Subgroups — C₃×C₅×#3304 #14276338

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×C₅×#550	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#486	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#482	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#465	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#460	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#452	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, complemented
11	C₃×C₅×#416	C₂	1	2	yes	maximal, complemented
12	C₅×#3304	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	1	yes	characteristic
15	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
16	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
17	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
18	C₃×C₅×#127	—	2	1	no	—
19	C₃×C₅×#127	C₂²	1	1	yes	characteristic
20	C₃×C₅×#126	—	2	2	no	—
21	C₃×C₅×#124	—	2	1	no	—
22	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
23	C₃×C₅×#121	—	2	2	no	—
24	C₃×C₅×#121	C₂²	1	2	yes	—
25	C₃×C₄×C₅×Q₈	—	2	1	no	—
26	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
27	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
28	C₃×C₄×C₅×D₄	—	2	1	no	—
29	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
30	C₃×C₅×#117	C₂²	1	2	yes	—
31	C₃×C₅×#107	C₂²	1	1	yes	characteristic
32	C₃×C₅×#106	C₂²	1	2	yes	—
33	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
34	C₃×C₅×#103	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	1	yes	characteristic
36	C₃×C₅×#103	C₂²	1	1	yes	characteristic
37	C₃×C₅×#102	C₂²	1	2	yes	—
38	C₃×C₅×#102	C₂²	1	2	yes	—
39	C₃×C₅×#102	C₂²	1	2	yes	—
40	C₃×C₅×C₂²⋊C₈	C₂²	1	2	yes	—
41	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
42	C₃×#3304	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
43	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#550	C₂×C₃	1	1	yes	characteristic
45	C₅×#486	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#482	C₂×C₃	1	2	yes	complemented
47	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
48	C₅×#465	C₂×C₃	1	2	yes	complemented
49	C₅×#460	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#452	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, complemented
53	C₅×#416	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	1	yes	characteristic
59	C₂×C₃×C₅×D₄	—	2	2	no	—
60	C₂×C₃×C₅×D₄	—	2	2	no	—
61	C₂×C₃×C₅×D₄	—	2	1	no	—
62	C₂×C₃×C₅×D₄	—	2	1	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	C₂³	1	2	yes	—
67	C₃×C₅×Q₁₆	—	2	2	no	—
68	C₃×C₅×SD₁₆	—	4	2	no	—
69	C₂×C₃×C₅×C₈	—	4	2	no	—
70	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
71	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₃×C₅×C₄⋊C₄	—	2	2	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	D₄	1	1	yes	characteristic
78	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
80	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
81	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
82	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
83	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
84	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
85	C₃×C₄²×C₅	—	2	2	no	—
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×#556	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#550	C₂×C₅	1	1	yes	characteristic
91	C₃×#486	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#482	C₂×C₅	1	2	yes	complemented
93	C₃×#475	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×#465	C₂×C₅	1	2	yes	complemented
95	C₃×#460	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×#452	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, complemented
