Subgroups — C₃×D₅×#541 #14481188

Order 1920.

2008 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#541	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#66065	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×D₅×#126	C₂	1	4	yes	maximal
5	C₃×#66035	C₂	1	4	yes	maximal, complemented
6	C₃×#66031	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#66030	C₂	1	4	yes	maximal, complemented
8	C₃×D₅×#125	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₅×#125	C₂	1	4	yes	maximal, complemented
10	C₃×D₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
11	C₃×#65959	C₂	1	2	yes	maximal, complemented
12	C₃×#65917	C₂	1	2	yes	maximal, complemented
13	C₃×C₄×Q₈×D₅	C₂	1	2	yes	maximal, complemented
14	C₃×D₅×#117	C₂	1	1	yes	maximal, characteristic
15	C₃×#65852	C₂	1	1	yes	maximal, characteristic, complemented
16	D₅×#541	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
17	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
18	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
20	C₃×C₅×#126	C₂²	1	4	yes	—
21	C₃×C₅×#125	C₂²	1	4	yes	complemented
22	C₃×C₅×#125	C₂²	1	1	yes	characteristic, complemented
23	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
24	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	complemented
25	C₃×C₅×#117	C₂²	1	1	yes	characteristic
26	C₃×#4092	C₂²	1	2	yes	—
27	C₃×Q₈×Dic₅	C₂²	1	2	yes	complemented
28	C₃×#4090	C₂²	1	2	yes	complemented
29	C₃×#4072	C₂²	1	1	yes	characteristic
30	C₃×#4070	C₂²	1	2	yes	—
31	C₃×#4044	C₂²	1	4	yes	—
32	C₃×#4044	C₂²	1	4	yes	—
33	C₃×#4044	C₂²	1	4	yes	—
34	C₃×#4043	C₂²	1	2	yes	—
35	C₃×#4042	C₂²	1	4	yes	—
36	C₃×#4038	C₂²	1	2	yes	—
37	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
38	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
39	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
40	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
41	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
42	C₃×D₅×C₄⋊C₄	C₂²	1	4	yes	—
43	C₃×#4036	C₂²	1	2	yes	complemented
44	C₃×#4036	C₂²	1	4	yes	complemented
45	C₃×#4036	C₂²	1	4	yes	complemented
46	C₃×#4035	C₂²	1	4	yes	complemented
47	C₃×#4035	C₂²	1	4	yes	complemented
48	C₃×#4035	C₂²	1	4	yes	complemented
49	C₃×#4035	C₂²	1	4	yes	complemented
50	C₃×#4035	C₂²	1	4	yes	complemented
51	C₃×#4034	C₂²	1	4	yes	complemented
52	C₃×#4033	C₂²	1	2	yes	complemented
53	C₃×#4033	C₂²	1	4	yes	complemented
54	C₃×D₅×C₂²⋊C₄	C₂²	1	2	yes	—
55	C₃×D₅×C₂²⋊C₄	C₂²	1	4	yes	—
56	C₃×#4025	C₂²	1	4	yes	—
57	C₃×#4025	C₂²	1	4	yes	—
58	C₃×#4025	C₂²	1	4	yes	—
59	C₃×#4024	C₂²	1	4	yes	—
60	C₃×#4023	C₂²	1	2	yes	—
61	C₃×#4022	C₂²	1	4	yes	—
62	C₃×#4018	C₂²	1	1	yes	characteristic
63	C₃×#4018	C₂²	1	1	yes	characteristic
64	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
65	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
66	C₃×C₄²×D₅	C₂²	1	4	yes	—
67	C₃×#4016	C₂²	1	1	yes	characteristic, complemented
68	C₃×#4016	C₂²	1	4	yes	complemented
69	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
70	C₃×C₄×Dic₁₀	C₂²	1	2	yes	complemented
71	C₃×C₄×Dic₁₀	C₂²	1	4	yes	complemented
72	C₂×C₃×#541	—	5	1	no	maximal, Hall
73	C₅×#541	C₂×C₃	1	1	yes	characteristic, complemented
74	#66065	C₂×C₃	1	1	yes	characteristic, complemented
75	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
76	D₅×#126	C₂×C₃	1	4	yes	—
77	#66035	C₂×C₃	1	4	yes	complemented
78	#66031	C₂×C₃	1	1	yes	characteristic, complemented
79	#66030	C₂×C₃	1	4	yes	complemented
80	D₅×#125	C₂×C₃	1	4	yes	complemented
81	D₅×#125	C₂×C₃	1	1	yes	characteristic, complemented
