Subgroups — C₃×C₅×#2007 #14275041

Order 1920.

740 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal, complemented
2	C₃×C₅×#537	C₂	1	1	yes	maximal, characteristic
3	C₂×C₃×C₅×#104	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#343	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×#2007	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂×C₃×C₅×#41	C₂²	1	2	yes	—
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₃×C₅×#137	—	2	4	no	—
10	C₃×C₅×#137	—	2	4	no	—
11	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
12	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
13	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
14	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
15	C₃×C₅×#121	—	2	2	no	—
16	C₃×C₅×#121	—	2	2	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
19	C₃×C₅×#104	—	2	4	no	—
20	C₃×C₅×#95	—	2	2	no	—
21	C₃×#2007	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
22	C₂×C₅×#137	C₂×C₃	1	2	yes	complemented
23	C₅×#537	C₂×C₃	1	1	yes	characteristic
24	C₂×C₅×#104	C₂×C₃	1	2	yes	complemented
25	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
26	C₅×#343	C₂×C₃	1	1	yes	characteristic, complemented
27	C₃×C₅×#41	—	2	2	no	—
28	C₃×C₅×#41	—	2	2	no	—
29	C₃×C₅×#41	—	2	2	no	—
30	C₃×C₅×#41	—	2	2	no	—
31	C₂×C₃×C₅×Q₈	—	2	1	no	—
32	C₂×C₃×C₅×Q₈	—	2	2	no	—
33	C₂×C₃×C₅×Q₈	—	2	2	no	—
34	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
35	C₂×C₃×C₅×Q₈	D₄	1	2	yes	complemented
36	C₂×C₃×C₅×D₄	—	2	2	no	—
37	C₂×C₃×C₅×D₄	—	2	2	no	—
38	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
39	C₂²×C₃×C₄×C₅	—	2	1	no	—
40	C₂²×C₃×C₄×C₅	—	2	1	no	—
41	C₂²×C₃×C₄×C₅	—	2	2	no	—
42	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₃×C₅×Q₁₆	—	2	8	no	—
45	C₃×C₅×SD₁₆	—	2	8	no	—
46	C₃×C₅×M₁₆	—	2	2	no	—
47	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
48	C₂×C₃×C₅×C₈	—	2	2	no	—
49	C₃×C₅×C₄⋊C₄	—	2	2	no	—
50	C₃×C₅×C₄⋊C₄	—	2	2	no	—
51	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
52	C₃×C₄²×C₅	—	2	2	no	—
53	C₂×C₃×#137	C₂×C₅	1	2	yes	complemented
54	C₃×#537	C₂×C₅	1	1	yes	characteristic
55	C₂×C₃×#104	C₂×C₅	1	2	yes	complemented
56	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
57	C₃×#343	C₂×C₅	1	1	yes	characteristic, complemented
58	C₂×C₅×#41	C₂²×C₃	1	2	yes	—
59	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
60	C₅×#137	—	2	4	no	—
61	C₅×#137	—	2	4	no	—
62	C₂×C₅×Q₁₆	—	2	2	no	—
63	C₂×C₅×SD₁₆	—	2	2	no	—
64	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
65	C₅×C₂²⋊Q₈	—	2	2	no	—
66	C₅×#121	—	2	2	no	—
67	C₅×#121	—	2	2	no	—
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
69	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
