	—	2	2	no	—
420	C₂×Q₈	—	2	4	no	—
421	C₂×Q₈	—	4	2	no	—
422	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
423	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
424	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
427	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
428	C₂²×C₄	—	2	2	no	—
429	C₂²×C₄	—	2	1	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
432	Q₁₆	—	2	4	no	—
433	Q₁₆	—	2	4	no	—
434	Q₁₆	—	4	2	no	—
435	SD₁₆	—	2	4	no	—
436	SD₁₆	C₃×C₅×D₄	1	4	yes	complemented
437	M₁₆	—	2	4	no	—
438	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
439	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
440	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
441	C₄⋊C₄	—	2	1	no	—
442	C₄⋊C₄	—	2	2	no	—
443	C₄⋊C₄	—	2	1	no	—
444	C₄⋊C₄	—	2	1	no	—
445	C₄⋊C₄	—	2	1	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	—	2	1	no	—
448	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
449	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
450	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	—	2	1	no	—
454	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
455	C₄²	—	2	1	no	—
456	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
457	C₃×C₅	#3276	1	1	yes	characteristic, direct product factor, Hall
458	C₂²×C₃	—	2	2	no	—
459	C₂²×C₃	—	2	2	no	—
460	C₂²×C₃	—	2	2	no	—
461	C₂²×C₃	—	2	2	no	—
462	C₂²×C₃	—	4	1	no	—
463	C₂²×C₃	—	4	1	no	—
464	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
465	C₃×C₄	—	2	2	no	—
466	C₃×C₄	—	2	2	no	—
467	C₃×C₄	—	2	1	no	—
468	C₃×C₄	—	4	2	no	—
469	C₃×C₄	—	4	2	no	—
470	C₃×C₄	—	4	1	no	—
471	C₃×C₄	—	4	1	no	—
472	C₃×C₄	C₅×#137	1	2	yes	complemented
473	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
474	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
475	C₂×C₅	—	4	2	no	—
476	C₂×C₅	—	4	2	no	—
477	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
478	C₂×C₅	C₂×C₃×#137	1	1	yes	characteristic
479	C₂×C₅	C₃×#578	1	1	yes	characteristic
480	C₂³	—	2	1	no	—
481	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
482	Q₈	—	2	1	no	—
483	Q₈	—	2	2	no	—
484	Q₈	—	2	2	no	—
485	Q₈	—	2	2	no	—
486	Q₈	—	2	2	no	—
487	Q₈	—	4	4	no	—
488	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
489	D₄	—	2	1	no	—
490	D₄	—	2	2	no	—
491	D₄	—	4	4	no	—
492	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
493	C₂×C₄	—	2	1	no	—
494	C₂×C₄	—	2	2	no	—
495	C₂×C₄	—	2	2	no	—
496	C₂×C₄	—	2	1	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	2	no	—
499	C₂×C₄	—	2	2	no	—
500	C₂×C₄	—	4	4	no	—
501	C₂×C₄	—	4	4	no	—
502	C₂×C₄	—	4	2	no	—
503	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
504	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
505	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
507	C₈	—	2	2	no	—
508	C₈	—	2	1	no	—
509	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
510	C₂×C₃	—	4	2	no	—
511	C₂×C₃	—	4	2	no	—
512	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