82	D₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
83	#65959	C₂×C₃	1	2	yes	complemented
84	#65917	C₂×C₃	1	2	yes	complemented
85	C₄×Q₈×D₅	C₂×C₃	1	2	yes	complemented
86	D₅×#117	C₂×C₃	1	1	yes	characteristic
87	#65852	C₂×C₃	1	1	yes	characteristic, complemented
88	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
90	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
91	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
92	C₃×Q₈×D₅	—	2	8	no	—
93	C₂×C₃×C₄×D₅	—	2	4	no	—
94	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
95	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
96	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
97	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
98	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
99	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
100	C₂×C₃×C₄×D₅	C₂³	1	4	yes	—
101	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
102	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
103	C₂×C₃×Dic₁₀	C₂³	1	4	yes	—
104	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
105	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
106	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
107	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
108	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
109	C₃×C₅×C₄⋊C₄	C₂³	1	4	yes	—
110	C₃×C₅×C₂²⋊C₄	C₂³	1	2	yes	—
111	C₃×C₅×C₂²⋊C₄	C₂³	1	4	yes	—
112	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
113	C₃×C₄²×C₅	C₂³	1	4	yes	—
114	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
115	C₃×C₂²⋊Dic₅	C₂³	1	2	yes	—
116	C₃×C₂²⋊Dic₅	C₂³	1	4	yes	—
117	C₃×#685	C₂³	1	4	yes	—
118	C₃×#685	C₂³	1	2	yes	—
119	C₃×#685	C₂³	1	2	yes	—
120	C₃×#685	C₂³	1	4	yes	—
121	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
122	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
123	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
124	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
125	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
126	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
127	C₃×#683	C₂³	1	4	yes	—
128	C₃×#683	C₂³	1	4	yes	—
129	C₃×#683	C₂³	1	4	yes	—
130	C₃×#683	C₂³	1	4	yes	—
131	C₃×#683	C₂³	1	4	yes	—
132	C₃×#683	C₂³	1	4	yes	—
133	C₃×#683	C₂³	1	2	yes	—
134	C₃×#683	C₂³	1	4	yes	—
135	C₃×#683	C₂³	1	2	yes	—
136	C₃×#683	C₂³	1	4	yes	—
137	C₃×#683	C₂³	1	4	yes	—
138	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
139	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
140	C₃×C₄×Dic₅	C₂³	1	4	yes	—
141	C₃×C₄×Dic₅	C₂³	1	2	yes	—
142	C₃×C₄×Dic₅	C₂³	1	4	yes	—
143	C₃×C₄×Dic₅	C₂³	1	2	yes	—
144	C₃×C₄×Dic₅	C₂³	1	4	yes	—
145	C₃×#541	—	5	1	no	—
146	C₃×#541	—	5	4	no	—
147	C₃×#541	—	5	4	no	—
148	C₃×#541	—	5	1	no	—
149	C₃×#541	—	5	2	no	—
150	C₃×#541	—	5	2	no	—
151	C₃×#541	—	5	1	no	—
152	C₃×#541	D₅	1	1	yes	characteristic, direct product factor
153	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
154	C₂×C₃×#126	—	5	4	no	—
155	C₂×C₃×#125	—	5	1	no	—
156	C₂×C₃×#125	—	5	4	no	—
157	C₂×C₃×C₂²⋊Q₈	—	5	2	no	—
158	C₂×C₃×C₄×Q₈	—	5	2	no	—
159	C₂×C₃×#117	—	5	1	no	—
160	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
161	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic
162	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic, complemented
163	C₅×#126	C₂²×C₃	1	4	yes	—
164	C₅×#125	C₂²×C₃	1	4	yes	complemented
165	C₅×#125	C₂²×C₃	1	1	yes	characteristic, complemented
166	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
