Subgroups — C₃×C₅×#3289 #14276323

Order 1920.

896 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×#578	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#577	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#473	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#471	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#456	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#455	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#454	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×C₅×#444	C₂	1	2	yes	maximal, complemented
10	C₅×#3289	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×2₋¹⁺⁴	C₂²	1	2	yes	—
12	C₃×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
13	C₃×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic
14	C₃×C₅×#137	—	2	2	no	—
15	C₃×C₅×#137	—	2	2	no	—
16	C₃×C₅×#137	—	2	2	no	—
17	C₃×C₅×#137	C₂²	1	2	yes	—
18	C₃×C₅×#137	C₂²	1	2	yes	—
19	C₃×C₅×#137	C₂²	1	2	yes	complemented
20	C₃×C₅×AGL(1,ℤ/8)	—	2	2	no	—
21	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
22	C₃×C₅×#135	—	2	2	no	—
23	C₃×C₅×#135	—	2	2	no	—
24	C₃×C₅×#135	C₂²	1	2	yes	—
25	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
26	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
27	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
28	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
29	C₃×C₅×#131	C₂²	1	2	yes	—
30	C₃×C₅×#131	C₂²	1	2	yes	complemented
31	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
32	C₃×C₅×#124	C₂²	1	1	yes	characteristic
33	C₃×C₅×#108	C₂²	1	2	yes	complemented
34	C₃×C₅×#104	C₂²	1	2	yes	—
35	C₃×C₅×#104	C₂²	1	2	yes	complemented
36	C₃×C₅×#101	C₂²	1	1	yes	characteristic, complemented
37	C₃×C₅×#101	C₂²	1	2	yes	complemented
38	C₃×C₅×#100	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3289	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₅×#578	C₂×C₃	1	2	yes	complemented
42	C₅×#577	C₂×C₃	1	2	yes	complemented
43	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#473	C₂×C₃	1	2	yes	complemented
45	C₅×#471	C₂×C₃	1	2	yes	complemented
46	C₅×#456	C₂×C₃	1	2	yes	complemented
47	C₅×#455	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#454	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#444	C₂×C₃	1	2	yes	complemented
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	—	2	2	no	—
52	C₃×C₅×#41	—	2	2	no	—
53	C₃×C₅×#41	—	2	2	no	—
54	C₃×C₅×#41	—	4	2	no	—
55	C₃×C₅×#41	—	4	1	no	—
56	C₃×C₅×#41	C₂³	1	2	yes	—
57	C₃×C₅×#41	C₂³	1	2	yes	—
58	C₂×C₃×C₅×Q₈	—	2	2	no	—
59	C₂×C₃×C₅×Q₈	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
63	C₂×C₃×C₅×D₄	—	2	2	no	—
64	C₂×C₃×C₅×D₄	—	4	1	no	—
65	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
66	C₃×C₅×Q₁₆	—	2	2	no	—
67	C₃×C₅×Q₁₆	—	2	2	no	—
68	C₃×C₅×Q₁₆	—	2	2	no	—
69	C₃×C₅×Q₁₆	—	2	2	no	—
70	C₃×C₅×Q₁₆	—	2	2	no	—
71	C₃×C₅×Q₁₆	D₄	1	2	yes	—
