Subgroups — C₃×C₅×#2127 #14275161

Order 1920.

572 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#99	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#354	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#353	C₂	1	2	yes	maximal, complemented
5	C₅×#2127	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
6	C₂×C₃×C₅×#41	C₄	1	1	yes	characteristic, complemented
7	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
8	C₃×C₅×#127	C₄	1	1	yes	characteristic, complemented
9	C₃×C₅×#127	C₂²	1	1	yes	characteristic
10	C₃×C₅×#124	C₄	1	1	yes	characteristic, complemented
11	C₃×C₅×#124	C₂²	1	1	yes	characteristic
12	C₃×C₅×#121	—	2	2	no	—
13	C₃×C₅×#120	—	2	2	no	—
14	C₃×C₅×#117	C₄	1	1	yes	characteristic, complemented
15	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
16	C₃×C₅×#99	—	2	2	no	—
17	C₃×C₅×#99	C₂²	1	4	yes	—
18	C₃×#2127	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
19	C₅×#535	C₂×C₃	1	1	yes	characteristic
20	C₂×C₅×#99	C₂×C₃	1	2	yes	complemented
21	C₅×#354	C₂×C₃	1	2	yes	complemented
22	C₅×#353	C₂×C₃	1	2	yes	complemented
23	C₂⁴×C₃×C₅	D₄	1	2	yes	—
24	C₃×C₅×#41	—	4	2	no	—
25	C₂×C₃×C₅×Q₈	C₂×C₄	1	1	yes	characteristic, complemented
26	C₂×C₃×C₅×D₄	—	2	1	no	—
27	C₂×C₃×C₅×D₄	—	2	2	no	—
28	C₂×C₃×C₅×D₄	—	2	2	no	—
29	C₂×C₃×C₅×D₄	—	4	2	no	—
30	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic
31	C₂×C₃×C₅×D₄	C₂×C₄	1	1	yes	characteristic, complemented
32	C₂×C₃×C₅×D₄	D₄	1	2	yes	—
33	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	—	4	2	no	—
36	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
37	C₃×C₅×C₄⋊C₄	—	2	1	no	—
38	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
39	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
40	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
41	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
42	C₃×C₅×C₂²⋊C₄	—	4	2	no	—
43	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
44	C₃×C₄²×C₅	C₂×C₄	1	1	yes	characteristic, complemented
45	C₃×#535	C₂×C₅	1	1	yes	characteristic
46	C₂×C₃×#99	C₂×C₅	1	2	yes	complemented
47	C₃×#354	C₂×C₅	1	2	yes	complemented
48	C₃×#353	C₂×C₅	1	2	yes	complemented
49	C₂×C₅×#41	C₃×C₄	1	1	yes	characteristic, complemented
50	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
51	C₅×#127	C₃×C₄	1	1	yes	characteristic, complemented
52	C₅×#127	C₂²×C₃	1	1	yes	characteristic
53	C₅×#124	C₃×C₄	1	1	yes	characteristic, complemented
54	C₅×#124	C₂²×C₃	1	1	yes	characteristic
55	C₅×#121	—	2	2	no	—
56	C₅×#120	—	2	2	no	—
57	C₅×#117	C₃×C₄	1	1	yes	characteristic, complemented
58	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
59	C₅×#99	—	2	2	no	—
60	C₅×#99	C₂²×C₃	1	4	yes	—
61	#2127	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
62	C₂³×C₃×C₅	—	2	2	no	—
63	C₂³×C₃×C₅	—	2	2	no	—