167	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	complemented
168	C₅×#117	C₂²×C₃	1	1	yes	characteristic
169	#4092	C₂²×C₃	1	2	yes	—
170	Q₈×Dic₅	C₂²×C₃	1	2	yes	complemented
171	#4090	C₂²×C₃	1	2	yes	complemented
172	#4072	C₂²×C₃	1	1	yes	characteristic
173	#4070	C₂²×C₃	1	2	yes	—
174	#4044	C₂²×C₃	1	4	yes	—
175	#4044	C₂²×C₃	1	4	yes	—
176	#4044	C₂²×C₃	1	4	yes	—
177	#4043	C₂²×C₃	1	2	yes	—
178	#4042	C₂²×C₃	1	4	yes	—
179	#4038	C₂²×C₃	1	2	yes	—
180	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
181	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
182	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
183	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
184	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
185	D₅×C₄⋊C₄	C₂²×C₃	1	4	yes	—
186	#4036	C₂²×C₃	1	2	yes	complemented
187	#4036	C₂²×C₃	1	4	yes	complemented
188	#4036	C₂²×C₃	1	4	yes	complemented
189	#4035	C₂²×C₃	1	4	yes	complemented
190	#4035	C₂²×C₃	1	4	yes	complemented
191	#4035	C₂²×C₃	1	4	yes	complemented
192	#4035	C₂²×C₃	1	4	yes	complemented
193	#4035	C₂²×C₃	1	4	yes	complemented
194	#4034	C₂²×C₃	1	4	yes	complemented
195	#4033	C₂²×C₃	1	2	yes	complemented
196	#4033	C₂²×C₃	1	4	yes	complemented
197	D₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
198	D₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
199	#4025	C₂²×C₃	1	4	yes	—
200	#4025	C₂²×C₃	1	4	yes	—
201	#4025	C₂²×C₃	1	4	yes	—
202	#4024	C₂²×C₃	1	4	yes	—
203	#4023	C₂²×C₃	1	2	yes	—
204	#4022	C₂²×C₃	1	4	yes	—
205	#4018	C₂²×C₃	1	1	yes	characteristic
206	#4018	C₂²×C₃	1	1	yes	characteristic
207	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
208	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
209	C₄²×D₅	C₂²×C₃	1	4	yes	—
210	#4016	C₂²×C₃	1	1	yes	characteristic, complemented
211	#4016	C₂²×C₃	1	4	yes	complemented
212	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
213	C₄×Dic₁₀	C₂²×C₃	1	2	yes	complemented
214	C₄×Dic₁₀	C₂²×C₃	1	4	yes	complemented
215	C₂×#541	—	5	1	no	Sylow
216	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
217	C₂²×C₃×D₅	—	2	2	no	—
218	C₂²×C₃×D₅	—	2	4	no	—
219	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
220	C₂²×C₃×D₅	C₂⁴	1	1	yes	characteristic
221	C₃×C₅×Q₈	—	2	4	no	—
222	C₂×C₃×C₄×C₅	—	2	2	no	—
223	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
224	C₂×C₃×C₄×C₅	C₂⁴	1	2	yes	—
225	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
226	C₂×C₃×C₄×C₅	C₂⁴	1	4	yes	—
227	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
228	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
229	C₂×C₃×Dic₅	—	2	2	no	—
230	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
231	C₂×C₃×Dic₅	C₂⁴	1	2	yes	—
232	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
233	C₂×C₃×Dic₅	C₂⁴	1	4	yes	—
234	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
235	C₂×C₃×Dic₅	C₂⁴	1	1	yes	characteristic
236	C₃×C₄×D₅	—	2	2	no	—
237	C₃×C₄×D₅	—	2	8	no	—
238	C₃×C₄×D₅	—	2	4	no	—
239	C₃×C₄×D₅	—	2	4	no	—
240	C₃×C₄×D₅	—	2	8	no	—
241	C₃×C₄×D₅	—	2	2	no	—
242	C₃×C₄×D₅	—	2	2	no	—
243	C₃×C₄×D₅	#41	1	4	yes	—
244	C₃×Dic₁₀	—	2	4	no	—
245	C₃×Dic₁₀	—	2	8	no	—
246	C₂²×C₃×Q₈	—	5	2	no	—
247	C₂³×C₃×C₄	—	5	1	no	—
248	C₃×C₄⋊Q₈	—	5	2	no	—
249	C₃×C₄⋊Q₈	—	5	4	no	—
250	C₃×C₄⋊Q₈	—	5	1	no	—
251	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
252	C₃×#126	—	5	4	no	—
253	C₃×#126	—	5	4	no	—
254	C₃×#126	—	5	4	no	—
255	C₃×#126	—	5	4	no	—
256	C₃×#126	—	5	4	no	—
257	C₃×#126	—	5	4	no	—
258	C₃×#126	—	5	4	no	—
259	C₃×#126	C₂×D₅	1	4	yes	—
260	C₃×#125	—	5	4	no	—