99	C₃×#416	C₂×C₅	1	2	yes	complemented
100	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
101	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
102	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
103	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
104	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
105	C₅×#127	—	2	1	no	—
106	C₅×#127	C₂²×C₃	1	1	yes	characteristic
107	C₅×#126	—	2	2	no	—
108	C₅×#124	—	2	1	no	—
109	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
110	C₅×#121	—	2	2	no	—
111	C₅×#121	C₂²×C₃	1	2	yes	—
112	C₄×C₅×Q₈	—	2	1	no	—
113	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₄×C₅×D₄	—	2	1	no	—
116	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
117	C₅×#117	C₂²×C₃	1	2	yes	—
118	C₅×#107	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	1	yes	characteristic
122	C₅×#103	C₂²×C₃	1	2	yes	—
123	C₅×#103	C₂²×C₃	1	1	yes	characteristic
124	C₅×#102	C₂²×C₃	1	2	yes	—
125	C₅×#102	C₂²×C₃	1	2	yes	—
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	#3304	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
130	C₂³×C₃×C₅	—	2	2	no	—
131	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	2	1	no	—
134	C₃×C₅×Q₈	—	2	1	no	—
135	C₃×C₅×Q₈	—	4	2	no	—
136	C₃×C₅×Q₈	#41	1	2	yes	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	4	4	no	—
141	C₃×C₅×D₄	—	4	2	no	—
142	C₃×C₅×D₄	—	8	1	no	—
143	C₃×C₅×D₄	—	8	2	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	1	no	—
151	C₂×C₃×C₄×C₅	—	4	4	no	—
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	C₂×D₄	1	1	yes	characteristic
155	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
156	C₃×C₅×C₈	—	2	1	no	—
157	C₃×C₅×C₈	—	2	1	no	—
158	C₃×C₅×C₈	—	2	2	no	—
159	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
160	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
162	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
163	C₃×C₄⋊Q₈	C₂²×C₅	1	1	yes	characteristic
164	C₃×#127	—	2	1	no	—
165	C₃×#127	C₂²×C₅	1	1	yes	characteristic
166	C₃×#126	—	2	2	no	—
167	C₃×#124	—	2	1	no	—
168	C₃×C₂²⋊Q₈	C₂²×C₅	1	2	yes	—
169	C₃×#121	—	2	2	no	—
170	C₃×#121	C₂²×C₅	1	2	yes	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
173	C₃×C₄×Q₈	C₂²×C₅	1	1	yes	characteristic
174	C₃×C₄×D₄	—	2	1	no	—
175	C₃×C₄×D₄	C₂²×C₅	1	1	yes	characteristic
176	C₃×#117	C₂²×C₅	1	2	yes	—
177	C₃×#107	C₂²×C₅	1	1	yes	characteristic
178	C₃×#106	C₂²×C₅	1	2	yes	—
179	C₃×C₄⋊C₈	C₂²×C₅	1	1	yes	characteristic
180	C₃×#103	C₂²×C₅	1	1	yes	characteristic
181	C₃×#103	C₂²×C₅	1	2	yes	—
182	C₃×#103	C₂²×C₅	1	1	yes	characteristic
183	C₃×#102	C₂²×C₅	1	2	yes	—
184	C₃×#102	C₂²×C₅	1	2	yes	—
185	C₃×#102	C₂²×C₅	1	2	yes	—
186	C₃×C₂²⋊C₈	C₂²×C₅	1	2	yes	—
187	C₃×C₄×C₈	C₂²×C₅	1	1	yes	characteristic
188	C₅×#41	—	2	4	no	—
189	C₅×#41	—	4	2	no	—
190	C₂×C₅×Q₈	—	2	1	no	—
191	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×D₄	—	2	2	no	—
194	C₂×C₅×D₄	—	2	2	no	—
195	C₂×C₅×D₄	—	2	1	no	—
196	C₂×C₅×D₄	—	2	1	no	—
197	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
198	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
199	C₂²×C₄×C₅	—	2	2	no	—
200	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
201	C₅×Q₁₆	—	2	2	no	—
202	C₅×SD₁₆	—	4	2	no	—
203	C₂×C₅×C₈	—	4	2	no	—
204	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
206	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
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	1	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	—	2	2	no	—
218	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