72	C₃×C₅×SD₁₆	—	2	2	no	—
73	C₃×C₅×SD₁₆	—	2	2	no	—
74	C₃×C₅×SD₁₆	—	2	2	no	—
75	C₃×C₅×SD₁₆	—	2	2	no	—
76	C₃×C₅×SD₁₆	—	2	2	no	—
77	C₃×C₅×SD₁₆	—	2	2	no	—
78	C₃×C₅×SD₁₆	D₄	1	2	yes	—
79	C₃×C₅×SD₁₆	D₄	1	2	yes	—
80	C₃×C₅×D₈	—	2	2	no	—
81	C₃×C₅×D₈	D₄	1	2	yes	—
82	C₃×C₅×M₁₆	—	2	2	no	—
83	C₃×C₅×M₁₆	—	2	2	no	—
84	C₃×C₅×M₁₆	C₂³	1	2	yes	—
85	C₃×C₅×M₁₆	C₂³	1	2	yes	—
86	C₂×C₃×C₅×C₈	—	2	2	no	—
87	C₂×C₃×C₅×C₈	—	2	2	no	—
88	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
89	C₃×C₅×C₄⋊C₄	—	4	1	no	—
90	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
91	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
92	C₃×#578	C₂×C₅	1	2	yes	complemented
93	C₃×#577	C₂×C₅	1	2	yes	complemented
94	C₃×#497	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#473	C₂×C₅	1	2	yes	complemented
96	C₃×#471	C₂×C₅	1	2	yes	complemented
97	C₃×#456	C₂×C₅	1	2	yes	complemented
98	C₃×#455	C₂×C₅	1	1	yes	characteristic, complemented
99	C₃×#454	C₂×C₅	1	1	yes	characteristic, complemented
100	C₃×#444	C₂×C₅	1	2	yes	complemented
101	C₅×2₋¹⁺⁴	C₂²×C₃	1	2	yes	—
102	C₅×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic, complemented
103	C₅×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic
104	C₅×#137	—	2	2	no	—
105	C₅×#137	—	2	2	no	—
106	C₅×#137	—	2	2	no	—
107	C₅×#137	C₂²×C₃	1	2	yes	—
108	C₅×#137	C₂²×C₃	1	2	yes	—
109	C₅×#137	C₂²×C₃	1	2	yes	complemented
110	C₅×AGL(1,ℤ/8)	—	2	2	no	—
111	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
112	C₅×#135	—	2	2	no	—
113	C₅×#135	—	2	2	no	—
114	C₅×#135	C₂²×C₃	1	2	yes	—
115	C₂×C₅×Q₁₆	—	2	2	no	—
116	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
117	C₂×C₅×SD₁₆	—	2	2	no	—
118	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
119	C₅×#131	C₂²×C₃	1	2	yes	—
120	C₅×#131	C₂²×C₃	1	2	yes	complemented
121	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
122	C₅×#124	C₂²×C₃	1	1	yes	characteristic
123	C₅×#108	C₂²×C₃	1	2	yes	complemented
124	C₅×#104	C₂²×C₃	1	2	yes	—
125	C₅×#104	C₂²×C₃	1	2	yes	complemented
126	C₅×#101	C₂²×C₃	1	1	yes	characteristic, complemented
127	C₅×#101	C₂²×C₃	1	2	yes	complemented
128	C₅×#100	C₂²×C₃	1	1	yes	characteristic
129	C₅×#97	C₂²×C₃	1	1	yes	characteristic, complemented
130	#3289	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	4	1	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	2	2	no	—
136	C₃×C₅×Q₈	—	4	2	no	—
137	C₃×C₅×Q₈	—	4	1	no	—
138	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
139	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
140	C₃×C₅×D₄	—	2	2	no	—
141	C₃×C₅×D₄	—	2	2	no	—
142	C₃×C₅×D₄	—	2	2	no	—
143	C₃×C₅×D₄	—	4	2	no	—
144	C₃×C₅×D₄	—	4	1	no	—
145	C₃×C₅×D₄	—	4	2	no	—
146	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
147	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
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	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	4	1	no	—
