Subgroups — C₃×C₄×C₅×#67 #13087939

Order 1440.

430 conjugacy classes of subgroups.

The subgroup lattice has 320 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃²×C₄×C₅	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#67	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×(C₂×D₃)⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₅×D₄	—	3	1	no	maximal
9	C₄×C₅×#67	C₃	1	1	yes	maximal, characteristic, direct product factor
10	C₂³×C₃²×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄×C₅	—	2	2	no	—
13	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂×C₃²×C₄×C₅	C₂²	1	1	yes	characteristic
15	C₃×C₅×#67	C₄	1	4	yes	direct product factor
16	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic
17	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×Dic₃	C₂²	1	1	yes	characteristic
19	C₃×C₄×C₅×D₃	—	2	2	no	—
20	C₃×C₄×#67	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂×C₃×C₅×D₄	—	3	1	no	—
22	C₂²×C₃×C₄×C₅	—	2	1	no	—
23	C₂²×C₃×C₄×C₅	—	3	1	no	—
24	C₂²×C₃×C₄×C₅	D₃	1	1	yes	characteristic, complemented
25	C₂²×C₃×C₄×C₅	C₂×C₃	1	1	yes	characteristic, complemented
26	C₂×C₅×#67	C₂×C₃	1	1	yes	characteristic
27	C₂×C₄×C₅×D₃	C₂×C₃	1	1	yes	characteristic, complemented
28	C₃×C₅×C₄⋊C₄	—	3	1	no	—
29	C₃×C₅×C₂²⋊C₄	—	3	1	no	—
30	C₃×C₅×C₂²⋊C₄	—	3	1	no	—
31	C₃×C₄²×C₅	—	3	1	no	—
32	C₅×#217	C₂×C₃	1	1	yes	characteristic, complemented
33	C₅×(C₂×D₃)⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
34	C₅×Dic₃⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
35	C₄×C₅×Dic₃	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂²×C₃²×C₅	—	2	1	no	—
37	C₂²×C₃²×C₅	—	2	1	no	—
38	C₂²×C₃²×C₅	C₂×C₄	1	2	yes	complemented
39	C₂²×C₃²×C₅	C₂³	1	1	yes	characteristic
40	C₂×C₃×C₅×D₃	—	2	1	no	—
41	C₂×C₃×C₅×D₃	—	2	1	no	—
42	C₂×C₃×C₅×D₃	C₂×C₄	1	2	yes	complemented
43	C₃²×C₄×C₅	—	2	1	no	—
44	C₃²×C₄×C₅	D₄	1	2	yes	complemented
45	C₃×C₅×Dic₃	—	2	1	no	—
46	C₃×C₅×Dic₃	—	2	1	no	—
47	C₃×C₅×Dic₃	C₂×C₄	1	2	yes	complemented
48	C₄×C₅×D₄	—	3	1	no	Hall
49	C₂²×C₃²×C₄	C₂×C₅	1	1	yes	characteristic, complemented
50	C₂×C₃×#67	C₂×C₅	1	1	yes	characteristic
51	C₂×C₃×C₄×D₃	C₂×C₅	1	1	yes	characteristic, complemented
52	C₃×#217	C₂×C₅	1	1	yes	characteristic, complemented
53	C₃×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
54	C₃×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