513	C₂×C₃	C₂×C₅×#137	1	1	yes	characteristic
514	C₂×C₃	C₅×#578	1	1	yes	characteristic
515	C₅	C₃×#3276	1	1	yes	characteristic, direct product factor, Sylow
516	C₂²	—	2	2	no	—
517	C₂²	—	2	2	no	—
518	C₂²	—	2	2	no	—
519	C₂²	—	2	2	no	—
520	C₂²	—	4	1	no	—
521	C₂²	—	4	1	no	—
522	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
523	C₄	—	2	2	no	—
524	C₄	—	2	2	no	—
525	C₄	—	2	1	no	—
526	C₄	—	4	2	no	—
527	C₄	—	4	2	no	—
528	C₄	—	4	1	no	—
529	C₄	—	4	1	no	—
530	C₄	C₃×C₅×#137	1	2	yes	complemented
531	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
532	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
533	C₃	C₅×#3276	1	1	yes	characteristic, direct product factor, Sylow
534	C₂	—	4	2	no	—
535	C₂	—	4	2	no	—
536	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
537	C₂	C₂×C₃×C₅×#137	1	1	yes	characteristic
538	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
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. C₂×C₃×C₅×#137	C₂	semidirect
2. C₃×C₅×D₄×Q₈	C₂	semidirect
4. C₃×C₅×#494	C₂	semidirect
5. C₃×C₅×#470	C₂	semidirect
6. C₃×C₅×#462	C₂	semidirect
7. C₃×C₅×#461	C₂	semidirect
8. C₃×C₅×#452	C₂	semidirect
9. C₃×C₅×#451	C₂	semidirect
10. C₃×C₄×C₅×SD₁₆	C₂	semidirect
11. C₃×C₅×#436	C₂	semidirect
12. C₅×#3276	C₃	direct (N × H)
43. C₃×#3276	C₅	direct (N × H)
44. C₂×C₅×#137	C₂×C₃	semidirect
45. C₅×D₄×Q₈	C₂×C₃	semidirect
47. C₅×#494	C₂×C₃	semidirect
48. C₅×#470	C₂×C₃	semidirect
49. C₅×#462	C₂×C₃	semidirect
50. C₅×#461	C₂×C₃	semidirect
51. C₅×#452	C₂×C₃	semidirect
52. C₅×#451	C₂×C₃	semidirect
53. C₄×C₅×SD₁₆	C₂×C₃	semidirect
54. C₅×#436	C₂×C₃	semidirect
74. C₃×C₅×SD₁₆	D₄	semidirect
95. C₂×C₃×#137	C₂×C₅	semidirect
96. C₃×D₄×Q₈	C₂×C₅	semidirect
98. C₃×#494	C₂×C₅	semidirect
99. C₃×#470	C₂×C₅	semidirect
100. C₃×#462	C₂×C₅	semidirect
101. C₃×#461	C₂×C₅	semidirect
102. C₃×#452	C₂×C₅	semidirect
103. C₃×#451	C₂×C₅	semidirect
104. C₃×C₄×SD₁₆	C₂×C₅	semidirect
105. C₃×#436	C₂×C₅	semidirect
136. #3276	C₃×C₅	direct (N × H)
216. C₅×SD₁₆	C₃×D₄	semidirect
237. C₂×#137	C₂×C₃×C₅	semidirect
238. D₄×Q₈	C₂×C₃×C₅	semidirect
240. #494	C₂×C₃×C₅	semidirect
241. #470	C₂×C₃×C₅	semidirect
242. #462	C₂×C₃×C₅	semidirect
243. #461	C₂×C₃×C₅	semidirect
244. #452	C₂×C₃×C₅	semidirect
245. #451	C₂×C₃×C₅	semidirect
246. C₄×SD₁₆	C₂×C₃×C₅	semidirect
247. #436	C₂×C₃×C₅	semidirect
262. C₃×C₄×C₅	#137	semidirect
284. C₃×SD₁₆	C₅×D₄	semidirect
414. C₄×C₅	C₃×#137	semidirect
436. SD₁₆	C₃×C₅×D₄	semidirect
457. C₃×C₅	#3276	direct (N × H)
472. C₃×C₄	C₅×#137	semidirect
515. C₅	C₃×#3276	direct (N × H)
530. C₄	C₃×C₅×#137	semidirect
533. C₃	C₅×#3276	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×#137	2
C₃×C₅×D₄×Q₈	2
C₃×C₅×#547	2
C₃×C₅×#494	2
C₃×C₅×#470	2
C₃×C₅×#462	2
C₃×C₅×#461	2
C₃×C₅×#452	2
C₃×C₅×#451	2
C₃×C₄×C₅×SD₁₆	2
C₃×C₅×#436	2
C₅×#3276	3
C₃×#3276	5

Subgroups — C3×C5×#3276 #14276310

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3276 #14276310