154	C₂×C₃×C₄×C₅	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	4	2	no	—
156	C₂×C₃×C₄×C₅	—	4	2	no	—
157	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
158	C₃×C₅×C₈	—	2	2	no	—
159	C₃×C₅×C₈	—	2	2	no	—
160	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
161	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
162	C₃×2₋¹⁺⁴	C₂²×C₅	1	2	yes	—
163	C₃×2₋¹⁺⁴	C₂²×C₅	1	1	yes	characteristic, complemented
164	C₃×H(5,𝔽₂)	C₂²×C₅	1	1	yes	characteristic
165	C₃×#137	—	2	2	no	—
166	C₃×#137	—	2	2	no	—
167	C₃×#137	—	2	2	no	—
168	C₃×#137	C₂²×C₅	1	2	yes	—
169	C₃×#137	C₂²×C₅	1	2	yes	—
170	C₃×#137	C₂²×C₅	1	2	yes	complemented
171	C₃×AGL(1,ℤ/8)	—	2	2	no	—
172	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	2	yes	—
173	C₃×#135	—	2	2	no	—
174	C₃×#135	—	2	2	no	—
175	C₃×#135	C₂²×C₅	1	2	yes	—
176	C₂×C₃×Q₁₆	—	2	2	no	—
177	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
178	C₂×C₃×SD₁₆	—	2	2	no	—
179	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
180	C₃×#131	C₂²×C₅	1	2	yes	—
181	C₃×#131	C₂²×C₅	1	2	yes	complemented
182	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic, complemented
183	C₃×#124	C₂²×C₅	1	1	yes	characteristic
184	C₃×#108	C₂²×C₅	1	2	yes	complemented
185	C₃×#104	C₂²×C₅	1	2	yes	—
186	C₃×#104	C₂²×C₅	1	2	yes	complemented
187	C₃×#101	C₂²×C₅	1	1	yes	characteristic, complemented
188	C₃×#101	C₂²×C₅	1	2	yes	complemented
189	C₃×#100	C₂²×C₅	1	1	yes	characteristic
190	C₃×#97	C₂²×C₅	1	1	yes	characteristic, complemented
191	C₅×#41	—	2	2	no	—
192	C₅×#41	—	2	2	no	—
193	C₅×#41	—	2	2	no	—
194	C₅×#41	—	2	2	no	—
195	C₅×#41	—	4	2	no	—
196	C₅×#41	—	4	1	no	—
197	C₅×#41	C₂³×C₃	1	2	yes	—
198	C₅×#41	C₂³×C₃	1	2	yes	—
199	C₂×C₅×Q₈	—	2	2	no	—
200	C₂×C₅×Q₈	—	2	2	no	—
201	C₂×C₅×Q₈	—	2	2	no	—
202	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
203	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
204	C₂×C₅×D₄	—	2	2	no	—
205	C₂×C₅×D₄	—	4	1	no	—
206	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
207	C₅×Q₁₆	—	2	2	no	—
208	C₅×Q₁₆	—	2	2	no	—
209	C₅×Q₁₆	—	2	2	no	—
210	C₅×Q₁₆	—	2	2	no	—
211	C₅×Q₁₆	—	2	2	no	—
212	C₅×Q₁₆	C₃×D₄	1	2	yes	—
213	C₅×SD₁₆	—	2	2	no	—
214	C₅×SD₁₆	—	2	2	no	—
215	C₅×SD₁₆	—	2	2	no	—
216	C₅×SD₁₆	—	2	2	no	—
217	C₅×SD₁₆	—	2	2	no	—
218	C₅×SD₁₆	—	2	2	no	—
219	C₅×SD₁₆	C₃×D₄	1	2	yes	—
220	C₅×SD₁₆	C₃×D₄	1	2	yes	—
221	C₅×D₈	—	2	2	no	—
222	C₅×D₈	C₃×D₄	1	2	yes	—
223	C₅×M₁₆	—	2	2	no	—
224	C₅×M₁₆	—	2	2	no	—
225	C₅×M₁₆	C₂³×C₃	1	2	yes	—
226	C₅×M₁₆	C₂³×C₃	1	2	yes	—
227	C₂×C₅×C₈	—	2	2	no	—
228	C₂×C₅×C₈	—	2	2	no	—
229	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
230	C₅×C₄⋊C₄	—	4	1	no	—
231	C₅×C₂²⋊C₄	—	4	1	no	—
232	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
233	#578	C₂×C₃×C₅	1	2	yes	complemented
234	#577	C₂×C₃×C₅	1	2	yes	complemented
235	#497	C₂×C₃×C₅	1	1	yes	characteristic, complemented