55	C₃×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
56	C₂³×C₃×C₅	—	2	1	no	—
57	C₂³×C₃×C₅	—	3	1	no	—
58	C₂³×C₃×C₅	C₂×D₃	1	1	yes	characteristic
59	C₂³×C₃×C₅	C₂²×C₃	1	1	yes	characteristic
60	C₂²×C₅×D₃	C₂²×C₃	1	1	yes	characteristic
61	C₃×C₅×D₄	—	3	4	no	—
62	C₂×C₃×C₄×C₅	—	2	4	no	—
63	C₂×C₃×C₄×C₅	—	2	1	no	—
64	C₂×C₃×C₄×C₅	—	2	1	no	—
65	C₂×C₃×C₄×C₅	—	2	2	no	—
66	C₂×C₃×C₄×C₅	—	2	2	no	—
67	C₂×C₃×C₄×C₅	—	3	1	no	—
68	C₂×C₃×C₄×C₅	—	3	1	no	—
69	C₂×C₃×C₄×C₅	—	3	1	no	—
70	C₂×C₃×C₄×C₅	—	6	2	no	—
71	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	C₂×D₃	1	1	yes	characteristic
73	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
74	C₂×C₃×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₅×#67	C₃×C₄	1	4	yes	direct product factor
76	C₂×C₅×Dic₃	C₂²×C₃	1	1	yes	characteristic
77	C₂×C₅×Dic₃	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×Dic₃	C₂²×C₃	1	1	yes	characteristic
79	C₄×C₅×D₃	—	2	2	no	—
80	C₃×C₄×D₄	—	3	1	no	—
81	C₄×#67	C₃×C₅	1	1	yes	characteristic, direct product factor
82	C₂×C₃²×C₅	—	2	2	no	—
83	C₂×C₃²×C₅	C₂²×C₄	1	1	yes	characteristic
84	C₂×C₃²×C₅	C₂×D₄	1	1	yes	characteristic
85	C₂×C₃²×C₅	#41	1	1	yes	characteristic
86	C₃×C₅×D₃	—	2	2	no	—
87	C₂×C₅×D₄	—	3	1	no	—
88	C₂²×C₄×C₅	—	3	1	no	—
89	C₂²×C₄×C₅	C₃×D₃	1	1	yes	characteristic, complemented
90	C₅×C₄⋊C₄	—	3	1	no	—
91	C₅×C₂²⋊C₄	—	3	1	no	—
92	C₅×C₂²⋊C₄	—	3	1	no	—
93	C₄²×C₅	—	3	1	no	—
94	C₂³×C₃²	C₂²×C₅	1	1	yes	characteristic
95	C₂²×C₃×D₃	C₂²×C₅	1	1	yes	characteristic
96	C₂×C₃²×C₄	—	2	2	no	—
97	C₂×C₃²×C₄	C₂²×C₅	1	1	yes	characteristic
98	C₂×C₃²×C₄	C₂²×C₅	1	1	yes	characteristic
99	C₃×#67	C₄×C₅	1	4	yes	direct product factor
100	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic
101	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic
102	C₂×C₃×Dic₃	C₂²×C₅	1	1	yes	characteristic
103	C₃×C₄×D₃	—	2	2	no	—
104	C₂²×C₃×C₅	—	2	2	no	—
105	C₂²×C₃×C₅	—	2	2	no	—
106	C₂²×C₃×C₅	—	2	1	no	—
107	C₂²×C₃×C₅	—	2	1	no	—
108	C₂²×C₃×C₅	—	2	1	no	—
109	C₂²×C₃×C₅	—	2	1	no	—
110	C₂²×C₃×C₅	—	2	2	no	—
111	C₂²×C₃×C₅	—	2	1	no	—
112	C₂²×C₃×C₅	—	3	2	no	—
113	C₂²×C₃×C₅	—	6	1	no	—
114	C₂²×C₃×C₅	—	6	1	no	—
115	C₂²×C₃×C₅	C₄×D₃	1	2	yes	complemented
116	C₂²×C₃×C₅	C₂×C₃×C₄	1	2	yes	complemented
117	C₂²×C₃×C₅	C₂²×D₃	1	1	yes	characteristic
118	C₂²×C₃×C₅	C₂³×C₃	1	1	yes	characteristic
119	C₂×C₅×D₃	—	2	1	no	—
120	C₂×C₅×D₃	—	2	1	no	—
121	C₂×C₅×D₃	C₂×C₃×C₄	1	2	yes	complemented