261	C₃×#125	—	5	4	no	—
262	C₃×#125	—	5	4	no	—
263	C₃×#125	—	5	4	no	—
264	C₃×#125	—	5	4	no	—
265	C₃×#125	—	5	2	no	—
266	C₃×#125	—	5	4	no	—
267	C₃×#125	—	5	4	no	—
268	C₃×#125	—	5	1	no	—
269	C₃×#125	—	5	4	no	—
270	C₃×#125	C₂×D₅	1	1	yes	characteristic, complemented
271	C₃×#125	C₂×D₅	1	4	yes	complemented
272	C₃×C₂²⋊Q₈	—	5	2	no	—
273	C₃×C₂²⋊Q₈	—	5	2	no	—
274	C₃×C₂²⋊Q₈	—	5	4	no	—
275	C₃×C₂²⋊Q₈	—	5	2	no	—
276	C₃×C₂²⋊Q₈	—	5	4	no	—
277	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
278	C₃×C₄×Q₈	—	5	2	no	—
279	C₃×C₄×Q₈	—	5	4	no	—
280	C₃×C₄×Q₈	—	5	2	no	—
281	C₃×C₄×Q₈	—	5	4	no	—
282	C₃×C₄×Q₈	—	5	2	no	—
283	C₃×C₄×Q₈	C₂×D₅	1	2	yes	complemented
284	C₃×#117	—	5	1	no	—
285	C₃×#117	—	5	2	no	—
286	C₃×#117	—	5	2	no	—
287	C₃×#117	—	5	1	no	—
288	C₃×#117	—	5	1	no	—
289	C₃×#117	C₂×D₅	1	1	yes	characteristic
290	C₂×C₃×C₄⋊C₄	—	5	2	no	—
291	C₂×C₃×C₄⋊C₄	—	5	2	no	—
292	C₂×C₃×C₄⋊C₄	—	5	4	no	—
293	C₂×C₃×C₄⋊C₄	—	5	4	no	—
294	C₂×C₃×C₄⋊C₄	—	5	4	no	—
295	C₂×C₃×C₄⋊C₄	—	5	4	no	—
296	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
297	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
298	C₂×C₃×C₄²	—	5	1	no	—
299	C₂×C₃×C₄²	—	5	1	no	—
300	C₂×C₃×C₄²	—	5	4	no	—
301	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
302	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
303	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
304	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
305	Q₈×D₅	—	2	8	no	—
306	C₂×C₄×D₅	—	2	4	no	—
307	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
308	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
309	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
310	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
311	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
312	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
313	C₂×C₄×D₅	C₂³×C₃	1	4	yes	—
314	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
315	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
316	C₂×Dic₁₀	C₂³×C₃	1	4	yes	—
317	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
318	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
319	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
320	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
321	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
322	C₅×C₄⋊C₄	C₂³×C₃	1	4	yes	—
323	C₅×C₂²⋊C₄	C₂³×C₃	1	2	yes	—
324	C₅×C₂²⋊C₄	C₂³×C₃	1	4	yes	—
325	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
326	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
327	C₄²×C₅	C₂³×C₃	1	4	yes	—
328	C₂²⋊Dic₅	C₂³×C₃	1	2	yes	—
329	C₂²⋊Dic₅	C₂³×C₃	1	4	yes	—
330	#685	C₂³×C₃	1	2	yes	—
331	#685	C₂³×C₃	1	2	yes	—
332	#685	C₂³×C₃	1	4	yes	—
333	#685	C₂³×C₃	1	4	yes	—
334	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
335	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
336	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
337	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
338	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
339	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
340	#683	C₂³×C₃	1	4	yes	—
341	#683	C₂³×C₃	1	4	yes	—
342	#683	C₂³×C₃	1	4	yes	—
343	#683	C₂³×C₃	1	2	yes	—
344	#683	C₂³×C₃	1	4	yes	—
345	#683	C₂³×C₃	1	4	yes	—
346	#683	C₂³×C₃	1	4	yes	—
347	#683	C₂³×C₃	1	2	yes	—
348	#683	C₂³×C₃	1	4	yes	—
349	#683	C₂³×C₃	1	4	yes	—
350	#683	C₂³×C₃	1	4	yes	—
351	C₄×Dic₅	C₂³×C₃	1	2	yes	—
352	C₄×Dic₅	C₂³×C₃	1	4	yes	—
353	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
