Subgroups — C₃×C₅×#3285 #14276319

Order 1920.

964 conjugacy classes of subgroups.

The subgroup lattice has 548 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#548	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#495	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#467	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#466	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#464	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#452	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#448	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×C₅×C₈×D₄	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3285	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×#135	—	2	4	no	—
16	C₂×C₃×C₅×Q₁₆	—	2	4	no	—
17	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
18	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
21	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
22	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic
23	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#124	—	2	2	no	—
26	C₃×C₅×#124	C₂²	1	2	yes	—
27	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
28	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
29	C₃×C₅×#121	—	2	2	no	—
30	C₃×C₅×#121	C₂²	1	2	yes	—
31	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
32	C₃×C₄×C₅×D₄	—	2	2	no	—
33	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
34	C₃×C₅×#107	C₂²	1	1	yes	characteristic
35	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
36	C₃×C₅×#103	C₂²	1	2	yes	—
37	C₃×C₅×#103	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
40	C₃×C₅×C₂²⋊C₈	C₂²	1	1	yes	characteristic
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×#3285	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
44	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#548	C₂×C₃	1	2	yes	complemented
46	C₅×#495	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#467	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#466	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#464	C₂×C₃	1	2	yes	complemented
50	C₅×#452	C₂×C₃	1	2	yes	complemented
51	C₅×#448	C₂×C₃	1	2	yes	complemented
52	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
53	C₅×C₈×D₄	C₂×C₃	1	1	yes	characteristic, complemented
54	C₃×C₅×#41	—	2	4	no	—
55	C₃×C₅×#41	—	4	2	no	—
56	C₂×C₃×C₅×Q₈	—	2	2	no	—
57	C₂×C₃×C₅×Q₈	—	2	4	no	—
58	C₂×C₃×C₅×Q₈	—	4	2	no	—
59	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
60	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
61	C₂×C₃×C₅×D₄	—	2	2	no	—
62	C₂×C₃×C₅×D₄	—	2	2	no	—
63	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	—	2	2	no	—
66	C₂²×C₃×C₄×C₅	—	2	2	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₃×C₅×Q₁₆	—	2	4	no	—
70	C₃×C₅×Q₁₆	—	2	2	no	—
71	C₃×C₅×Q₁₆	D₄	1	4	yes	complemented
72	C₃×C₅×SD₁₆	—	2	4	no	—
73	C₃×C₅×SD₁₆	—	4	2	no	—
74	C₃×C₅×D₈	—	2	2	no	—
75	C₂×C₃×C₅×C₈	—	2	2	no	—
76	C₂×C₃×C₅×C₈	—	2	2	no	—
77	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
78	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
79	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
80	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₄⋊C₄	—	2	2	no	—
82	C₃×C₅×C₄⋊C₄	—	2	2	no	—
83	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
84	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
85	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
87	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
88	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
89	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