236	#473	C₂×C₃×C₅	1	2	yes	complemented
237	#471	C₂×C₃×C₅	1	2	yes	complemented
238	#456	C₂×C₃×C₅	1	2	yes	complemented
239	#455	C₂×C₃×C₅	1	1	yes	characteristic, complemented
240	#454	C₂×C₃×C₅	1	1	yes	characteristic, complemented
241	#444	C₂×C₃×C₅	1	2	yes	complemented
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	2	2	no	—
244	C₂²×C₃×C₅	—	4	1	no	—
245	C₂²×C₃×C₅	—	8	1	no	—
246	C₂²×C₃×C₅	—	16	1	no	—
247	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
248	C₃×C₄×C₅	—	2	2	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	4	1	no	—
251	C₃×C₄×C₅	—	4	1	no	—
252	C₃×C₄×C₅	—	4	2	no	—
253	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
254	C₃×#41	—	2	2	no	—
255	C₃×#41	—	2	2	no	—
256	C₃×#41	—	2	2	no	—
257	C₃×#41	—	2	2	no	—
258	C₃×#41	—	4	2	no	—
259	C₃×#41	—	4	1	no	—
260	C₃×#41	C₂³×C₅	1	2	yes	—
261	C₃×#41	C₂³×C₅	1	2	yes	—
262	C₂×C₃×Q₈	—	2	2	no	—
263	C₂×C₃×Q₈	—	2	2	no	—
264	C₂×C₃×Q₈	—	2	2	no	—
265	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
266	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
267	C₂×C₃×D₄	—	2	2	no	—
268	C₂×C₃×D₄	—	4	1	no	—
269	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
270	C₃×Q₁₆	—	2	2	no	—
271	C₃×Q₁₆	—	2	2	no	—
272	C₃×Q₁₆	—	2	2	no	—
273	C₃×Q₁₆	—	2	2	no	—
274	C₃×Q₁₆	—	2	2	no	—
275	C₃×Q₁₆	C₅×D₄	1	2	yes	—
276	C₃×SD₁₆	—	2	2	no	—
277	C₃×SD₁₆	—	2	2	no	—
278	C₃×SD₁₆	—	2	2	no	—
279	C₃×SD₁₆	—	2	2	no	—
280	C₃×SD₁₆	—	2	2	no	—
281	C₃×SD₁₆	—	2	2	no	—
282	C₃×SD₁₆	C₅×D₄	1	2	yes	—
283	C₃×SD₁₆	C₅×D₄	1	2	yes	—
284	C₃×D₈	—	2	2	no	—
285	C₃×D₈	C₅×D₄	1	2	yes	—
286	C₃×M₁₆	—	2	2	no	—
287	C₃×M₁₆	—	2	2	no	—
288	C₃×M₁₆	C₂³×C₅	1	2	yes	—
289	C₃×M₁₆	C₂³×C₅	1	2	yes	—
290	C₂×C₃×C₈	—	2	2	no	—
291	C₂×C₃×C₈	—	2	2	no	—
292	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
293	C₃×C₄⋊C₄	—	4	1	no	—
294	C₃×C₂²⋊C₄	—	4	1	no	—
295	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	4	1	no	—
298	C₅×Q₈	—	2	2	no	—
299	C₅×Q₈	—	2	2	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	4	2	no	—
302	C₅×Q₈	—	4	1	no	—
303	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
304	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
305	C₅×D₄	—	2	2	no	—
306	C₅×D₄	—	2	2	no	—
307	C₅×D₄	—	2	2	no	—
308	C₅×D₄	—	4	2	no	—
309	C₅×D₄	—	4	1	no	—
310	C₅×D₄	—	4	2	no	—
311	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
312	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	2	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	2	no	—
318	C₂×C₄×C₅	—	4	1	no	—
319	C₂×C₄×C₅	—	4	2	no	—
320	C₂×C₄×C₅	—	4	2	no	—
321	C₂×C₄×C₅	—	4	2	no	—
322	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
323	C₅×C₈	—	2	2	no	—
324	C₅×C₈	—	2	2	no	—
325	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
326	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
327	2₋¹⁺⁴	C₂²×C₃×C₅	1	2	yes	—
328	2₋¹⁺⁴	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