70	C₅×#104	—	2	4	no	—
71	C₅×#95	—	2	2	no	—
72	#2007	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
73	C₂³×C₃×C₅	—	2	2	no	—
74	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
75	C₃×C₅×Q₈	—	2	4	no	—
76	C₃×C₅×Q₈	—	2	2	no	—
77	C₃×C₅×Q₈	—	2	2	no	—
78	C₃×C₅×Q₈	—	4	2	no	—
79	C₃×C₅×D₄	—	2	2	no	—
80	C₃×C₅×D₄	—	2	2	no	—
81	C₃×C₅×D₄	—	4	2	no	—
82	C₃×C₅×D₄	—	4	2	no	—
83	C₃×C₅×D₄	—	8	2	no	—
84	C₂×C₃×C₄×C₅	—	2	2	no	—
85	C₂×C₃×C₄×C₅	—	2	2	no	—
86	C₂×C₃×C₄×C₅	—	2	2	no	—
87	C₂×C₃×C₄×C₅	—	2	2	no	—
88	C₂×C₃×C₄×C₅	—	4	1	no	—
89	C₂×C₃×C₄×C₅	—	4	1	no	—
90	C₂×C₃×C₄×C₅	—	4	1	no	—
91	C₂×C₃×C₄×C₅	—	4	1	no	—
92	C₂×C₃×C₄×C₅	—	4	2	no	—
93	C₂×C₃×C₄×C₅	—	4	2	no	—
94	C₂×C₃×C₄×C₅	—	4	2	no	—
95	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
96	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
97	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
98	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
99	C₃×C₅×C₈	—	2	4	no	—
100	C₂×C₃×#41	C₂²×C₅	1	2	yes	—
101	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
102	C₃×#137	—	2	4	no	—
103	C₃×#137	—	2	4	no	—
104	C₂×C₃×Q₁₆	—	2	2	no	—
105	C₂×C₃×SD₁₆	—	2	2	no	—
106	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
107	C₃×C₂²⋊Q₈	—	2	2	no	—
108	C₃×#121	—	2	2	no	—
109	C₃×#121	—	2	2	no	—
110	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
111	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
112	C₃×#104	—	2	4	no	—
113	C₃×#95	—	2	2	no	—
114	C₅×#41	—	2	2	no	—
115	C₅×#41	—	2	2	no	—
116	C₅×#41	—	2	2	no	—
117	C₅×#41	—	2	2	no	—
118	C₂×C₅×Q₈	—	2	1	no	—
119	C₂×C₅×Q₈	—	2	2	no	—
120	C₂×C₅×Q₈	—	2	2	no	—
121	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
122	C₂×C₅×Q₈	C₃×D₄	1	2	yes	complemented
123	C₂×C₅×D₄	—	2	2	no	—
124	C₂×C₅×D₄	—	2	2	no	—
125	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
126	C₂²×C₄×C₅	—	2	1	no	—
127	C₂²×C₄×C₅	—	2	1	no	—
128	C₂²×C₄×C₅	—	2	2	no	—
129	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
130	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
131	C₅×Q₁₆	—	2	8	no	—
132	C₅×SD₁₆	—	2	8	no	—
133	C₅×M₁₆	—	2	2	no	—
134	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
135	C₂×C₅×C₈	—	2	2	no	—
136	C₅×C₄⋊C₄	—	2	2	no	—
137	C₅×C₄⋊C₄	—	2	2	no	—
138	C₅×C₂²⋊C₄	—	2	4	no	—
139	C₄²×C₅	—	2	2	no	—
140	C₂×#137	C₂×C₃×C₅	1	2	yes	complemented
141	#537	C₂×C₃×C₅	1	1	yes	characteristic
142	C₂×#104	C₂×C₃×C₅	1	2	yes	complemented
143	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
144	#343	C₂×C₃×C₅	1	1	yes	characteristic, complemented
145	C₂²×C₃×C₅	—	2	1	no	—
146	C₂²×C₃×C₅	—	2	1	no	—
147	C₂²×C₃×C₅	—	4	2	no	—
148	C₂²×C₃×C₅	—	4	2	no	—
149	C₂²×C₃×C₅	—	4	2	no	—