90	C₃×C₅×C₂²⋊C₄	D₄	1	1	yes	characteristic
91	C₃×C₄²×C₅	—	2	2	no	—
92	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
93	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#548	C₂×C₅	1	2	yes	complemented
96	C₃×#495	C₂×C₅	1	1	yes	characteristic, complemented
97	C₃×#467	C₂×C₅	1	1	yes	characteristic, complemented
98	C₃×#466	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#464	C₂×C₅	1	2	yes	complemented
100	C₃×#452	C₂×C₅	1	2	yes	complemented
101	C₃×#448	C₂×C₅	1	2	yes	complemented
102	C₃×C₄×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
103	C₃×C₈×D₄	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
105	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
106	C₅×#135	—	2	4	no	—
107	C₂×C₅×Q₁₆	—	2	4	no	—
108	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
109	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
111	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
112	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
113	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
116	C₅×#124	—	2	2	no	—
117	C₅×#124	C₂²×C₃	1	2	yes	—
118	C₅×C₂²⋊Q₈	—	2	2	no	—
119	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
120	C₅×#121	—	2	2	no	—
121	C₅×#121	C₂²×C₃	1	2	yes	—
122	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
123	C₄×C₅×D₄	—	2	2	no	—
124	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
125	C₅×#107	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×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
131	C₅×C₂²⋊C₈	C₂²×C₃	1	1	yes	characteristic
132	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
133	#3285	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
134	C₂³×C₃×C₅	—	2	2	no	—
135	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
136	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₅×Q₈	—	2	2	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×Q₈	—	4	4	no	—
141	C₃×C₅×Q₈	C₂×D₄	1	4	yes	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	2	2	no	—
144	C₃×C₅×D₄	—	2	2	no	—
145	C₃×C₅×D₄	—	4	4	no	—
146	C₃×C₅×D₄	—	4	4	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	4	4	no	—
155	C₂×C₃×C₄×C₅	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
159	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
160	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
161	C₃×C₅×C₈	—	2	1	no	—
162	C₃×C₅×C₈	—	2	1	no	—
163	C₃×C₅×C₈	—	2	1	no	—
164	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
165	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
166	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
167	C₃×#135	—	2	4	no	—
168	C₂×C₃×Q₁₆	—	2	4	no	—
169	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	—
170	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
171	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
173	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
174	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic
175	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
176	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
177	C₃×#124	—	2	2	no	—
178	C₃×#124	C₂²×C₅	1	2	yes	—
179	C₃×C₂²⋊Q₈	—	2	2	no	—
180	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
181	C₃×#121	—	2	2	no	—
182	C₃×#121	C₂²×C₅	1	2	yes	—
183	C₃×C₄×Q₈	C₂²×C₅	1	2	yes	—
184	C₃×C₄×D₄	—	2	2	no	—
185	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
186	C₃×#107	C₂²×C₅	1	1	yes	characteristic
187	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
188	C₃×#103	C₂²×C₅	1	2	yes	—
189	C₃×#103	C₂²×C₅	1	2	yes	—
190	C₃×#102	C₂²×C₅	1	2	yes	—
191	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