122	C₃×C₄×C₅	—	2	2	no	—
123	C₃×C₄×C₅	—	2	1	no	—
124	C₃×C₄×C₅	—	2	1	no	—
125	C₃×C₄×C₅	—	2	2	no	—
126	C₃×C₄×C₅	—	3	2	no	—
127	C₃×C₄×C₅	—	6	1	no	—
128	C₃×C₄×C₅	—	6	1	no	—
129	C₃×C₄×C₅	#67	1	2	yes	direct product factor
130	C₃×C₄×C₅	C₃×D₄	1	2	yes	complemented
131	C₅×Dic₃	—	2	1	no	—
132	C₅×Dic₃	—	2	1	no	—
133	C₅×Dic₃	C₂×C₃×C₄	1	2	yes	complemented
134	C₂×C₃×D₄	—	3	1	no	—
135	C₂²×C₃×C₄	—	2	1	no	—
136	C₂²×C₃×C₄	—	3	1	no	—
137	C₂²×C₃×C₄	C₅×D₃	1	1	yes	characteristic, complemented
138	C₂²×C₃×C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
139	C₂×#67	C₂×C₃×C₅	1	1	yes	characteristic
140	C₂×C₄×D₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
141	C₃×C₄⋊C₄	—	3	1	no	—
142	C₃×C₂²⋊C₄	—	3	1	no	—
143	C₃×C₂²⋊C₄	—	3	1	no	—
144	C₃×C₄²	—	3	1	no	—
145	#217	C₂×C₃×C₅	1	1	yes	characteristic, complemented
146	(C₂×D₃)⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
147	Dic₃⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
148	C₄×Dic₃	C₂×C₃×C₅	1	1	yes	characteristic, complemented
149	C₃²×C₅	C₄×D₄	1	1	yes	characteristic, complemented, Hall
150	C₂³×C₅	—	3	1	no	—
151	C₂³×C₅	C₂×C₃×D₃	1	1	yes	characteristic
152	C₅×D₄	—	3	4	no	—
153	C₂×C₄×C₅	—	2	2	no	—
154	C₂×C₄×C₅	—	3	1	no	—
155	C₂×C₄×C₅	—	3	1	no	—
156	C₂×C₄×C₅	—	3	1	no	—
157	C₂×C₄×C₅	—	6	2	no	—
158	C₂×C₄×C₅	C₂×C₃×D₃	1	1	yes	characteristic
159	C₂×C₄×C₅	C₂×C₃×D₃	1	1	yes	characteristic
160	C₂²×C₃²	—	2	1	no	—
161	C₂²×C₃²	—	2	1	no	—
162	C₂²×C₃²	C₂×C₄×C₅	1	2	yes	complemented
163	C₂²×C₃²	C₂³×C₅	1	1	yes	characteristic
164	C₂×C₃×D₃	—	2	1	no	—
165	C₂×C₃×D₃	—	2	1	no	—
166	C₂×C₃×D₃	C₂×C₄×C₅	1	2	yes	complemented
167	C₃²×C₄	—	2	1	no	—
168	C₃²×C₄	C₅×D₄	1	2	yes	complemented
169	C₃×Dic₃	—	2	1	no	—
170	C₃×Dic₃	—	2	1	no	—
171	C₃×Dic₃	C₂×C₄×C₅	1	2	yes	complemented
172	C₄×D₄	—	3	1	no	Sylow
173	C₂×C₃×C₅	—	2	4	no	—
174	C₂×C₃×C₅	—	2	2	no	—
175	C₂×C₃×C₅	—	2	2	no	—
176	C₂×C₃×C₅	—	2	1	no	—
177	C₂×C₃×C₅	—	2	1	no	—
178	C₂×C₃×C₅	—	2	1	no	—
179	C₂×C₃×C₅	—	6	2	no	—
180	C₂×C₃×C₅	C₂×C₄×D₃	1	1	yes	characteristic
181	C₂×C₃×C₅	#235	1	1	yes	characteristic
182	C₂×C₃×C₅	C₂×#67	1	1	yes	characteristic
183	C₂×C₃×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
184	C₂×C₃×C₅	C₂×C₃×D₄	1	1	yes	characteristic
185	C₂×C₃×C₅	C₃×#41	1	1	yes	characteristic
186	C₅×D₃	—	2	2	no	—
187	C₂³×C₃	—	2	1	no	—
188	C₂³×C₃	—	3	1	no	—
189	C₂³×C₃	C₂×C₅×D₃	1	1	yes	characteristic