219	C₄²×C₅	—	2	2	no	—
220	C₄²×C₅	—	2	1	no	—
221	C₄²×C₅	—	2	1	no	—
222	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
223	#556	C₂×C₃×C₅	1	1	yes	characteristic, complemented
224	#550	C₂×C₃×C₅	1	1	yes	characteristic
225	#486	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	#482	C₂×C₃×C₅	1	2	yes	complemented
227	#475	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#465	C₂×C₃×C₅	1	2	yes	complemented
229	#460	C₂×C₃×C₅	1	1	yes	characteristic, complemented
230	#452	C₂×C₃×C₅	1	2	yes	complemented
231	C₄×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	C₈×D₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#416	C₂×C₃×C₅	1	2	yes	complemented
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	2	no	—
238	C₂²×C₃×C₅	—	4	2	no	—
239	C₂²×C₃×C₅	—	4	2	no	—
240	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
241	C₃×C₄×C₅	—	2	2	no	—
242	C₃×C₄×C₅	—	2	2	no	—
243	C₃×C₄×C₅	—	2	1	no	—
244	C₃×C₄×C₅	—	4	1	no	—
245	C₃×C₄×C₅	—	4	2	no	—
246	C₃×C₄×C₅	—	4	1	no	—
247	C₃×C₄×C₅	—	4	1	no	—
248	C₃×C₄×C₅	#135	1	2	yes	—
249	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
250	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
251	C₃×#41	—	2	4	no	—
252	C₃×#41	—	4	2	no	—
253	C₂×C₃×Q₈	—	2	1	no	—
254	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
255	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
256	C₂×C₃×D₄	—	2	2	no	—
257	C₂×C₃×D₄	—	2	2	no	—
258	C₂×C₃×D₄	—	2	1	no	—
259	C₂×C₃×D₄	—	2	1	no	—
260	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
261	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
262	C₂²×C₃×C₄	—	2	2	no	—
263	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
264	C₃×Q₁₆	—	2	2	no	—
265	C₃×SD₁₆	—	4	2	no	—
266	C₂×C₃×C₈	—	4	2	no	—
267	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
268	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
269	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
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	1	no	—
274	C₃×C₄⋊C₄	C₅×D₄	1	1	yes	characteristic
275	C₃×C₄⋊C₄	C₂³×C₅	1	2	yes	—
276	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
277	C₃×C₄⋊C₄	C₂³×C₅	1	1	yes	characteristic
278	C₃×C₂²⋊C₄	—	2	2	no	—
279	C₃×C₂²⋊C₄	—	2	2	no	—
280	C₃×C₂²⋊C₄	—	2	2	no	—
281	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
282	C₃×C₄²	—	2	2	no	—
283	C₃×C₄²	—	2	1	no	—
284	C₃×C₄²	—	2	1	no	—
285	C₃×C₄²	C₂³×C₅	1	1	yes	characteristic
286	C₂³×C₅	—	2	2	no	—
287	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×Q₈	—	2	1	no	—
290	C₅×Q₈	—	2	1	no	—
291	C₅×Q₈	—	4	2	no	—
292	C₅×Q₈	C₃×#41	1	2	yes	—
293	C₅×D₄	—	2	2	no	—
294	C₅×D₄	—	2	2	no	—
295	C₅×D₄	—	2	2	no	—
296	C₅×D₄	—	4	4	no	—
297	C₅×D₄	—	4	2	no	—
298	C₅×D₄	—	8	1	no	—
299	C₅×D₄	—	8	2	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	—	2	1	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	4	4	no	—
308	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
309	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
310	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
312	C₅×C₈	—	2	1	no	—
313	C₅×C₈	—	2	1	no	—
314	C₅×C₈	—	2	2	no	—
315	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
316	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
318	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
319	C₄⋊Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
320	#127	—	2	1	no	—
321	#127	C₂²×C₃×C₅	1	1	yes	characteristic
322	#126	—	2	2	no	—
323	#124	—	2	1	no	—
324	C₂²⋊Q₈	C₂²×C₃×C₅	1	2	yes	—
325	#121	—	2	2	no	—
326	#121	C₂²×C₃×C₅	1	2	yes	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