150	C₂²×C₃×C₅	#120	1	1	yes	characteristic
151	C₂²×C₃×C₅	#121	1	1	yes	characteristic
152	C₂²×C₃×C₅	#127	1	1	yes	characteristic
153	C₃×C₄×C₅	—	4	2	no	—
154	C₃×C₄×C₅	—	4	2	no	—
155	C₃×C₄×C₅	—	4	2	no	—
156	C₃×C₄×C₅	—	4	2	no	—
157	C₃×C₄×C₅	#120	1	2	yes	—
158	C₃×C₄×C₅	#121	1	2	yes	—
159	C₃×#41	—	2	2	no	—
160	C₃×#41	—	2	2	no	—
161	C₃×#41	—	2	2	no	—
162	C₃×#41	—	2	2	no	—
163	C₂×C₃×Q₈	—	2	1	no	—
164	C₂×C₃×Q₈	—	2	2	no	—
165	C₂×C₃×Q₈	—	2	2	no	—
166	C₂×C₃×Q₈	C₅×D₄	1	2	yes	—
167	C₂×C₃×Q₈	C₅×D₄	1	2	yes	complemented
168	C₂×C₃×D₄	—	2	2	no	—
169	C₂×C₃×D₄	—	2	2	no	—
170	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
171	C₂²×C₃×C₄	—	2	1	no	—
172	C₂²×C₃×C₄	—	2	1	no	—
173	C₂²×C₃×C₄	—	2	2	no	—
174	C₂²×C₃×C₄	C₅×D₄	1	2	yes	—
175	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
176	C₃×Q₁₆	—	2	8	no	—
177	C₃×SD₁₆	—	2	8	no	—
178	C₃×M₁₆	—	2	2	no	—
179	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
180	C₂×C₃×C₈	—	2	2	no	—
181	C₃×C₄⋊C₄	—	2	2	no	—
182	C₃×C₄⋊C₄	—	2	2	no	—
183	C₃×C₂²⋊C₄	—	2	4	no	—
184	C₃×C₄²	—	2	2	no	—
185	C₂³×C₅	—	2	2	no	—
186	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
187	C₅×Q₈	—	2	4	no	—
188	C₅×Q₈	—	2	2	no	—
189	C₅×Q₈	—	2	2	no	—
190	C₅×Q₈	—	4	2	no	—
191	C₅×D₄	—	2	2	no	—
192	C₅×D₄	—	2	2	no	—
193	C₅×D₄	—	4	2	no	—
194	C₅×D₄	—	4	2	no	—
195	C₅×D₄	—	8	2	no	—
196	C₂×C₄×C₅	—	2	2	no	—
197	C₂×C₄×C₅	—	2	2	no	—
198	C₂×C₄×C₅	—	2	2	no	—
199	C₂×C₄×C₅	—	2	2	no	—
200	C₂×C₄×C₅	—	4	1	no	—
201	C₂×C₄×C₅	—	4	1	no	—
202	C₂×C₄×C₅	—	4	1	no	—
203	C₂×C₄×C₅	—	4	1	no	—
204	C₂×C₄×C₅	—	4	2	no	—
205	C₂×C₄×C₅	—	4	2	no	—
206	C₂×C₄×C₅	—	4	2	no	—
207	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
208	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
209	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
210	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
211	C₅×C₈	—	2	4	no	—
212	C₂×#41	C₂²×C₃×C₅	1	2	yes	—
213	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
214	#137	—	2	4	no	—
215	#137	—	2	4	no	—
216	C₂×Q₁₆	—	2	2	no	—
217	C₂×SD₁₆	—	2	2	no	—
218	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
219	C₂²⋊Q₈	—	2	2	no	—
220	#121	—	2	2	no	—
221	#121	—	2	2	no	—
222	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
223	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
224	#104	—	2	4	no	—
225	#95	—	2	2	no	—
226	C₂×C₃×C₅	—	2	1	no	—
227	C₂×C₃×C₅	—	2	1	no	—
228	C₂×C₃×C₅	—	8	2	no	—
229	C₂×C₃×C₅	#392	1	1	yes	characteristic
230	C₂×C₃×C₅	#455	1	1	yes	characteristic
231	C₂×C₃×C₅	#456	1	1	yes	characteristic
232	C₂³×C₃	—	2	2	no	—
233	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
234	C₃×Q₈	—	2	4	no	—
235	C₃×Q₈	—	2	2	no	—
236	C₃×Q₈	—	2	2	no	—