190	C₂³×C₃	C₂²×C₃×C₅	1	1	yes	characteristic
191	C₂²×D₃	C₂²×C₃×C₅	1	1	yes	characteristic
192	C₃×D₄	—	3	4	no	—
193	C₂×C₃×C₄	—	2	4	no	—
194	C₂×C₃×C₄	—	2	2	no	—
195	C₂×C₃×C₄	—	2	2	no	—
196	C₂×C₃×C₄	—	2	1	no	—
197	C₂×C₃×C₄	—	2	1	no	—
198	C₂×C₃×C₄	—	3	1	no	—
199	C₂×C₃×C₄	—	3	1	no	—
200	C₂×C₃×C₄	—	3	1	no	—
201	C₂×C₃×C₄	—	6	2	no	—
202	C₂×C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic
203	C₂×C₃×C₄	C₂×C₅×D₃	1	1	yes	characteristic
204	C₂×C₃×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
205	C₂×C₃×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
206	#67	C₃×C₄×C₅	1	4	yes	direct product factor
207	C₂×Dic₃	C₂²×C₃×C₅	1	1	yes	characteristic
208	C₂×Dic₃	C₂²×C₃×C₅	1	1	yes	characteristic
209	C₂×Dic₃	C₂²×C₃×C₅	1	1	yes	characteristic
210	C₄×D₃	—	2	2	no	—
211	C₂²×C₅	—	2	1	no	—
212	C₂²×C₅	—	2	1	no	—
213	C₂²×C₅	—	3	2	no	—
214	C₂²×C₅	—	6	1	no	—
215	C₂²×C₅	—	6	1	no	—
216	C₂²×C₅	C₃×C₄×D₃	1	2	yes	complemented
217	C₂²×C₅	C₂²×C₃×D₃	1	1	yes	characteristic
218	C₄×C₅	—	2	1	no	—
219	C₄×C₅	—	3	2	no	—
220	C₄×C₅	—	6	1	no	—
221	C₄×C₅	—	6	1	no	—
222	C₄×C₅	C₃×#67	1	2	yes	direct product factor
223	C₂×C₃²	—	2	2	no	—
224	C₂×C₃²	C₂²×C₄×C₅	1	1	yes	characteristic
225	C₂×C₃²	C₂×C₅×D₄	1	1	yes	characteristic
226	C₂×C₃²	C₅×#41	1	1	yes	characteristic
227	C₃×D₃	—	2	2	no	—
228	C₂×D₄	—	3	1	no	—
229	C₂²×C₄	—	3	1	no	—
230	C₂²×C₄	C₃×C₅×D₃	1	1	yes	characteristic, complemented
231	C₄⋊C₄	—	3	1	no	—
232	C₂²⋊C₄	—	3	1	no	—
233	C₂²⋊C₄	—	3	1	no	—
234	C₄²	—	3	1	no	—
235	C₃×C₅	—	2	1	no	—
236	C₃×C₅	C₄×#67	1	1	yes	characteristic, direct product factor
237	C₃×C₅	C₃×C₄×D₄	1	1	yes	characteristic, complemented
238	C₂²×C₃	—	2	2	no	—
239	C₂²×C₃	—	2	2	no	—
240	C₂²×C₃	—	2	1	no	—
241	C₂²×C₃	—	2	1	no	—
242	C₂²×C₃	—	2	1	no	—
243	C₂²×C₃	—	2	1	no	—
244	C₂²×C₃	—	2	2	no	—
245	C₂²×C₃	—	2	1	no	—
246	C₂²×C₃	—	3	2	no	—
247	C₂²×C₃	—	6	1	no	—
248	C₂²×C₃	—	6	1	no	—
249	C₂²×C₃	C₄×C₅×D₃	1	2	yes	complemented
250	C₂²×C₃	C₂×C₃×C₄×C₅	1	2	yes	complemented
251	C₂²×C₃	C₂²×C₅×D₃	1	1	yes	characteristic
252	C₂²×C₃	C₂³×C₃×C₅	1	1	yes	characteristic
253	C₂×D₃	—	2	1	no	—
254	C₂×D₃	—	2	1	no	—
255	C₂×D₃	C₂×C₃×C₄×C₅	1	2	yes	complemented
256	C₃×C₄	—	2	2	no	—
257	C₃×C₄	—	2	1	no	—
258	C₃×C₄	—	2	1	no	—
259	C₃×C₄	—	2	2	no	—
260	C₃×C₄	—	3	2	no	—
261	C₃×C₄	—	6	1	no	—
262	C₃×C₄	—	6	1	no	—
263	C₃×C₄	C₅×#67	1	2	yes	direct product factor
264	C₃×C₄	C₃×C₅×D₄	1	2	yes	complemented