329	H(5,𝔽₂)	C₂²×C₃×C₅	1	1	yes	characteristic
330	#137	—	2	2	no	—
331	#137	—	2	2	no	—
332	#137	—	2	2	no	—
333	#137	C₂²×C₃×C₅	1	2	yes	—
334	#137	C₂²×C₃×C₅	1	2	yes	—
335	#137	C₂²×C₃×C₅	1	2	yes	complemented
336	AGL(1,ℤ/8)	—	2	2	no	—
337	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	2	yes	—
338	#135	—	2	2	no	—
339	#135	—	2	2	no	—
340	#135	C₂²×C₃×C₅	1	2	yes	—
341	C₂×Q₁₆	—	2	2	no	—
342	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	complemented
343	C₂×SD₁₆	—	2	2	no	—
344	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
345	#131	C₂²×C₃×C₅	1	2	yes	—
346	#131	C₂²×C₃×C₅	1	2	yes	complemented
347	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
348	#124	C₂²×C₃×C₅	1	1	yes	characteristic
349	#108	C₂²×C₃×C₅	1	2	yes	complemented
350	#104	C₂²×C₃×C₅	1	2	yes	—
351	#104	C₂²×C₃×C₅	1	2	yes	complemented
352	#101	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
353	#101	C₂²×C₃×C₅	1	2	yes	complemented
354	#100	C₂²×C₃×C₅	1	1	yes	characteristic
355	#97	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
356	C₂×C₃×C₅	—	2	1	no	—
357	C₂×C₃×C₅	—	4	2	no	—
358	C₂×C₃×C₅	—	4	2	no	—
359	C₂×C₃×C₅	—	8	1	no	—
360	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	4	1	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	2	2	no	—
365	C₃×Q₈	—	2	2	no	—
366	C₃×Q₈	—	4	2	no	—
367	C₃×Q₈	—	4	1	no	—
368	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
369	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
370	C₃×D₄	—	2	2	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	2	2	no	—
373	C₃×D₄	—	4	2	no	—
374	C₃×D₄	—	4	1	no	—
375	C₃×D₄	—	4	2	no	—
376	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
377	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	2	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	4	1	no	—
384	C₂×C₃×C₄	—	4	2	no	—
385	C₂×C₃×C₄	—	4	2	no	—
386	C₂×C₃×C₄	—	4	2	no	—
387	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
388	C₃×C₈	—	2	2	no	—
389	C₃×C₈	—	2	2	no	—
390	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
391	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	2	2	no	—
394	C₂²×C₅	—	4	1	no	—
395	C₂²×C₅	—	8	1	no	—
396	C₂²×C₅	—	16	1	no	—
397	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	2	2	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	—	4	1	no	—
402	C₄×C₅	—	4	2	no	—
403	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
404	#41	—	2	2	no	—
405	#41	—	2	2	no	—
406	#41	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	4	2	no	—
409	#41	—	4	1	no	—
410	#41	C₂³×C₃×C₅	1	2	yes	—
411	#41	C₂³×C₃×C₅	1	2	yes	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	2	2	no	—
414	C₂×Q₈	—	2	2	no	—
415	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
416	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
417	C₂×D₄	—	2	2	no	—
418	C₂×D₄	—	4	1	no	—
419	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