354	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
355	C₄×Dic₅	C₂³×C₃	1	2	yes	—
356	C₄×Dic₅	C₂³×C₃	1	4	yes	—
357	C₄×Dic₅	C₂³×C₃	1	4	yes	—
358	#541	—	5	1	no	—
359	#541	—	5	4	no	—
360	#541	—	5	4	no	—
361	#541	—	5	1	no	—
362	#541	—	5	2	no	—
363	#541	—	5	2	no	—
364	#541	—	5	1	no	—
365	#541	C₃×D₅	1	1	yes	characteristic, direct product factor
366	C₂×C₄⋊Q₈	—	5	1	no	—
367	C₂×#126	—	5	4	no	—
368	C₂×#125	—	5	1	no	—
369	C₂×#125	—	5	4	no	—
370	C₂×C₂²⋊Q₈	—	5	2	no	—
371	C₂×C₄×Q₈	—	5	2	no	—
372	C₂×#117	—	5	1	no	—
373	C₂²×C₃×C₅	—	2	1	no	—
374	C₂²×C₃×C₅	—	2	2	no	—
375	C₂²×C₃×C₅	C₂⁵	1	1	yes	characteristic
376	C₂×C₃×D₅	—	2	1	no	—
377	C₂×C₃×D₅	—	2	2	no	—
378	C₂×C₃×D₅	—	4	4	no	—
379	C₂×C₃×D₅	C₂×#41	1	2	yes	—
380	C₂×C₃×D₅	2₋¹⁺⁴	1	4	yes	—
381	C₃×C₄×C₅	—	2	4	no	—
382	C₃×C₄×C₅	—	2	1	no	—
383	C₃×C₄×C₅	—	2	2	no	—
384	C₃×C₄×C₅	—	2	2	no	—
385	C₃×C₄×C₅	—	2	4	no	—
386	C₃×C₄×C₅	C₂×#41	1	2	yes	—
387	C₃×Dic₅	—	2	4	no	—
388	C₃×Dic₅	—	2	1	no	—
389	C₃×Dic₅	—	2	2	no	—
390	C₃×Dic₅	—	2	2	no	—
391	C₃×Dic₅	—	2	4	no	—
392	C₃×Dic₅	C₂×#41	1	2	yes	—
393	C₂⁴×C₃	—	5	1	no	—
394	C₂×C₃×Q₈	—	5	4	no	—
395	C₂×C₃×Q₈	—	5	2	no	—
396	C₂×C₃×Q₈	—	10	8	no	—
397	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
398	C₂²×C₃×C₄	—	5	1	no	—
399	C₂²×C₃×C₄	—	5	1	no	—
400	C₂²×C₃×C₄	—	5	2	no	—
401	C₂²×C₃×C₄	—	5	2	no	—
402	C₂²×C₃×C₄	—	5	4	no	—
403	C₂²×C₃×C₄	—	5	4	no	—
404	C₂²×C₃×C₄	—	5	1	no	—
405	C₂²×C₃×C₄	—	5	1	no	—
406	C₂²×C₃×C₄	—	5	1	no	—
407	C₂²×C₃×C₄	—	10	4	no	—
408	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
409	C₃×C₄⋊C₄	—	5	2	no	—
410	C₃×C₄⋊C₄	—	5	2	no	—
411	C₃×C₄⋊C₄	—	5	4	no	—
412	C₃×C₄⋊C₄	—	5	4	no	—
413	C₃×C₄⋊C₄	—	5	4	no	—
414	C₃×C₄⋊C₄	—	5	4	no	—
415	C₃×C₄⋊C₄	—	5	4	no	—
416	C₃×C₄⋊C₄	—	5	4	no	—
417	C₃×C₄⋊C₄	—	5	4	no	—
418	C₃×C₄⋊C₄	—	5	4	no	—
419	C₃×C₄⋊C₄	—	5	4	no	—
420	C₃×C₄⋊C₄	—	5	2	no	—
421	C₃×C₄⋊C₄	—	5	2	no	—
422	C₃×C₄⋊C₄	—	5	4	no	—
423	C₃×C₄⋊C₄	—	5	4	no	—
424	C₃×C₄⋊C₄	—	5	4	no	—
425	C₃×C₄⋊C₄	—	5	4	no	—
426	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
427	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
428	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
429	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
430	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
431	C₃×C₄⋊C₄	C₂²×D₅	1	4	yes	—
432	C₃×C₂²⋊C₄	—	5	2	no	—
433	C₃×C₂²⋊C₄	—	5	4	no	—
434	C₃×C₂²⋊C₄	—	5	2	no	—
435	C₃×C₂²⋊C₄	—	5	2	no	—
436	C₃×C₂²⋊C₄	—	5	4	no	—
437	C₃×C₂²⋊C₄	—	5	4	no	—
438	C₃×C₂²⋊C₄	C₂²×D₅	1	2	yes	—
439	C₃×C₂²⋊C₄	C₂²×D₅	1	4	yes	—
440	C₃×C₄²	—	5	2	no	—
441	C₃×C₄²	—	5	1	no	—
442	C₃×C₄²	—	5	2	no	—
443	C₃×C₄²	—	5	1	no	—
444	C₃×C₄²	—	5	4	no	—
445	C₃×C₄²	—	5	4	no	—
446	C₃×C₄²	—	5	4	no	—
447	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
448	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
449	C₃×C₄²	C₂²×D₅	1	4	yes	—
450	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
451	C₂²×D₅	—	2	2	no	—
452	C₂²×D₅	—	2	4	no	—
453	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
454	C₂²×D₅	C₂⁴×C₃	1	1	yes	characteristic
455	C₅×Q₈	—	2	4	no	—
456	C₂×C₄×C₅	—	2	2	no	—
457	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
458	C₂×C₄×C₅	C₂⁴×C₃	1	2	yes	—
459	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
460	C₂×C₄×C₅	C₂⁴×C₃	1	4	yes	—
461	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
462	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
463	C₂×Dic₅	—	2	2	no	—
464	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
465	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
466	C₂×Dic₅	C₂⁴×C₃	1	2	yes	—