192	C₃×C₂²⋊C₈	C₂²×C₅	1	1	yes	characteristic
193	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
194	C₅×#41	—	2	4	no	—
195	C₅×#41	—	4	2	no	—
196	C₂×C₅×Q₈	—	2	2	no	—
197	C₂×C₅×Q₈	—	2	4	no	—
198	C₂×C₅×Q₈	—	4	2	no	—
199	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
200	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
201	C₂×C₅×D₄	—	2	2	no	—
202	C₂×C₅×D₄	—	2	2	no	—
203	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
204	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
205	C₂²×C₄×C₅	—	2	2	no	—
206	C₂²×C₄×C₅	—	2	2	no	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₅×Q₁₆	—	2	4	no	—
210	C₅×Q₁₆	—	2	2	no	—
211	C₅×Q₁₆	C₃×D₄	1	4	yes	complemented
212	C₅×SD₁₆	—	2	4	no	—
213	C₅×SD₁₆	—	4	2	no	—
214	C₅×D₈	—	2	2	no	—
215	C₂×C₅×C₈	—	2	2	no	—
216	C₂×C₅×C₈	—	2	2	no	—
217	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
218	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	2	no	—
222	C₅×C₄⋊C₄	—	2	2	no	—
223	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
224	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
225	C₅×C₂²⋊C₄	—	2	2	no	—
226	C₅×C₂²⋊C₄	—	2	2	no	—
227	C₅×C₂²⋊C₄	—	2	2	no	—
228	C₅×C₂²⋊C₄	—	2	2	no	—
229	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
230	C₅×C₂²⋊C₄	C₃×D₄	1	1	yes	characteristic
231	C₄²×C₅	—	2	2	no	—
232	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
233	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
234	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#548	C₂×C₃×C₅	1	2	yes	complemented
236	#495	C₂×C₃×C₅	1	1	yes	characteristic, complemented
237	#467	C₂×C₃×C₅	1	1	yes	characteristic, complemented
238	#466	C₂×C₃×C₅	1	1	yes	characteristic, complemented
239	#464	C₂×C₃×C₅	1	2	yes	complemented
240	#452	C₂×C₃×C₅	1	2	yes	complemented
241	#448	C₂×C₃×C₅	1	2	yes	complemented
242	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
243	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
244	C₂²×C₃×C₅	—	2	1	no	—
245	C₂²×C₃×C₅	—	2	1	no	—
246	C₂²×C₃×C₅	—	2	1	no	—
247	C₂²×C₃×C₅	—	2	1	no	—
248	C₂²×C₃×C₅	—	2	1	no	—
249	C₂²×C₃×C₅	—	4	2	no	—
250	C₂²×C₃×C₅	—	4	2	no	—
251	C₂²×C₃×C₅	—	4	2	no	—
252	C₂²×C₃×C₅	#135	1	2	yes	complemented
253	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₃×C₄×C₅	—	2	1	no	—
255	C₃×C₄×C₅	—	2	1	no	—
256	C₃×C₄×C₅	—	2	4	no	—
257	C₃×C₄×C₅	—	2	1	no	—
258	C₃×C₄×C₅	—	2	1	no	—
259	C₃×C₄×C₅	—	4	2	no	—
260	C₃×C₄×C₅	—	4	2	no	—
261	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
262	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
263	C₃×#41	—	2	4	no	—
264	C₃×#41	—	4	2	no	—
265	C₂×C₃×Q₈	—	2	2	no	—
266	C₂×C₃×Q₈	—	2	4	no	—
267	C₂×C₃×Q₈	—	4	2	no	—
268	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
269	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
270	C₂×C₃×D₄	—	2	2	no	—
271	C₂×C₃×D₄	—	2	2	no	—
272	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
273	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
274	C₂²×C₃×C₄	—	2	2	no	—
275	C₂²×C₃×C₄	—	2	2	no	—
276	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₃×Q₁₆	—	2	4	no	—
279	C₃×Q₁₆	—	2	2	no	—
280	C₃×Q₁₆	C₅×D₄	1	4	yes	complemented
281	C₃×SD₁₆	—	2	4	no	—
282	C₃×SD₁₆	—	4	2	no	—
283	C₃×D₈	—	2	2	no	—
284	C₂×C₃×C₈	—	2	2	no	—
285	C₂×C₃×C₈	—	2	2	no	—
286	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
287	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
288	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
289	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
290	C₃×C₄⋊C₄	—	2	2	no	—
291	C₃×C₄⋊C₄	—	2	2	no	—
292	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