265	Dic₃	—	2	1	no	—
266	Dic₃	—	2	1	no	—
267	Dic₃	C₂×C₃×C₄×C₅	1	2	yes	complemented
268	C₂×C₅	—	2	2	no	—
269	C₂×C₅	—	6	2	no	—
270	C₂×C₅	C₂×C₃×C₄×D₃	1	1	yes	characteristic
271	C₂×C₅	C₃×#235	1	1	yes	characteristic
272	C₂×C₅	C₂×C₃×#67	1	1	yes	characteristic
273	C₃²	C₄×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
274	C₂³	—	3	1	no	—
275	C₂³	C₂×C₃×C₅×D₃	1	1	yes	characteristic
276	D₄	—	3	4	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	3	1	no	—
279	C₂×C₄	—	3	1	no	—
280	C₂×C₄	—	3	1	no	—
281	C₂×C₄	—	6	2	no	—
282	C₂×C₄	C₂×C₃×C₅×D₃	1	1	yes	characteristic
283	C₂×C₄	C₂×C₃×C₅×D₃	1	1	yes	characteristic
284	C₂×C₃	—	2	4	no	—
285	C₂×C₃	—	2	2	no	—
286	C₂×C₃	—	2	2	no	—
287	C₂×C₃	—	2	1	no	—
288	C₂×C₃	—	2	1	no	—
289	C₂×C₃	—	2	1	no	—
290	C₂×C₃	—	6	2	no	—
291	C₂×C₃	C₂×C₄×C₅×D₃	1	1	yes	characteristic
292	C₂×C₃	C₅×#235	1	1	yes	characteristic
293	C₂×C₃	C₂×C₅×#67	1	1	yes	characteristic
294	C₂×C₃	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
295	C₂×C₃	C₂×C₃×C₅×D₄	1	1	yes	characteristic
296	C₂×C₃	C₃×C₅×#41	1	1	yes	characteristic
297	D₃	—	2	2	no	—
298	C₅	C₃×C₄×#67	1	1	yes	characteristic, direct product factor, Sylow
299	C₂²	—	2	1	no	—
300	C₂²	—	2	1	no	—
301	C₂²	—	3	2	no	—
302	C₂²	—	6	1	no	—
303	C₂²	—	6	1	no	—
304	C₂²	C₃×C₄×C₅×D₃	1	2	yes	complemented
305	C₂²	C₂²×C₃×C₅×D₃	1	1	yes	characteristic
306	C₄	—	2	1	no	—
307	C₄	—	3	2	no	—
308	C₄	—	6	1	no	—
309	C₄	—	6	1	no	—
310	C₄	C₃×C₅×#67	1	2	yes	direct product factor
311	C₃	—	2	1	no	—
312	C₃	C₄×C₅×#67	1	1	yes	characteristic, direct product factor
313	C₃	C₃×C₄×C₅×D₄	1	1	yes	characteristic, complemented
314	C₂	—	2	2	no	—
315	C₂	—	6	2	no	—
316	C₂	C₂×C₃×C₄×C₅×D₃	1	1	yes	characteristic
317	C₂	C₃×C₅×#235	1	1	yes	characteristic
318	C₂	C₂×C₃×C₅×#67	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₃
commutator	C₂×C₃	C₂²×C₃×C₄×C₅
Frattini	C₂²	C₂²×C₃×C₅×D₃
Fitting	C₂²×C₃²×C₄×C₅	C₂
socle	C₂²×C₃²×C₅	C₂³
prime radical	C₂×C₃×C₅×#67	C₂
cosocle	C₂²×C₃	C₂³×C₃×C₅
hypercenter	C₂²×C₃×C₄×C₅	D₃
hypocenter	C₃	C₃×C₄×C₅×D₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂²×C₃×C₄×C₅

Complements

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

N	H ≅ G/N	type
1. C₂²×C₃²×C₄×C₅	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₃	C₂	semidirect
4. C₃×C₅×#217	C₂	semidirect
5. C₃×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