467	C₂×Dic₅	C₂⁴×C₃	1	4	yes	—
468	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
469	C₂×Dic₅	C₂⁴×C₃	1	1	yes	characteristic
470	C₄×D₅	—	2	2	no	—
471	C₄×D₅	—	2	8	no	—
472	C₄×D₅	—	2	4	no	—
473	C₄×D₅	—	2	4	no	—
474	C₄×D₅	—	2	8	no	—
475	C₄×D₅	—	2	2	no	—
476	C₄×D₅	—	2	2	no	—
477	C₄×D₅	C₃×#41	1	4	yes	—
478	Dic₁₀	—	2	4	no	—
479	Dic₁₀	—	2	8	no	—
480	C₂²×Q₈	—	5	2	no	—
481	C₂³×C₄	—	5	1	no	—
482	C₄⋊Q₈	—	5	2	no	—
483	C₄⋊Q₈	—	5	4	no	—
484	C₄⋊Q₈	—	5	1	no	—
485	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
486	#126	—	5	4	no	—
487	#126	—	5	4	no	—
488	#126	—	5	4	no	—
489	#126	—	5	4	no	—
490	#126	—	5	4	no	—
491	#126	—	5	4	no	—
492	#126	—	5	4	no	—
493	#126	C₂×C₃×D₅	1	4	yes	—
494	#125	—	5	4	no	—
495	#125	—	5	4	no	—
496	#125	—	5	4	no	—
497	#125	—	5	4	no	—
498	#125	—	5	4	no	—
499	#125	—	5	2	no	—
500	#125	—	5	4	no	—
501	#125	—	5	4	no	—
502	#125	—	5	1	no	—
503	#125	—	5	4	no	—
504	#125	C₂×C₃×D₅	1	1	yes	characteristic, complemented
505	#125	C₂×C₃×D₅	1	4	yes	complemented
506	C₂²⋊Q₈	—	5	2	no	—
507	C₂²⋊Q₈	—	5	2	no	—
508	C₂²⋊Q₈	—	5	4	no	—
509	C₂²⋊Q₈	—	5	2	no	—
510	C₂²⋊Q₈	—	5	4	no	—
511	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	—
512	C₄×Q₈	—	5	2	no	—
513	C₄×Q₈	—	5	4	no	—
514	C₄×Q₈	—	5	2	no	—
515	C₄×Q₈	—	5	4	no	—
516	C₄×Q₈	—	5	2	no	—
517	C₄×Q₈	C₂×C₃×D₅	1	2	yes	complemented
518	#117	—	5	1	no	—
519	#117	—	5	2	no	—
520	#117	—	5	2	no	—
521	#117	—	5	1	no	—
522	#117	—	5	1	no	—
523	#117	C₂×C₃×D₅	1	1	yes	characteristic
524	C₂×C₄⋊C₄	—	5	2	no	—
525	C₂×C₄⋊C₄	—	5	2	no	—
526	C₂×C₄⋊C₄	—	5	4	no	—
527	C₂×C₄⋊C₄	—	5	4	no	—
528	C₂×C₄⋊C₄	—	5	4	no	—
529	C₂×C₄⋊C₄	—	5	4	no	—
530	C₂×C₂²⋊C₄	—	5	2	no	—
531	C₂×C₂²⋊C₄	—	5	4	no	—
532	C₂×C₄²	—	5	1	no	—
533	C₂×C₄²	—	5	1	no	—
534	C₂×C₄²	—	5	4	no	—
535	C₂×C₃×C₅	—	4	1	no	—
536	C₂×C₃×C₅	C₂²×#41	1	1	yes	characteristic
537	C₂×C₃×C₅	C₂×2₋¹⁺⁴	1	2	yes	—
538	C₃×D₅	—	4	1	no	—
539	C₃×D₅	#541	1	4	yes	direct product factor
540	C₂³×C₃	—	5	1	no	—
541	C₂³×C₃	—	5	1	no	—
542	C₂³×C₃	—	10	2	no	—
543	C₂³×C₃	—	10	4	no	—
544	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
545	C₃×Q₈	—	2	4	no	—
546	C₃×Q₈	—	10	8	no	—
547	C₃×Q₈	—	10	4	no	—
548	C₂×C₃×C₄	—	2	2	no	—
549	C₂×C₃×C₄	—	5	1	no	—
550	C₂×C₃×C₄	—	5	4	no	—
551	C₂×C₃×C₄	—	5	2	no	—
552	C₂×C₃×C₄	—	5	2	no	—
553	C₂×C₃×C₄	—	5	4	no	—
554	C₂×C₃×C₄	—	5	4	no	—
555	C₂×C₃×C₄	—	5	1	no	—
556	C₂×C₃×C₄	—	10	2	no	—
557	C₂×C₃×C₄	—	10	4	no	—
558	C₂×C₃×C₄	—	10	4	no	—
559	C₂×C₃×C₄	—	10	8	no	—
560	C₂×C₃×C₄	—	10	2	no	—
561	C₂×C₃×C₄	—	10	8	no	—
562	C₂×C₃×C₄	—	10	2	no	—
563	C₂×C₃×C₄	—	10	2	no	—
564	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
565	C₂×C₃×C₄	C₂³×D₅	1	2	yes	—
566	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
567	C₂×C₃×C₄	C₂³×D₅	1	4	yes	—
568	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
569	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
570	C₂²×C₅	—	2	1	no	—
571	C₂²×C₅	—	2	2	no	—
572	C₂²×C₅	C₂⁵×C₃	1	1	yes	characteristic
573	C₂×D₅	—	2	1	no	—
574	C₂×D₅	—	2	2	no	—
575	C₂×D₅	—	4	4	no	—
576	C₂×D₅	C₂×C₃×#41	1	2	yes	—
577	C₂×D₅	C₃×2₋¹⁺⁴	1	4	yes	—
578	C₄×C₅	—	2	4	no	—
579	C₄×C₅	—	2	1	no	—
580	C₄×C₅	—	2	2	no	—
581	C₄×C₅	—	2	2	no	—
582	C₄×C₅	—	2	4	no	—
583	C₄×C₅	C₂×C₃×#41	1	2	yes	—
584	Dic₅	—	2	4	no	—
585	Dic₅	—	2	1	no	—
586	Dic₅	—	2	2	no	—
587	Dic₅	—	2	4	no	—
588	Dic₅	—	2	2	no	—
589	Dic₅	C₂×C₃×#41	1	2	yes	—
590	C₂⁴	—	5	1	no	—
591	C₂×Q₈	—	5	4	no	—
592	C₂×Q₈	—	5	2	no	—
593	C₂×Q₈	—	10	8	no	—
594	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
595	C₂²×C₄	—	5	1	no	—
596	C₂²×C₄	—	5	1	no	—
597	C₂²×C₄	—	5	2	no	—