293	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
294	C₃×C₂²⋊C₄	—	2	2	no	—
295	C₃×C₂²⋊C₄	—	2	2	no	—
296	C₃×C₂²⋊C₄	—	2	2	no	—
297	C₃×C₂²⋊C₄	—	2	2	no	—
298	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
299	C₃×C₂²⋊C₄	C₅×D₄	1	1	yes	characteristic
300	C₃×C₄²	—	2	2	no	—
301	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
302	C₂³×C₅	—	2	2	no	—
303	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
304	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
305	C₅×Q₈	—	2	2	no	—
306	C₅×Q₈	—	2	2	no	—
307	C₅×Q₈	—	2	2	no	—
308	C₅×Q₈	—	4	4	no	—
309	C₅×Q₈	C₂×C₃×D₄	1	4	yes	—
310	C₅×D₄	—	2	2	no	—
311	C₅×D₄	—	2	2	no	—
312	C₅×D₄	—	2	2	no	—
313	C₅×D₄	—	4	4	no	—
314	C₅×D₄	—	4	4	no	—
315	C₂×C₄×C₅	—	2	2	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	4	4	no	—
323	C₂×C₄×C₅	—	4	4	no	—
324	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
325	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
326	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
327	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
329	C₅×C₈	—	2	1	no	—
330	C₅×C₈	—	2	1	no	—
331	C₅×C₈	—	2	1	no	—
332	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
333	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
334	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
335	#135	—	2	4	no	—
336	C₂×Q₁₆	—	2	4	no	—
337	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	—
338	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
339	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
340	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
341	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
342	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic
343	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
345	#124	—	2	2	no	—
346	#124	C₂²×C₃×C₅	1	2	yes	—
347	C₂²⋊Q₈	—	2	2	no	—
348	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
349	#121	—	2	2	no	—
350	#121	C₂²×C₃×C₅	1	2	yes	—
351	C₄×Q₈	C₂²×C₃×C₅	1	2	yes	—
352	C₄×D₄	—	2	2	no	—
353	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
354	#107	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
356	#103	C₂²×C₃×C₅	1	2	yes	—
357	#103	C₂²×C₃×C₅	1	2	yes	—
358	#102	C₂²×C₃×C₅	1	2	yes	—
359	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
360	C₂²⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
361	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
362	C₂×C₃×C₅	—	2	2	no	—
363	C₂×C₃×C₅	—	4	1	no	—
364	C₂×C₃×C₅	—	8	2	no	—
365	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
366	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
367	C₂×C₃×C₅	#578	1	1	yes	characteristic
368	C₂³×C₃	—	2	2	no	—
369	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
370	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
371	C₃×Q₈	—	2	2	no	—
372	C₃×Q₈	—	2	2	no	—
373	C₃×Q₈	—	2	2	no	—
374	C₃×Q₈	—	4	4	no	—
375	C₃×Q₈	C₂×C₅×D₄	1	4	yes	—
376	C₃×D₄	—	2	2	no	—
377	C₃×D₄	—	2	2	no	—
378	C₃×D₄	—	2	2	no	—
379	C₃×D₄	—	4	4	no	—
380	C₃×D₄	—	4	4	no	—
381	C₂×C₃×C₄	—	2	2	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	1	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	4	4	no	—
389	C₂×C₃×C₄	—	4	4	no	—
390	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
391	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
392	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
393	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
394	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
395	C₃×C₈	—	2	1	no	—
396	C₃×C₈	—	2	1	no	—
397	C₃×C₈	—	2	1	no	—