329	C₄×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
330	C₄×D₄	—	2	1	no	—
331	C₄×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
332	#117	C₂²×C₃×C₅	1	2	yes	—
333	#107	C₂²×C₃×C₅	1	1	yes	characteristic
334	#106	C₂²×C₃×C₅	1	2	yes	—
335	C₄⋊C₈	C₂²×C₃×C₅	1	1	yes	characteristic
336	#103	C₂²×C₃×C₅	1	1	yes	characteristic
337	#103	C₂²×C₃×C₅	1	2	yes	—
338	#103	C₂²×C₃×C₅	1	1	yes	characteristic
339	#102	C₂²×C₃×C₅	1	2	yes	—
340	#102	C₂²×C₃×C₅	1	2	yes	—
341	#102	C₂²×C₃×C₅	1	2	yes	—
342	C₂²⋊C₈	C₂²×C₃×C₅	1	2	yes	—
343	C₄×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₂×C₃×C₅	—	4	2	no	—
345	C₂×C₃×C₅	—	8	2	no	—
346	C₂×C₃×C₅	#546	1	1	yes	characteristic
347	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
348	C₂×C₃×C₅	#577	1	1	yes	characteristic
349	C₂³×C₃	—	2	2	no	—
350	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
351	C₃×Q₈	—	2	1	no	—
352	C₃×Q₈	—	2	1	no	—
353	C₃×Q₈	—	2	1	no	—
354	C₃×Q₈	—	4	2	no	—
355	C₃×Q₈	C₅×#41	1	2	yes	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	2	2	no	—
358	C₃×D₄	—	2	2	no	—
359	C₃×D₄	—	4	4	no	—
360	C₃×D₄	—	4	2	no	—
361	C₃×D₄	—	8	1	no	—
362	C₃×D₄	—	8	2	no	—
363	C₂×C₃×C₄	—	2	1	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	2	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	1	no	—
368	C₂×C₃×C₄	—	2	2	no	—
369	C₂×C₃×C₄	—	2	1	no	—
370	C₂×C₃×C₄	—	4	4	no	—
371	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
372	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
375	C₃×C₈	—	2	1	no	—
376	C₃×C₈	—	2	1	no	—
377	C₃×C₈	—	2	2	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	2	2	no	—
380	C₂²×C₅	—	2	2	no	—
381	C₂²×C₅	—	4	2	no	—
382	C₂²×C₅	—	4	2	no	—
383	C₂²×C₅	—	4	2	no	—
384	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	2	2	no	—
388	C₄×C₅	—	4	2	no	—
389	C₄×C₅	—	4	1	no	—
390	C₄×C₅	—	4	1	no	—
391	C₄×C₅	—	4	1	no	—
392	C₄×C₅	C₃×#135	1	2	yes	—
393	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
394	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
395	#41	—	2	4	no	—
396	#41	—	4	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
399	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
400	C₂×D₄	—	2	2	no	—
401	C₂×D₄	—	2	2	no	—
402	C₂×D₄	—	2	1	no	—
403	C₂×D₄	—	2	1	no	—
404	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
405	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
406	C₂²×C₄	—	2	2	no	—
407	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
408	Q₁₆	—	2	2	no	—
409	SD₁₆	—	4	2	no	—
410	C₂×C₈	—	4	2	no	—
411	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
412	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
413	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	2	1	no	—
418	C₄⋊C₄	C₃×C₅×D₄	1	1	yes	characteristic
419	C₄⋊C₄	C₂³×C₃×C₅	1	2	yes	—
420	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
421	C₄⋊C₄	C₂³×C₃×C₅	1	1	yes	characteristic
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	2	2	no	—
425	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	2	1	no	—
429	C₄²	C₂³×C₃×C₅	1	1	yes	characteristic
430	C₃×C₅	#3304	1	1	yes	characteristic, direct product factor, Hall
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	4	2	no	—
435	C₂²×C₃	—	4	2	no	—
436	C₂²×C₃	—	4	2	no	—
437	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	2	2	no	—
440	C₃×C₄	—	2	1	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	2	no	—
443	C₃×C₄	—	4	1	no	—
444	C₃×C₄	—	4	1	no	—
445	C₃×C₄	C₅×#135	1	2	yes	—
446	C₃×C₄	C₂×C₅×#41	1	1	yes	characteristic
447	C₃×C₄	C₅×H(5,𝔽₂)	1	1	yes	characteristic
448	C₂×C₅	—	4	2	no	—