598	C₂²×C₄	—	5	2	no	—
599	C₂²×C₄	—	5	4	no	—
600	C₂²×C₄	—	5	4	no	—
601	C₂²×C₄	—	5	1	no	—
602	C₂²×C₄	—	5	1	no	—
603	C₂²×C₄	—	5	1	no	—
604	C₂²×C₄	—	10	4	no	—
605	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
606	C₄⋊C₄	—	5	2	no	—
607	C₄⋊C₄	—	5	2	no	—
608	C₄⋊C₄	—	5	2	no	—
609	C₄⋊C₄	—	5	4	no	—
610	C₄⋊C₄	—	5	2	no	—
611	C₄⋊C₄	—	5	4	no	—
612	C₄⋊C₄	—	5	4	no	—
613	C₄⋊C₄	—	5	4	no	—
614	C₄⋊C₄	—	5	4	no	—
615	C₄⋊C₄	—	5	4	no	—
616	C₄⋊C₄	—	5	4	no	—
617	C₄⋊C₄	—	5	4	no	—
618	C₄⋊C₄	—	5	4	no	—
619	C₄⋊C₄	—	5	4	no	—
620	C₄⋊C₄	—	5	4	no	—
621	C₄⋊C₄	—	5	4	no	—
622	C₄⋊C₄	—	5	4	no	—
623	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
624	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
625	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
626	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
627	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
628	C₄⋊C₄	C₂²×C₃×D₅	1	4	yes	—
629	C₂²⋊C₄	—	5	2	no	—
630	C₂²⋊C₄	—	5	4	no	—
631	C₂²⋊C₄	—	5	2	no	—
632	C₂²⋊C₄	—	5	2	no	—
633	C₂²⋊C₄	—	5	4	no	—
634	C₂²⋊C₄	—	5	4	no	—
635	C₂²⋊C₄	C₂²×C₃×D₅	1	2	yes	—
636	C₂²⋊C₄	C₂²×C₃×D₅	1	4	yes	—
637	C₄²	—	5	2	no	—
638	C₄²	—	5	1	no	—
639	C₄²	—	5	2	no	—
640	C₄²	—	5	1	no	—
641	C₄²	—	5	4	no	—
642	C₄²	—	5	4	no	—
643	C₄²	—	5	4	no	—
644	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
645	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
646	C₄²	C₂²×C₃×D₅	1	4	yes	—
647	C₃×C₅	C₂×#541	1	1	yes	characteristic, complemented, Hall
648	C₂²×C₃	—	2	1	no	—
649	C₂²×C₃	—	2	2	no	—
650	C₂²×C₃	—	5	2	no	—
651	C₂²×C₃	—	5	4	no	—
652	C₂²×C₃	—	10	1	no	—
653	C₂²×C₃	—	10	2	no	—
654	C₂²×C₃	—	20	4	no	—
655	C₂²×C₃	C₂⁴×D₅	1	1	yes	characteristic
656	C₃×C₄	—	2	1	no	—
657	C₃×C₄	—	2	4	no	—
658	C₃×C₄	—	2	2	no	—
659	C₃×C₄	—	2	2	no	—
660	C₃×C₄	—	2	4	no	—
661	C₃×C₄	—	5	2	no	—
662	C₃×C₄	—	10	1	no	—
663	C₃×C₄	—	10	4	no	—
664	C₃×C₄	—	10	2	no	—
665	C₃×C₄	—	10	2	no	—
666	C₃×C₄	—	10	4	no	—
667	C₃×C₄	D₅×#41	1	2	yes	—
668	C₂×C₅	—	4	1	no	—
669	C₂×C₅	C₂²×C₃×#41	1	1	yes	characteristic
670	C₂×C₅	C₂×C₃×2₋¹⁺⁴	1	2	yes	—
671	D₅	—	4	1	no	—
672	D₅	C₃×#541	1	4	yes	direct product factor
673	C₂³	—	5	1	no	—
674	C₂³	—	5	1	no	—
675	C₂³	—	10	2	no	—
676	C₂³	—	10	4	no	—
677	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
678	Q₈	—	2	4	no	—
679	Q₈	—	10	8	no	—
680	Q₈	—	10	4	no	—
681	C₂×C₄	—	2	2	no	—
682	C₂×C₄	—	5	1	no	—
683	C₂×C₄	—	5	4	no	—
684	C₂×C₄	—	5	2	no	—
685	C₂×C₄	—	5	2	no	—
686	C₂×C₄	—	5	4	no	—
687	C₂×C₄	—	5	4	no	—
688	C₂×C₄	—	5	1	no	—
689	C₂×C₄	—	10	2	no	—
690	C₂×C₄	—	10	2	no	—
691	C₂×C₄	—	10	8	no	—
692	C₂×C₄	—	10	4	no	—
693	C₂×C₄	—	10	4	no	—
694	C₂×C₄	—	10	8	no	—
695	C₂×C₄	—	10	2	no	—
696	C₂×C₄	—	10	2	no	—
697	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
698	C₂×C₄	C₂³×C₃×D₅	1	2	yes	—
699	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
700	C₂×C₄	C₂³×C₃×D₅	1	4	yes	—
701	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
702	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
703	C₂×C₃	—	4	1	no	—
704	C₂×C₃	—	5	4	no	—
705	C₂×C₃	—	20	1	no	—
706	C₂×C₃	C₂×D₅×#41	1	1	yes	characteristic
707	C₂×C₃	D₅×2₋¹⁺⁴	1	2	yes	—
708	C₅	C₂×C₃×#541	1	1	yes	characteristic, complemented, Sylow
709	C₂²	—	2	1	no	—
710	C₂²	—	2	2	no	—
711	C₂²	—	5	2	no	—
712	C₂²	—	5	4	no	—
713	C₂²	—	10	1	no	—
714	C₂²	—	10	2	no	—
715	C₂²	—	20	4	no	—
716	C₂²	C₂⁴×C₃×D₅	1	1	yes	characteristic
717	C₄	—	2	1	no	—
718	C₄	—	2	4	no	—
719	C₄	—	2	2	no	—
720	C₄	—	2	2	no	—
721	C₄	—	2	4	no	—
722	C₄	—	5	2	no	—
723	C₄	—	10	1	no	—
724	C₄	—	10	4	no	—
725	C₄	—	10	2	no	—
726	C₄	—	10	2	no	—