237	C₃×Q₈	—	4	2	no	—
238	C₃×D₄	—	2	2	no	—
239	C₃×D₄	—	2	2	no	—
240	C₃×D₄	—	4	2	no	—
241	C₃×D₄	—	4	2	no	—
242	C₃×D₄	—	8	2	no	—
243	C₂×C₃×C₄	—	2	2	no	—
244	C₂×C₃×C₄	—	2	2	no	—
245	C₂×C₃×C₄	—	2	2	no	—
246	C₂×C₃×C₄	—	2	2	no	—
247	C₂×C₃×C₄	—	4	1	no	—
248	C₂×C₃×C₄	—	4	1	no	—
249	C₂×C₃×C₄	—	4	1	no	—
250	C₂×C₃×C₄	—	4	1	no	—
251	C₂×C₃×C₄	—	4	2	no	—
252	C₂×C₃×C₄	—	4	2	no	—
253	C₂×C₃×C₄	—	4	2	no	—
254	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
255	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
256	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
257	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
258	C₃×C₈	—	2	4	no	—
259	C₂²×C₅	—	2	1	no	—
260	C₂²×C₅	—	2	1	no	—
261	C₂²×C₅	—	4	2	no	—
262	C₂²×C₅	—	4	2	no	—
263	C₂²×C₅	—	4	2	no	—
264	C₂²×C₅	C₃×#120	1	1	yes	characteristic
265	C₂²×C₅	C₃×#121	1	1	yes	characteristic
266	C₂²×C₅	C₃×#127	1	1	yes	characteristic
267	C₄×C₅	—	4	2	no	—
268	C₄×C₅	—	4	2	no	—
269	C₄×C₅	—	4	2	no	—
270	C₄×C₅	—	4	2	no	—
271	C₄×C₅	C₃×#120	1	2	yes	—
272	C₄×C₅	C₃×#121	1	2	yes	—
273	#41	—	2	2	no	—
274	#41	—	2	2	no	—
275	#41	—	2	2	no	—
276	#41	—	2	2	no	—
277	C₂×Q₈	—	2	1	no	—
278	C₂×Q₈	—	2	2	no	—
279	C₂×Q₈	—	2	2	no	—
280	C₂×Q₈	C₃×C₅×D₄	1	2	yes	—
281	C₂×Q₈	C₃×C₅×D₄	1	2	yes	complemented
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
285	C₂²×C₄	—	2	1	no	—
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	2	2	no	—
288	C₂²×C₄	C₃×C₅×D₄	1	2	yes	—
289	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
290	Q₁₆	—	2	8	no	—
291	SD₁₆	—	2	8	no	—
292	M₁₆	—	2	2	no	—
293	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
294	C₂×C₈	—	2	2	no	—
295	C₄⋊C₄	—	2	2	no	—
296	C₄⋊C₄	—	2	2	no	—
297	C₂²⋊C₄	—	2	4	no	—
298	C₄²	—	2	2	no	—
299	C₃×C₅	#2007	1	1	yes	characteristic, direct product factor, Hall
300	C₂²×C₃	—	2	1	no	—
301	C₂²×C₃	—	2	1	no	—
302	C₂²×C₃	—	4	2	no	—
303	C₂²×C₃	—	4	2	no	—
304	C₂²×C₃	—	4	2	no	—
305	C₂²×C₃	C₅×#120	1	1	yes	characteristic
306	C₂²×C₃	C₅×#121	1	1	yes	characteristic
307	C₂²×C₃	C₅×#127	1	1	yes	characteristic
308	C₃×C₄	—	4	2	no	—
309	C₃×C₄	—	4	2	no	—
310	C₃×C₄	—	4	2	no	—
311	C₃×C₄	—	4	2	no	—
312	C₃×C₄	C₅×#120	1	2	yes	—
313	C₃×C₄	C₅×#121	1	2	yes	—
314	C₂×C₅	—	2	1	no	—
315	C₂×C₅	—	2	1	no	—
316	C₂×C₅	—	8	2	no	—
317	C₂×C₅	C₃×#392	1	1	yes	characteristic
318	C₂×C₅	C₃×#455	1	1	yes	characteristic
319	C₂×C₅	C₃×#456	1	1	yes	characteristic
320	C₂³	—	2	2	no	—
321	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
322	Q₈	—	2	4	no	—
323	Q₈	—	2	2	no	—
324	Q₈	—	2	2	no	—
325	Q₈	—	4	2	no	—
326	D₄	—	2	2	no	—
327	D₄	—	2	2	no	—
328	D₄	—	4	2	no	—
329	D₄	—	4	2	no	—
330	D₄	—	8	2	no	—
331	C₂×C₄	—	2	2	no	—
332	C₂×C₄	—	2	2	no	—