64	C₂³×C₃×C₅	—	2	1	no	—
65	C₂³×C₃×C₅	—	8	2	no	—
66	C₂³×C₃×C₅	C₂²⋊C₄	1	2	yes	—
67	C₂³×C₃×C₅	C₂²⋊C₄	1	1	yes	characteristic
68	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
69	C₃×C₅×Q₈	—	4	1	no	—
70	C₃×C₅×D₄	—	4	1	no	—
71	C₃×C₅×D₄	—	4	2	no	—
72	C₃×C₅×D₄	—	4	1	no	—
73	C₃×C₅×D₄	—	4	1	no	—
74	C₃×C₅×D₄	—	4	2	no	—
75	C₃×C₅×D₄	—	8	2	no	—
76	C₃×C₅×D₄	—	8	2	no	—
77	C₂×C₃×C₄×C₅	—	2	2	no	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	—	2	1	no	—
80	C₂×C₃×C₄×C₅	—	2	1	no	—
81	C₂×C₃×C₄×C₅	—	4	2	no	—
82	C₂×C₃×C₄×C₅	—	4	4	no	—
83	C₂×C₃×C₄×C₅	—	8	4	no	—
84	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	1	yes	characteristic
85	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
86	C₂×C₃×#41	C₄×C₅	1	1	yes	characteristic, complemented
87	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
88	C₃×#127	C₄×C₅	1	1	yes	characteristic, complemented
89	C₃×#127	C₂²×C₅	1	1	yes	characteristic
90	C₃×#124	C₄×C₅	1	1	yes	characteristic, complemented
91	C₃×#124	C₂²×C₅	1	1	yes	characteristic
92	C₃×#121	—	2	2	no	—
93	C₃×#120	—	2	2	no	—
94	C₃×#117	C₄×C₅	1	1	yes	characteristic, complemented
95	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
96	C₃×#99	—	2	2	no	—
97	C₃×#99	C₂²×C₅	1	4	yes	—
98	C₂⁴×C₅	C₃×D₄	1	2	yes	—
99	C₅×#41	—	4	2	no	—
100	C₂×C₅×Q₈	C₂×C₃×C₄	1	1	yes	characteristic, complemented
101	C₂×C₅×D₄	—	2	1	no	—
102	C₂×C₅×D₄	—	2	2	no	—
103	C₂×C₅×D₄	—	2	2	no	—
104	C₂×C₅×D₄	—	4	2	no	—
105	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic
106	C₂×C₅×D₄	C₂×C₃×C₄	1	1	yes	characteristic, complemented
107	C₂×C₅×D₄	C₃×D₄	1	2	yes	—
108	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
109	C₂²×C₄×C₅	—	2	1	no	—
110	C₂²×C₄×C₅	—	4	2	no	—
111	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
112	C₅×C₄⋊C₄	—	2	1	no	—
113	C₅×C₂²⋊C₄	—	2	1	no	—
114	C₅×C₂²⋊C₄	—	2	2	no	—
115	C₅×C₂²⋊C₄	—	2	2	no	—
116	C₅×C₂²⋊C₄	—	2	4	no	—
117	C₅×C₂²⋊C₄	—	4	2	no	—
118	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
119	C₄²×C₅	C₂×C₃×C₄	1	1	yes	characteristic, complemented
120	#535	C₂×C₃×C₅	1	1	yes	characteristic
121	C₂×#99	C₂×C₃×C₅	1	2	yes	complemented
122	#354	C₂×C₃×C₅	1	2	yes	complemented
123	#353	C₂×C₃×C₅	1	2	yes	complemented
124	C₂²×C₃×C₅	—	2	2	no	—
125	C₂²×C₃×C₅	—	2	2	no	—
126	C₂²×C₃×C₅	—	4	1	no	—
127	C₂²×C₃×C₅	—	4	2	no	—
128	C₂²×C₃×C₅	—	4	2	no	—
129	C₂²×C₃×C₅	—	4	4	no	—
130	C₂²×C₃×C₅	—	4	2	no	—
131	C₂²×C₃×C₅	—	4	1	no	—
132	C₂²×C₃×C₅	—	8	2	no	—
133	C₂²×C₃×C₅	#99	1	2	yes	—
134	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
135	C₃×C₄×C₅	—	2	1	no	—
136	C₃×C₄×C₅	—	2	1	no	—
137	C₃×C₄×C₅	—	4	1	no	—
138	C₃×C₄×C₅	—	4	1	no	—
139	C₃×C₄×C₅	—	4	1	no	—
140	C₃×C₄×C₅	—	8	4	no	—
141	C₂⁴×C₃	C₅×D₄	1	2	yes	—
142	C₃×#41	—	4	2	no	—
143	C₂×C₃×Q₈	C₂×C₄×C₅	1	1	yes	characteristic, complemented