420	Q₁₆	—	2	2	no	—
421	Q₁₆	—	2	2	no	—
422	Q₁₆	—	2	2	no	—
423	Q₁₆	—	2	2	no	—
424	Q₁₆	—	2	2	no	—
425	Q₁₆	C₃×C₅×D₄	1	2	yes	—
426	SD₁₆	—	2	2	no	—
427	SD₁₆	—	2	2	no	—
428	SD₁₆	—	2	2	no	—
429	SD₁₆	—	2	2	no	—
430	SD₁₆	—	2	2	no	—
431	SD₁₆	—	2	2	no	—
432	SD₁₆	C₃×C₅×D₄	1	2	yes	—
433	SD₁₆	C₃×C₅×D₄	1	2	yes	—
434	D₈	—	2	2	no	—
435	D₈	C₃×C₅×D₄	1	2	yes	—
436	M₁₆	—	2	2	no	—
437	M₁₆	—	2	2	no	—
438	M₁₆	C₂³×C₃×C₅	1	2	yes	—
439	M₁₆	C₂³×C₃×C₅	1	2	yes	—
440	C₂×C₈	—	2	2	no	—
441	C₂×C₈	—	2	2	no	—
442	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
443	C₄⋊C₄	—	4	1	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
446	C₃×C₅	#3289	1	1	yes	characteristic, direct product factor, Hall
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	4	1	no	—
450	C₂²×C₃	—	8	1	no	—
451	C₂²×C₃	—	16	1	no	—
452	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	2	2	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	4	1	no	—
457	C₃×C₄	—	4	2	no	—
458	C₃×C₄	C₂²×C₅×D₄	1	2	yes	—
459	C₂×C₅	—	2	1	no	—
460	C₂×C₅	—	4	2	no	—
461	C₂×C₅	—	4	2	no	—
462	C₂×C₅	—	8	1	no	—
463	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
464	C₂³	—	2	1	no	—
465	C₂³	—	4	1	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	2	2	no	—
468	Q₈	—	2	2	no	—
469	Q₈	—	4	2	no	—
470	Q₈	—	4	1	no	—
471	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
472	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	2	2	no	—
476	D₄	—	4	2	no	—
477	D₄	—	4	1	no	—
478	D₄	—	4	2	no	—
479	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
480	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	2	1	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	4	1	no	—
487	C₂×C₄	—	4	2	no	—
488	C₂×C₄	—	4	2	no	—
489	C₂×C₄	—	4	2	no	—
490	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	2	2	no	—
493	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
494	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	4	2	no	—
497	C₂×C₃	—	4	2	no	—
498	C₂×C₃	—	8	1	no	—
499	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
500	C₅	C₃×#3289	1	1	yes	characteristic, direct product factor, Sylow
501	C₂²	—	2	2	no	—
502	C₂²	—	2	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	8	1	no	—
505	C₂²	—	16	1	no	—
506	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	2	2	no	—
509	C₄	—	4	1	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	2	no	—
512	C₄	C₂²×C₃×C₅×D₄	1	2	yes	—
513	C₃	C₅×#3289	1	1	yes	characteristic, direct product factor, Sylow
514	C₂	—	2	1	no	—
515	C₂	—	4	2	no	—
516	C₂	—	4	2	no	—
517	C₂	—	8	1	no	—
518	C₂	C₃×C₅×D₄²	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	D₄²
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#578	C₂	semidirect
2. C₃×C₅×#577	C₂	semidirect
3. C₃×C₅×#497	C₂	semidirect
4. C₃×C₅×#473	C₂	semidirect
5. C₃×C₅×#471	C₂	semidirect
6. C₃×C₅×#456	C₂	semidirect