727	C₄	—	10	4	no	—
728	C₄	C₃×D₅×#41	1	2	yes	—
729	C₃	D₅×#541	1	1	yes	characteristic, direct product factor, Sylow
730	C₂	—	4	1	no	—
731	C₂	—	5	4	no	—
732	C₂	—	20	1	no	—
733	C₂	C₂×C₃×D₅×#41	1	1	yes	characteristic
734	C₂	C₃×D₅×2₋¹⁺⁴	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂⁴×D₅
commutator, cosocle	C₂²×C₅	C₂⁵×C₃
Frattini	C₂²	C₂⁴×C₃×D₅
Fitting	C₃×C₅×#541	C₂
socle	C₂²×C₃×C₅	C₂⁵
prime radical	C₂³×C₃×D₅	C₂³
hypercenter	C₃×#541	D₅
hypocenter	C₅	C₂×C₃×#541
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#541

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#541	C₂	semidirect
2. C₃×#66065	C₂	semidirect
3. C₃×D₅×C₄⋊Q₈	C₂	semidirect
5. C₃×#66035	C₂	semidirect
6. C₃×#66031	C₂	semidirect
7. C₃×#66030	C₂	semidirect
8. C₃×D₅×#125	C₂	semidirect
9. C₃×D₅×#125	C₂	semidirect
11. C₃×#65959	C₂	semidirect
12. C₃×#65917	C₂	semidirect
13. C₃×C₄×Q₈×D₅	C₂	semidirect
15. C₃×#65852	C₂	semidirect
16. D₅×#541	C₃	direct (N × H)
19. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
21. C₃×C₅×#125	C₂²	semidirect
22. C₃×C₅×#125	C₂²	semidirect
24. C₃×C₄×C₅×Q₈	C₂²	semidirect
27. C₃×Q₈×Dic₅	C₂²	semidirect
28. C₃×#4090	C₂²	semidirect
43. C₃×#4036	C₂²	semidirect
44. C₃×#4036	C₂²	semidirect
45. C₃×#4036	C₂²	semidirect
46. C₃×#4035	C₂²	semidirect
47. C₃×#4035	C₂²	semidirect
48. C₃×#4035	C₂²	semidirect
49. C₃×#4035	C₂²	semidirect
50. C₃×#4035	C₂²	semidirect
51. C₃×#4034	C₂²	semidirect
52. C₃×#4033	C₂²	semidirect
53. C₃×#4033	C₂²	semidirect
67. C₃×#4016	C₂²	semidirect
68. C₃×#4016	C₂²	semidirect
69. C₃×#4015	C₂²	semidirect
70. C₃×C₄×Dic₁₀	C₂²	semidirect
71. C₃×C₄×Dic₁₀	C₂²	semidirect
73. C₅×#541	C₂×C₃	semidirect
74. #66065	C₂×C₃	semidirect
75. D₅×C₄⋊Q₈	C₂×C₃	semidirect
77. #66035	C₂×C₃	semidirect
78. #66031	C₂×C₃	semidirect
79. #66030	C₂×C₃	semidirect
80. D₅×#125	C₂×C₃	semidirect
81. D₅×#125	C₂×C₃	semidirect
83. #65959	C₂×C₃	semidirect
84. #65917	C₂×C₃	semidirect
85. C₄×Q₈×D₅	C₂×C₃	semidirect
87. #65852	C₂×C₃	semidirect
152. C₃×#541	D₅	direct (N × H)
162. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
164. C₅×#125	C₂²×C₃	semidirect
165. C₅×#125	C₂²×C₃	semidirect
167. C₄×C₅×Q₈	C₂²×C₃	semidirect
170. Q₈×Dic₅	C₂²×C₃	semidirect
171. #4090	C₂²×C₃	semidirect
186. #4036	C₂²×C₃	semidirect
187. #4036	C₂²×C₃	semidirect
188. #4036	C₂²×C₃	semidirect
189. #4035	C₂²×C₃	semidirect
190. #4035	C₂²×C₃	semidirect
191. #4035	C₂²×C₃	semidirect
192. #4035	C₂²×C₃	semidirect
193. #4035	C₂²×C₃	semidirect
194. #4034	C₂²×C₃	semidirect
195. #4033	C₂²×C₃	semidirect
196. #4033	C₂²×C₃	semidirect
210. #4016	C₂²×C₃	semidirect
211. #4016	C₂²×C₃	semidirect
212. #4015	C₂²×C₃	semidirect
213. C₄×Dic₁₀	C₂²×C₃	semidirect
214. C₄×Dic₁₀	C₂²×C₃	semidirect
251. C₃×C₄⋊Q₈	C₂×D₅	semidirect
270. C₃×#125	C₂×D₅	semidirect
271. C₃×#125	C₂×D₅	semidirect
283. C₃×C₄×Q₈	C₂×D₅	semidirect
365. #541	C₃×D₅	direct (N × H)
485. C₄⋊Q₈	C₂×C₃×D₅	semidirect
504. #125	C₂×C₃×D₅	semidirect
505. #125	C₂×C₃×D₅	semidirect
517. C₄×Q₈	C₂×C₃×D₅	semidirect
539. C₃×D₅	#541	direct (N × H)
647. C₃×C₅	C₂×#541	semidirect
672. D₅	C₃×#541	direct (N × H)
708. C₅	C₂×C₃×#541	semidirect
729. C₃	D₅×#541	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×#541	2
C₃×#66065	2
C₃×D₅×C₄⋊Q₈	2
C₃×D₅×#126	2
C₃×#66035	2
C₃×#66031	2
C₃×#66030	2
C₃×D₅×#125	2
C₃×D₅×C₂²⋊Q₈	2
C₃×#65959	2
C₃×#65917	2
C₃×C₄×Q₈×D₅	2
C₃×D₅×#117	2
C₃×#65852	2
D₅×#541	3
C₂×C₃×#541	5

Subgroups — C3×D5×#541 #14481188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×D₅×#541 #14481188