449	C₂×C₅	—	8	2	no	—
450	C₂×C₅	C₃×#546	1	1	yes	characteristic
451	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
452	C₂×C₅	C₃×#577	1	1	yes	characteristic
453	C₂³	—	2	2	no	—
454	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	1	no	—
457	Q₈	—	2	1	no	—
458	Q₈	—	4	2	no	—
459	Q₈	C₃×C₅×#41	1	2	yes	—
460	D₄	—	2	2	no	—
461	D₄	—	2	2	no	—
462	D₄	—	2	2	no	—
463	D₄	—	4	4	no	—
464	D₄	—	4	2	no	—
465	D₄	—	8	1	no	—
466	D₄	—	8	2	no	—
467	C₂×C₄	—	2	1	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	1	no	—
472	C₂×C₄	—	2	2	no	—
473	C₂×C₄	—	2	1	no	—
474	C₂×C₄	—	4	4	no	—
475	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
476	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
477	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
478	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
479	C₈	—	2	1	no	—
480	C₈	—	2	1	no	—
481	C₈	—	2	2	no	—
482	C₂×C₃	—	4	2	no	—
483	C₂×C₃	—	8	2	no	—
484	C₂×C₃	C₅×#546	1	1	yes	characteristic
485	C₂×C₃	C₂×C₅×#135	1	1	yes	characteristic
486	C₂×C₃	C₅×#577	1	1	yes	characteristic
487	C₅	C₃×#3304	1	1	yes	characteristic, direct product factor, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	4	2	no	—
492	C₂²	—	4	2	no	—
493	C₂²	—	4	2	no	—
494	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	2	2	no	—
497	C₄	—	2	1	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	2	no	—
500	C₄	—	4	1	no	—
501	C₄	—	4	1	no	—
502	C₄	C₃×C₅×#135	1	2	yes	—
503	C₄	C₂×C₃×C₅×#41	1	1	yes	characteristic
504	C₄	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
505	C₃	C₅×#3304	1	1	yes	characteristic, direct product factor, Sylow
506	C₂	—	4	2	no	—
507	C₂	—	8	2	no	—
508	C₂	C₃×C₅×#546	1	1	yes	characteristic
509	C₂	C₂×C₃×C₅×#135	1	1	yes	characteristic
510	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×#550	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×#556	C₂	semidirect
3. C₃×C₅×#486	C₂	semidirect
4. C₃×C₅×#482	C₂	semidirect
5. C₃×C₅×#475	C₂	semidirect
6. C₃×C₅×#465	C₂	semidirect
7. C₃×C₅×#460	C₂	semidirect
8. C₃×C₅×#452	C₂	semidirect
9. C₃×C₄×C₅×Q₁₆	C₂	semidirect
10. C₃×C₅×C₈×D₄	C₂	semidirect
11. C₃×C₅×#416	C₂	semidirect
12. C₅×#3304	C₃	direct (N × H)
42. C₃×#3304	C₅	direct (N × H)
43. C₅×#556	C₂×C₃	semidirect
45. C₅×#486	C₂×C₃	semidirect
46. C₅×#482	C₂×C₃	semidirect
47. C₅×#475	C₂×C₃	semidirect
48. C₅×#465	C₂×C₃	semidirect
49. C₅×#460	C₂×C₃	semidirect
50. C₅×#452	C₂×C₃	semidirect
51. C₄×C₅×Q₁₆	C₂×C₃	semidirect
52. C₅×C₈×D₄	C₂×C₃	semidirect
53. C₅×#416	C₂×C₃	semidirect
89. C₃×#556	C₂×C₅	semidirect
91. C₃×#486	C₂×C₅	semidirect
92. C₃×#482	C₂×C₅	semidirect
93. C₃×#475	C₂×C₅	semidirect
94. C₃×#465	C₂×C₅	semidirect
95. C₃×#460	C₂×C₅	semidirect
96. C₃×#452	C₂×C₅	semidirect
97. C₃×C₄×Q₁₆	C₂×C₅	semidirect
98. C₃×C₈×D₄	C₂×C₅	semidirect
99. C₃×#416	C₂×C₅	semidirect
129. #3304	C₃×C₅	direct (N × H)
223. #556	C₂×C₃×C₅	semidirect
225. #486	C₂×C₃×C₅	semidirect
226. #482	C₂×C₃×C₅	semidirect
227. #475	C₂×C₃×C₅	semidirect
228. #465	C₂×C₃×C₅	semidirect
229. #460	C₂×C₃×C₅	semidirect
230. #452	C₂×C₃×C₅	semidirect
231. C₄×Q₁₆	C₂×C₃×C₅	semidirect
232. C₈×D₄	C₂×C₃×C₅	semidirect
233. #416	C₂×C₃×C₅	semidirect
430. C₃×C₅	#3304	direct (N × H)
487. C₅	C₃×#3304	direct (N × H)
505. C₃	C₅×#3304	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×#556	2
C₃×C₅×#550	2
C₃×C₅×#486	2
C₃×C₅×#482	2
C₃×C₅×#475	2
C₃×C₅×#465	2
C₃×C₅×#460	2
C₃×C₅×#452	2
C₃×C₄×C₅×Q₁₆	2
C₃×C₅×C₈×D₄	2
C₃×C₅×#416	2
C₅×#3304	3
C₃×#3304	5

Subgroups — C3×C5×#3304 #14276338

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3304 #14276338