398	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
399	C₂²×C₅	—	2	1	no	—
400	C₂²×C₅	—	2	1	no	—
401	C₂²×C₅	—	2	1	no	—
402	C₂²×C₅	—	2	1	no	—
403	C₂²×C₅	—	2	1	no	—
404	C₂²×C₅	—	4	2	no	—
405	C₂²×C₅	—	4	2	no	—
406	C₂²×C₅	—	4	2	no	—
407	C₂²×C₅	C₃×#135	1	2	yes	complemented
408	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
409	C₄×C₅	—	2	1	no	—
410	C₄×C₅	—	2	1	no	—
411	C₄×C₅	—	2	1	no	—
412	C₄×C₅	—	2	1	no	—
413	C₄×C₅	—	2	4	no	—
414	C₄×C₅	—	4	2	no	—
415	C₄×C₅	—	4	2	no	—
416	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
417	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
418	#41	—	2	4	no	—
419	#41	—	4	2	no	—
420	C₂×Q₈	—	2	2	no	—
421	C₂×Q₈	—	2	4	no	—
422	C₂×Q₈	—	4	2	no	—
423	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
424	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
425	C₂×D₄	—	2	2	no	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
428	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
429	C₂²×C₄	—	2	2	no	—
430	C₂²×C₄	—	2	2	no	—
431	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
432	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
433	Q₁₆	—	2	4	no	—
434	Q₁₆	—	2	2	no	—
435	Q₁₆	C₃×C₅×D₄	1	4	yes	complemented
436	SD₁₆	—	2	4	no	—
437	SD₁₆	—	4	2	no	—
438	D₈	—	2	2	no	—
439	C₂×C₈	—	2	2	no	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
442	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
443	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
444	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
445	C₄⋊C₄	—	2	2	no	—
446	C₄⋊C₄	—	2	2	no	—
447	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
448	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
449	C₂²⋊C₄	—	2	2	no	—
450	C₂²⋊C₄	—	2	2	no	—
451	C₂²⋊C₄	—	2	2	no	—
452	C₂²⋊C₄	—	2	2	no	—
453	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
454	C₂²⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
455	C₄²	—	2	2	no	—
456	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
457	C₃×C₅	#3285	1	1	yes	characteristic, direct product factor, Hall
458	C₂²×C₃	—	2	1	no	—
459	C₂²×C₃	—	2	1	no	—
460	C₂²×C₃	—	2	1	no	—
461	C₂²×C₃	—	2	1	no	—
462	C₂²×C₃	—	2	1	no	—
463	C₂²×C₃	—	4	2	no	—
464	C₂²×C₃	—	4	2	no	—
465	C₂²×C₃	—	4	2	no	—
466	C₂²×C₃	C₅×#135	1	2	yes	complemented
467	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
468	C₃×C₄	—	2	1	no	—
469	C₃×C₄	—	2	1	no	—
470	C₃×C₄	—	2	4	no	—
471	C₃×C₄	—	2	1	no	—
472	C₃×C₄	—	2	1	no	—
473	C₃×C₄	—	4	2	no	—
474	C₃×C₄	—	4	2	no	—
475	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
476	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
477	C₂×C₅	—	2	2	no	—
478	C₂×C₅	—	4	1	no	—
479	C₂×C₅	—	8	2	no	—
480	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
481	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
482	C₂×C₅	C₃×#578	1	1	yes	characteristic
483	C₂³	—	2	2	no	—
484	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
485	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
486	Q₈	—	2	2	no	—
487	Q₈	—	2	2	no	—
488	Q₈	—	2	2	no	—
489	Q₈	—	4	4	no	—
490	Q₈	C₂×C₃×C₅×D₄	1	4	yes	—
491	D₄	—	2	2	no	—
492	D₄	—	2	2	no	—
493	D₄	—	2	2	no	—
494	D₄	—	4	4	no	—
495	D₄	—	4	4	no	—
496	C₂×C₄	—	2	2	no	—
497	C₂×C₄	—	2	1	no	—
498	C₂×C₄	—	2	1	no	—
499	C₂×C₄	—	2	1	no	—
500	C₂×C₄	—	2	1	no	—
501	C₂×C₄	—	2	2	no	—
502	C₂×C₄	—	2	2	no	—
503	C₂×C₄	—	4	4	no	—
504	C₂×C₄	—	4	4	no	—
505	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
506	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
507	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
508	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