6. C₃×C₅×Dic₃⋊C₄	C₂	semidirect
7. C₃×C₄×C₅×Dic₃	C₂	semidirect
9. C₄×C₅×#67	C₃	direct (N × H)
15. C₃×C₅×#67	C₄	direct (N × H)
20. C₃×C₄×#67	C₅	direct (N × H)
24. C₂²×C₃×C₄×C₅	D₃	semidirect
25. C₂²×C₃×C₄×C₅	C₂×C₃	semidirect
27. C₂×C₄×C₅×D₃	C₂×C₃	semidirect
32. C₅×#217	C₂×C₃	semidirect
33. C₅×(C₂×D₃)⋊C₄	C₂×C₃	semidirect
34. C₅×Dic₃⋊C₄	C₂×C₃	semidirect
35. C₄×C₅×Dic₃	C₂×C₃	semidirect
38. C₂²×C₃²×C₅	C₂×C₄	semidirect
42. C₂×C₃×C₅×D₃	C₂×C₄	semidirect
44. C₃²×C₄×C₅	D₄	semidirect
47. C₃×C₅×Dic₃	C₂×C₄	semidirect
49. C₂²×C₃²×C₄	C₂×C₅	semidirect
51. C₂×C₃×C₄×D₃	C₂×C₅	semidirect
52. C₃×#217	C₂×C₅	semidirect
53. C₃×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
54. C₃×Dic₃⋊C₄	C₂×C₅	semidirect
55. C₃×C₄×Dic₃	C₂×C₅	semidirect
75. C₅×#67	C₃×C₄	direct (N × H)
81. C₄×#67	C₃×C₅	direct (N × H)
89. C₂²×C₄×C₅	C₃×D₃	semidirect
99. C₃×#67	C₄×C₅	direct (N × H)
115. C₂²×C₃×C₅	C₄×D₃	semidirect
116. C₂²×C₃×C₅	C₂×C₃×C₄	semidirect
121. C₂×C₅×D₃	C₂×C₃×C₄	semidirect
129. C₃×C₄×C₅	#67	direct (N × H)
130. C₃×C₄×C₅	C₃×D₄	semidirect
133. C₅×Dic₃	C₂×C₃×C₄	semidirect
137. C₂²×C₃×C₄	C₅×D₃	semidirect
138. C₂²×C₃×C₄	C₂×C₃×C₅	semidirect
140. C₂×C₄×D₃	C₂×C₃×C₅	semidirect
145. #217	C₂×C₃×C₅	semidirect
146. (C₂×D₃)⋊C₄	C₂×C₃×C₅	semidirect
147. Dic₃⋊C₄	C₂×C₃×C₅	semidirect
148. C₄×Dic₃	C₂×C₃×C₅	semidirect
149. C₃²×C₅	C₄×D₄	semidirect
162. C₂²×C₃²	C₂×C₄×C₅	semidirect
166. C₂×C₃×D₃	C₂×C₄×C₅	semidirect
168. C₃²×C₄	C₅×D₄	semidirect
171. C₃×Dic₃	C₂×C₄×C₅	semidirect
206. #67	C₃×C₄×C₅	direct (N × H)
216. C₂²×C₅	C₃×C₄×D₃	semidirect
222. C₄×C₅	C₃×#67	direct (N × H)
230. C₂²×C₄	C₃×C₅×D₃	semidirect
236. C₃×C₅	C₄×#67	direct (N × H)
237. C₃×C₅	C₃×C₄×D₄	semidirect
249. C₂²×C₃	C₄×C₅×D₃	semidirect
250. C₂²×C₃	C₂×C₃×C₄×C₅	semidirect
255. C₂×D₃	C₂×C₃×C₄×C₅	semidirect
263. C₃×C₄	C₅×#67	direct (N × H)
264. C₃×C₄	C₃×C₅×D₄	semidirect
267. Dic₃	C₂×C₃×C₄×C₅	semidirect
273. C₃²	C₄×C₅×D₄	semidirect
298. C₅	C₃×C₄×#67	direct (N × H)
304. C₂²	C₃×C₄×C₅×D₃	semidirect
310. C₄	C₃×C₅×#67	direct (N × H)
312. C₃	C₄×C₅×#67	direct (N × H)
313. C₃	C₃×C₄×C₅×D₄	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂²×C₃²×C₄×C₅	2
C₂×C₃×C₅×#67	2
C₂×C₃×C₄×C₅×D₃	2
C₃×C₅×#217	2
C₃×C₅×(C₂×D₃)⋊C₄	2
C₃×C₅×Dic₃⋊C₄	2
C₃×C₄×C₅×Dic₃	2
C₃×C₄×C₅×D₄	3
C₄×C₅×#67	3
C₃×C₄×#67	5

Subgroups — C3×C4×C5×#67 #13087939

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×#67 #13087939