Subgroups — C₃×C₅×#67⋊C₄ #13087893

Order 1440.

410 conjugacy classes of subgroups.

The subgroup lattice has 318 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

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

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

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×Dic₃	C₂	semidirect
3. C₂×C₃×C₄×C₅×D₃	C₂	semidirect
4. C₃²×C₅×C₂²⋊C₄	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. C₅×#67⋊C₄	C₃	direct (N × H)
14. C₃×C₅×#67	C₄	semidirect
20. C₃×#67⋊C₄	C₅	direct (N × H)
25. C₂²×C₅×Dic₃	C₂×C₃	semidirect
26. C₂×C₄×C₅×D₃	C₂×C₃	semidirect
30. C₃×C₅×C₂²⋊C₄	D₃	semidirect
31. C₃×C₅×C₂²⋊C₄	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
46. C₃×C₅×Dic₃	C₂×C₄	semidirect
47. C₃×C₅×Dic₃	D₄	semidirect
50. C₂²×C₃×Dic₃	C₂×C₅	semidirect
51. C₂×C₃×C₄×D₃	C₂×C₅	semidirect
52. C₃²×C₂²⋊C₄	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
73. C₅×#67	C₃×C₄	semidirect
80. #67⋊C₄	C₃×C₅	direct (N × H)
91. C₅×C₂²⋊C₄	C₃×D₃	semidirect
97. C₃×#67	C₄×C₅	semidirect
114. C₂²×C₃×C₅	C₄×D₃	semidirect
115. C₂²×C₃×C₅	C₂×C₃×C₄	semidirect
120. C₂×C₅×D₃	C₂×C₃×C₄	semidirect
131. C₅×Dic₃	C₂×C₃×C₄	semidirect
132. C₅×Dic₃	C₃×D₄	semidirect
137. C₂²×Dic₃	C₂×C₃×C₅	semidirect
138. C₂×C₄×D₃	C₂×C₃×C₅	semidirect
142. C₃×C₂²⋊C₄	C₅×D₃	semidirect
143. C₃×C₂²⋊C₄	C₂×C₃×C₅	semidirect
145. (C₂×D₃)⋊C₄	C₂×C₃×C₅	semidirect
146. Dic₃⋊C₄	C₂×C₃×C₅	semidirect
147. C₄×Dic₃	C₂×C₃×C₅	semidirect
148. C₃²×C₅	C₄×D₄	semidirect
161. C₂²×C₃²	C₂×C₄×C₅	semidirect
165. C₂×C₃×D₃	C₂×C₄×C₅	semidirect
169. C₃×Dic₃	C₂×C₄×C₅	semidirect
170. C₃×Dic₃	C₅×D₄	semidirect
203. #67	C₃×C₄×C₅	semidirect
214. C₂²×C₅	C₃×C₄×D₃	semidirect
231. C₂²⋊C₄	C₃×C₅×D₃	semidirect
234. C₃×C₅	#67⋊C₄	direct (N × H)
235. C₃×C₅	C₃×C₄×D₄	semidirect
247. C₂²×C₃	C₄×C₅×D₃	semidirect
248. C₂²×C₃	C₂×C₃×C₄×C₅	semidirect
253. C₂×D₃	C₂×C₃×C₄×C₅	semidirect
264. Dic₃	C₂×C₃×C₄×C₅	semidirect
265. Dic₃	C₃×C₅×D₄	semidirect
271. C₃²	C₄×C₅×D₄	semidirect
296. C₅	C₃×#67⋊C₄	direct (N × H)
302. C₂²	C₃×C₄×C₅×D₃	semidirect
310. C₃	C₅×#67⋊C₄	direct (N × H)
311. 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
C₂×C₃×C₅×#67	2
C₂²×C₃×C₅×Dic₃	2
C₂×C₃×C₄×C₅×D₃	2
C₃²×C₅×C₂²⋊C₄	2
C₃×C₅×(C₂×D₃)⋊C₄	2
C₃×C₅×Dic₃⋊C₄	2
C₃×C₄×C₅×Dic₃	2
C₃×C₄×C₅×D₄	3
C₅×#67⋊C₄	3
C₃×#67⋊C₄	5

Subgroups — C3×C5×#67⋊C4 #13087893

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#67⋊C₄ #13087893