144	C₂×C₃×D₄	—	2	1	no	—
145	C₂×C₃×D₄	—	2	2	no	—
146	C₂×C₃×D₄	—	2	2	no	—
147	C₂×C₃×D₄	—	4	2	no	—
148	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic
149	C₂×C₃×D₄	C₂×C₄×C₅	1	1	yes	characteristic, complemented
150	C₂×C₃×D₄	C₅×D₄	1	2	yes	—
151	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
152	C₂²×C₃×C₄	—	2	1	no	—
153	C₂²×C₃×C₄	—	4	2	no	—
154	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
155	C₃×C₄⋊C₄	—	2	1	no	—
156	C₃×C₂²⋊C₄	—	2	1	no	—
157	C₃×C₂²⋊C₄	—	2	2	no	—
158	C₃×C₂²⋊C₄	—	2	2	no	—
159	C₃×C₂²⋊C₄	—	2	4	no	—
160	C₃×C₂²⋊C₄	—	4	2	no	—
161	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic, complemented
162	C₃×C₄²	C₂×C₄×C₅	1	1	yes	characteristic, complemented
163	C₂³×C₅	—	2	2	no	—
164	C₂³×C₅	—	2	2	no	—
165	C₂³×C₅	—	2	1	no	—
166	C₂³×C₅	—	8	2	no	—
167	C₂³×C₅	C₃×C₂²⋊C₄	1	2	yes	—
168	C₂³×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
169	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
170	C₅×Q₈	—	4	1	no	—
171	C₅×D₄	—	4	1	no	—
172	C₅×D₄	—	4	2	no	—
173	C₅×D₄	—	4	1	no	—
174	C₅×D₄	—	4	1	no	—
175	C₅×D₄	—	4	2	no	—
176	C₅×D₄	—	8	2	no	—
177	C₅×D₄	—	8	2	no	—
178	C₂×C₄×C₅	—	2	2	no	—
179	C₂×C₄×C₅	—	2	1	no	—
180	C₂×C₄×C₅	—	2	1	no	—
181	C₂×C₄×C₅	—	2	1	no	—
182	C₂×C₄×C₅	—	4	2	no	—
183	C₂×C₄×C₅	—	4	4	no	—
184	C₂×C₄×C₅	—	8	4	no	—
185	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	1	yes	characteristic
186	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
187	C₂×#41	C₃×C₄×C₅	1	1	yes	characteristic, complemented
188	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
189	#127	C₃×C₄×C₅	1	1	yes	characteristic, complemented
190	#127	C₂²×C₃×C₅	1	1	yes	characteristic
191	#124	C₃×C₄×C₅	1	1	yes	characteristic, complemented
192	#124	C₂²×C₃×C₅	1	1	yes	characteristic
193	#121	—	2	2	no	—
194	#120	—	2	2	no	—
195	#117	C₃×C₄×C₅	1	1	yes	characteristic, complemented
196	C₂×C₂²⋊C₄	—	2	2	no	—
197	#99	—	2	2	no	—
198	#99	C₂²×C₃×C₅	1	4	yes	—
199	C₂×C₃×C₅	—	2	1	no	—
200	C₂×C₃×C₅	—	2	2	no	—
201	C₂×C₃×C₅	—	4	2	no	—
202	C₂×C₃×C₅	—	4	2	no	—
203	C₂×C₃×C₅	—	8	1	no	—
204	C₂×C₃×C₅	C₂×#99	1	1	yes	characteristic
205	C₂³×C₃	—	2	2	no	—
206	C₂³×C₃	—	2	2	no	—
207	C₂³×C₃	—	2	1	no	—
208	C₂³×C₃	—	8	2	no	—
209	C₂³×C₃	C₅×C₂²⋊C₄	1	2	yes	—
210	C₂³×C₃	C₅×C₂²⋊C₄	1	1	yes	characteristic
211	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
212	C₃×Q₈	—	4	1	no	—
213	C₃×D₄	—	4	1	no	—
214	C₃×D₄	—	4	2	no	—
215	C₃×D₄	—	4	1	no	—
216	C₃×D₄	—	4	1	no	—
217	C₃×D₄	—	4	2	no	—
218	C₃×D₄	—	8	2	no	—
219	C₃×D₄	—	8	2	no	—
220	C₂×C₃×C₄	—	2	2	no	—
221	C₂×C₃×C₄	—	2	1	no	—
222	C₂×C₃×C₄	—	2	1	no	—
223	C₂×C₃×C₄	—	2	1	no	—
224	C₂×C₃×C₄	—	4	2	no	—
225	C₂×C₃×C₄	—	4	4	no	—
226	C₂×C₃×C₄	—	8	4	no	—
227	C₂×C₃×C₄	C₅×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
229	C₂²×C₅	—	2	2	no	—
230	C₂²×C₅	—	2	2	no	—