509	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
510	C₈	—	2	1	no	—
511	C₈	—	2	1	no	—
512	C₈	—	2	1	no	—
513	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
514	C₂×C₃	—	2	2	no	—
515	C₂×C₃	—	4	1	no	—
516	C₂×C₃	—	8	2	no	—
517	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
518	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
519	C₂×C₃	C₅×#578	1	1	yes	characteristic
520	C₅	C₃×#3285	1	1	yes	characteristic, direct product factor, Sylow
521	C₂²	—	2	1	no	—
522	C₂²	—	2	1	no	—
523	C₂²	—	2	1	no	—
524	C₂²	—	2	1	no	—
525	C₂²	—	2	1	no	—
526	C₂²	—	4	2	no	—
527	C₂²	—	4	2	no	—
528	C₂²	—	4	2	no	—
529	C₂²	C₃×C₅×#135	1	2	yes	complemented
530	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
531	C₄	—	2	1	no	—
532	C₄	—	2	1	no	—
533	C₄	—	2	4	no	—
534	C₄	—	2	1	no	—
535	C₄	—	2	1	no	—
536	C₄	—	4	2	no	—
537	C₄	—	4	2	no	—
538	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
539	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
540	C₃	C₅×#3285	1	1	yes	characteristic, direct product factor, Sylow
541	C₂	—	2	2	no	—
542	C₂	—	4	1	no	—
543	C₂	—	8	2	no	—
544	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
545	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
546	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
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×#135	C₂	semidirect
2. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
3. C₃×C₅×#548	C₂	semidirect
4. C₃×C₅×#495	C₂	semidirect
5. C₃×C₅×#467	C₂	semidirect
6. C₃×C₅×#466	C₂	semidirect
7. C₃×C₅×#464	C₂	semidirect
8. C₃×C₅×#452	C₂	semidirect
9. C₃×C₅×#448	C₂	semidirect
10. C₃×C₄×C₅×Q₁₆	C₂	semidirect
11. C₃×C₅×C₈×D₄	C₂	semidirect
12. C₅×#3285	C₃	direct (N × H)
42. C₃×#3285	C₅	direct (N × H)
43. C₂×C₅×#135	C₂×C₃	semidirect
44. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
45. C₅×#548	C₂×C₃	semidirect
46. C₅×#495	C₂×C₃	semidirect
47. C₅×#467	C₂×C₃	semidirect
48. C₅×#466	C₂×C₃	semidirect
49. C₅×#464	C₂×C₃	semidirect
50. C₅×#452	C₂×C₃	semidirect
51. C₅×#448	C₂×C₃	semidirect
52. C₄×C₅×Q₁₆	C₂×C₃	semidirect
53. C₅×C₈×D₄	C₂×C₃	semidirect
71. C₃×C₅×Q₁₆	D₄	semidirect
93. C₂×C₃×#135	C₂×C₅	semidirect
94. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
95. C₃×#548	C₂×C₅	semidirect
96. C₃×#495	C₂×C₅	semidirect
97. C₃×#467	C₂×C₅	semidirect
98. C₃×#466	C₂×C₅	semidirect
99. C₃×#464	C₂×C₅	semidirect
100. C₃×#452	C₂×C₅	semidirect
101. C₃×#448	C₂×C₅	semidirect
102. C₃×C₄×Q₁₆	C₂×C₅	semidirect
103. C₃×C₈×D₄	C₂×C₅	semidirect
133. #3285	C₃×C₅	direct (N × H)
211. C₅×Q₁₆	C₃×D₄	semidirect
233. C₂×#135	C₂×C₃×C₅	semidirect
234. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
235. #548	C₂×C₃×C₅	semidirect
236. #495	C₂×C₃×C₅	semidirect
237. #467	C₂×C₃×C₅	semidirect
238. #466	C₂×C₃×C₅	semidirect
239. #464	C₂×C₃×C₅	semidirect
240. #452	C₂×C₃×C₅	semidirect
241. #448	C₂×C₃×C₅	semidirect
242. C₄×Q₁₆	C₂×C₃×C₅	semidirect
243. C₈×D₄	C₂×C₃×C₅	semidirect
252. C₂²×C₃×C₅	#135	semidirect
280. C₃×Q₁₆	C₅×D₄	semidirect
407. C₂²×C₅	C₃×#135	semidirect
435. Q₁₆	C₃×C₅×D₄	semidirect
457. C₃×C₅	#3285	direct (N × H)
466. C₂²×C₃	C₅×#135	semidirect
520. C₅	C₃×#3285	direct (N × H)
529. C₂²	C₃×C₅×#135	semidirect
540. C₃	C₅×#3285	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×#135	2
C₂²×C₃×C₅×Q₁₆	2
C₃×C₅×#548	2
C₃×C₅×#495	2
C₃×C₅×#467	2
C₃×C₅×#466	2
C₃×C₅×#464	2
C₃×C₅×#452	2
C₃×C₅×#448	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×C₈×D₄	2
C₅×#3285	3
C₃×#3285	5

Subgroups — C3×C5×#3285 #14276319

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3285 #14276319