333	C₂×C₄	—	2	2	no	—
334	C₂×C₄	—	2	2	no	—
335	C₂×C₄	—	4	1	no	—
336	C₂×C₄	—	4	1	no	—
337	C₂×C₄	—	4	1	no	—
338	C₂×C₄	—	4	1	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	4	2	no	—
342	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
343	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
344	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
345	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
346	C₈	—	2	4	no	—
347	C₂×C₃	—	2	1	no	—
348	C₂×C₃	—	2	1	no	—
349	C₂×C₃	—	8	2	no	—
350	C₂×C₃	C₅×#392	1	1	yes	characteristic
351	C₂×C₃	C₅×#455	1	1	yes	characteristic
352	C₂×C₃	C₅×#456	1	1	yes	characteristic
353	C₅	C₃×#2007	1	1	yes	characteristic, direct product factor, Sylow
354	C₂²	—	2	1	no	—
355	C₂²	—	2	1	no	—
356	C₂²	—	4	2	no	—
357	C₂²	—	4	2	no	—
358	C₂²	—	4	2	no	—
359	C₂²	C₃×C₅×#120	1	1	yes	characteristic
360	C₂²	C₃×C₅×#121	1	1	yes	characteristic
361	C₂²	C₃×C₅×#127	1	1	yes	characteristic
362	C₄	—	4	2	no	—
363	C₄	—	4	2	no	—
364	C₄	—	4	2	no	—
365	C₄	—	4	2	no	—
366	C₄	C₃×C₅×#120	1	2	yes	—
367	C₄	C₃×C₅×#121	1	2	yes	—
368	C₃	C₅×#2007	1	1	yes	characteristic, direct product factor, Sylow
369	C₂	—	2	1	no	—
370	C₂	—	2	1	no	—
371	C₂	—	8	2	no	—
372	C₂	C₃×C₅×#392	1	1	yes	characteristic
373	C₂	C₃×C₅×#455	1	1	yes	characteristic
374	C₂	C₃×C₅×#456	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#120
commutator, Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
prime radical	C₃×C₅×#537	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
3. C₂×C₃×C₅×#104	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#343	C₂	semidirect
6. C₅×#2007	C₃	direct (N × H)
21. C₃×#2007	C₅	direct (N × H)
22. C₂×C₅×#137	C₂×C₃	semidirect
24. C₂×C₅×#104	C₂×C₃	semidirect
25. C₅×#391	C₂×C₃	semidirect
26. C₅×#343	C₂×C₃	semidirect
35. C₂×C₃×C₅×Q₈	D₄	semidirect
47. C₃×C₅×M₁₆	D₄	semidirect
53. C₂×C₃×#137	C₂×C₅	semidirect
55. C₂×C₃×#104	C₂×C₅	semidirect
56. C₃×#391	C₂×C₅	semidirect
57. C₃×#343	C₂×C₅	semidirect
72. #2007	C₃×C₅	direct (N × H)
122. C₂×C₅×Q₈	C₃×D₄	semidirect
134. C₅×M₁₆	C₃×D₄	semidirect
140. C₂×#137	C₂×C₃×C₅	semidirect
142. C₂×#104	C₂×C₃×C₅	semidirect
143. #391	C₂×C₃×C₅	semidirect
144. #343	C₂×C₃×C₅	semidirect
167. C₂×C₃×Q₈	C₅×D₄	semidirect
179. C₃×M₁₆	C₅×D₄	semidirect
281. C₂×Q₈	C₃×C₅×D₄	semidirect
293. M₁₆	C₃×C₅×D₄	semidirect
299. C₃×C₅	#2007	direct (N × H)
353. C₅	C₃×#2007	direct (N × H)
368. C₃	C₅×#2007	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×C₅×#137	2
C₃×C₅×#537	2
C₂×C₃×C₅×#104	2
C₃×C₅×#391	2
C₃×C₅×#343	2
C₅×#2007	3
C₃×#2007	5

Subgroups — C3×C5×#2007 #14275041

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2007 #14275041