231	C₂²×C₅	—	4	1	no	—
232	C₂²×C₅	—	4	2	no	—
233	C₂²×C₅	—	4	2	no	—
234	C₂²×C₅	—	4	4	no	—
235	C₂²×C₅	—	4	2	no	—
236	C₂²×C₅	—	4	1	no	—
237	C₂²×C₅	—	8	2	no	—
238	C₂²×C₅	C₃×#99	1	2	yes	—
239	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
240	C₄×C₅	—	2	1	no	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	4	1	no	—
243	C₄×C₅	—	4	1	no	—
244	C₄×C₅	—	4	1	no	—
245	C₄×C₅	—	8	4	no	—
246	C₂⁴	C₃×C₅×D₄	1	2	yes	—
247	#41	—	4	2	no	—
248	C₂×Q₈	C₂×C₃×C₄×C₅	1	1	yes	characteristic, complemented
249	C₂×D₄	—	2	1	no	—
250	C₂×D₄	—	2	2	no	—
251	C₂×D₄	—	2	2	no	—
252	C₂×D₄	—	4	2	no	—
253	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
254	C₂×D₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic, complemented
255	C₂×D₄	C₃×C₅×D₄	1	2	yes	—
256	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
257	C₂²×C₄	—	2	1	no	—
258	C₂²×C₄	—	4	2	no	—
259	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
260	C₄⋊C₄	—	2	1	no	—
261	C₂²⋊C₄	—	2	1	no	—
262	C₂²⋊C₄	—	2	2	no	—
263	C₂²⋊C₄	—	2	2	no	—
264	C₂²⋊C₄	—	2	4	no	—
265	C₂²⋊C₄	—	4	2	no	—
266	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic, complemented
267	C₄²	C₂×C₃×C₄×C₅	1	1	yes	characteristic, complemented
268	C₃×C₅	#2127	1	1	yes	characteristic, direct product factor, Hall
269	C₂²×C₃	—	2	2	no	—
270	C₂²×C₃	—	2	2	no	—
271	C₂²×C₃	—	4	1	no	—
272	C₂²×C₃	—	4	2	no	—
273	C₂²×C₃	—	4	2	no	—
274	C₂²×C₃	—	4	4	no	—
275	C₂²×C₃	—	4	2	no	—
276	C₂²×C₃	—	4	1	no	—
277	C₂²×C₃	—	8	2	no	—
278	C₂²×C₃	C₅×#99	1	2	yes	—
279	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	1	yes	characteristic
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	—	2	1	no	—
282	C₃×C₄	—	4	1	no	—
283	C₃×C₄	—	4	1	no	—
284	C₃×C₄	—	4	1	no	—
285	C₃×C₄	—	8	4	no	—
286	C₂×C₅	—	2	1	no	—
287	C₂×C₅	—	2	2	no	—
288	C₂×C₅	—	4	2	no	—
289	C₂×C₅	—	4	2	no	—
290	C₂×C₅	—	8	1	no	—
291	C₂×C₅	C₂×C₃×#99	1	1	yes	characteristic
292	C₂³	—	2	2	no	—
293	C₂³	—	2	2	no	—
294	C₂³	—	2	1	no	—
295	C₂³	—	8	2	no	—
296	C₂³	C₃×C₅×C₂²⋊C₄	1	2	yes	—
297	C₂³	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
298	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
299	Q₈	—	4	1	no	—
300	D₄	—	4	1	no	—
301	D₄	—	4	2	no	—
302	D₄	—	4	1	no	—
303	D₄	—	4	1	no	—
304	D₄	—	4	2	no	—
305	D₄	—	8	2	no	—
306	D₄	—	8	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	1	no	—
309	C₂×C₄	—	2	1	no	—
310	C₂×C₄	—	2	1	no	—
311	C₂×C₄	—	4	2	no	—
312	C₂×C₄	—	4	4	no	—
313	C₂×C₄	—	8	4	no	—
314	C₂×C₄	C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
315	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
316	C₂×C₃	—	2	1	no	—
317	C₂×C₃	—	2	2	no	—
318	C₂×C₃	—	4	2	no	—
319	C₂×C₃	—	4	2	no	—
320	C₂×C₃	—	8	1	no	—
321	C₂×C₃	C₂×C₅×#99	1	1	yes	characteristic
322	C₅	C₃×#2127	1	1	yes	characteristic, direct product factor, Sylow