7. C₃×C₅×#455	C₂	semidirect
8. C₃×C₅×#454	C₂	semidirect
9. C₃×C₅×#444	C₂	semidirect
10. C₅×#3289	C₃	direct (N × H)
12. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
19. C₃×C₅×#137	C₂²	semidirect
26. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
30. C₃×C₅×#131	C₂²	semidirect
31. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
35. C₃×C₅×#104	C₂²	semidirect
36. C₃×C₅×#101	C₂²	semidirect
37. C₃×C₅×#101	C₂²	semidirect
39. C₃×C₅×#97	C₂²	semidirect
40. C₃×#3289	C₅	direct (N × H)
41. C₅×#578	C₂×C₃	semidirect
42. C₅×#577	C₂×C₃	semidirect
43. C₅×#497	C₂×C₃	semidirect
44. C₅×#473	C₂×C₃	semidirect
45. C₅×#471	C₂×C₃	semidirect
46. C₅×#456	C₂×C₃	semidirect
47. C₅×#455	C₂×C₃	semidirect
48. C₅×#454	C₂×C₃	semidirect
49. C₅×#444	C₂×C₃	semidirect
92. C₃×#578	C₂×C₅	semidirect
93. C₃×#577	C₂×C₅	semidirect
94. C₃×#497	C₂×C₅	semidirect
95. C₃×#473	C₂×C₅	semidirect
96. C₃×#471	C₂×C₅	semidirect
97. C₃×#456	C₂×C₅	semidirect
98. C₃×#455	C₂×C₅	semidirect
99. C₃×#454	C₂×C₅	semidirect
100. C₃×#444	C₂×C₅	semidirect
102. C₅×2₋¹⁺⁴	C₂²×C₃	semidirect
109. C₅×#137	C₂²×C₃	semidirect
116. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
120. C₅×#131	C₂²×C₃	semidirect
121. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
123. C₅×#108	C₂²×C₃	semidirect
125. C₅×#104	C₂²×C₃	semidirect
126. C₅×#101	C₂²×C₃	semidirect
127. C₅×#101	C₂²×C₃	semidirect
129. C₅×#97	C₂²×C₃	semidirect
130. #3289	C₃×C₅	direct (N × H)
163. C₃×2₋¹⁺⁴	C₂²×C₅	semidirect
170. C₃×#137	C₂²×C₅	semidirect
177. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
181. C₃×#131	C₂²×C₅	semidirect
182. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
184. C₃×#108	C₂²×C₅	semidirect
186. C₃×#104	C₂²×C₅	semidirect
187. C₃×#101	C₂²×C₅	semidirect
188. C₃×#101	C₂²×C₅	semidirect
190. C₃×#97	C₂²×C₅	semidirect
233. #578	C₂×C₃×C₅	semidirect
234. #577	C₂×C₃×C₅	semidirect
235. #497	C₂×C₃×C₅	semidirect
236. #473	C₂×C₃×C₅	semidirect
237. #471	C₂×C₃×C₅	semidirect
238. #456	C₂×C₃×C₅	semidirect
239. #455	C₂×C₃×C₅	semidirect
240. #454	C₂×C₃×C₅	semidirect
241. #444	C₂×C₃×C₅	semidirect
328. 2₋¹⁺⁴	C₂²×C₃×C₅	semidirect
335. #137	C₂²×C₃×C₅	semidirect
342. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
346. #131	C₂²×C₃×C₅	semidirect
347. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
349. #108	C₂²×C₃×C₅	semidirect
351. #104	C₂²×C₃×C₅	semidirect
352. #101	C₂²×C₃×C₅	semidirect
353. #101	C₂²×C₃×C₅	semidirect
355. #97	C₂²×C₃×C₅	semidirect
446. C₃×C₅	#3289	direct (N × H)
500. C₅	C₃×#3289	direct (N × H)
513. C₃	C₅×#3289	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×#578	2
C₃×C₅×#577	2
C₃×C₅×#497	2
C₃×C₅×#473	2
C₃×C₅×#471	2
C₃×C₅×#456	2
C₃×C₅×#455	2
C₃×C₅×#454	2
C₃×C₅×#444	2
C₅×#3289	3
C₃×#3289	5

Subgroups — C3×C5×#3289 #14276323

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3289 #14276323