323	C₂²	—	2	2	no	—
324	C₂²	—	2	2	no	—
325	C₂²	—	4	1	no	—
326	C₂²	—	4	2	no	—
327	C₂²	—	4	2	no	—
328	C₂²	—	4	4	no	—
329	C₂²	—	4	2	no	—
330	C₂²	—	4	1	no	—
331	C₂²	—	8	2	no	—
332	C₂²	C₃×C₅×#99	1	2	yes	—
333	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
334	C₄	—	2	1	no	—
335	C₄	—	2	1	no	—
336	C₄	—	4	1	no	—
337	C₄	—	4	1	no	—
338	C₄	—	4	1	no	—
339	C₄	—	8	4	no	—
340	C₃	C₅×#2127	1	1	yes	characteristic, direct product factor, Sylow
341	C₂	—	2	1	no	—
342	C₂	—	2	2	no	—
343	C₂	—	4	2	no	—
344	C₂	—	4	2	no	—
345	C₂	—	8	1	no	—
346	C₂	C₂×C₃×C₅×#99	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂×C₃×C₅	C₂×#99
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂×D₄	C₂³×C₃×C₅
prime radical	C₃×C₅×#535	C₂
LCS	G ▷ C₂×C₄ ▷ C₂² ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₅ ◁ C₂³×C₃×C₅ ◁ C₂²×C₃×C₅×D₄ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#99	C₂	semidirect
3. C₃×C₅×#354	C₂	semidirect
4. C₃×C₅×#353	C₂	semidirect
5. C₅×#2127	C₃	direct (N × H)
6. C₂×C₃×C₅×#41	C₄	semidirect
8. C₃×C₅×#127	C₄	semidirect
10. C₃×C₅×#124	C₄	semidirect
14. C₃×C₅×#117	C₄	semidirect
18. C₃×#2127	C₅	direct (N × H)
20. C₂×C₅×#99	C₂×C₃	semidirect
21. C₅×#354	C₂×C₃	semidirect
22. C₅×#353	C₂×C₃	semidirect
25. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
31. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
43. C₃×C₄²×C₅	C₂×C₄	semidirect
44. C₃×C₄²×C₅	C₂×C₄	semidirect
46. C₂×C₃×#99	C₂×C₅	semidirect
47. C₃×#354	C₂×C₅	semidirect
48. C₃×#353	C₂×C₅	semidirect
49. C₂×C₅×#41	C₃×C₄	semidirect
51. C₅×#127	C₃×C₄	semidirect
53. C₅×#124	C₃×C₄	semidirect
57. C₅×#117	C₃×C₄	semidirect
61. #2127	C₃×C₅	direct (N × H)
86. C₂×C₃×#41	C₄×C₅	semidirect
88. C₃×#127	C₄×C₅	semidirect
90. C₃×#124	C₄×C₅	semidirect
94. C₃×#117	C₄×C₅	semidirect
100. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
106. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
118. C₄²×C₅	C₂×C₃×C₄	semidirect
119. C₄²×C₅	C₂×C₃×C₄	semidirect
121. C₂×#99	C₂×C₃×C₅	semidirect
122. #354	C₂×C₃×C₅	semidirect
123. #353	C₂×C₃×C₅	semidirect
143. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
149. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
161. C₃×C₄²	C₂×C₄×C₅	semidirect
162. C₃×C₄²	C₂×C₄×C₅	semidirect
187. C₂×#41	C₃×C₄×C₅	semidirect
189. #127	C₃×C₄×C₅	semidirect
191. #124	C₃×C₄×C₅	semidirect
195. #117	C₃×C₄×C₅	semidirect
248. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
254. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
266. C₄²	C₂×C₃×C₄×C₅	semidirect
267. C₄²	C₂×C₃×C₄×C₅	semidirect
268. C₃×C₅	#2127	direct (N × H)
322. C₅	C₃×#2127	direct (N × H)
340. C₃	C₅×#2127	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×#535	2
C₂×C₃×C₅×#99	2
C₃×C₅×#354	2
C₃×C₅×#353	2
C₅×#2127	3
C₃×#2127	5

Subgroups — C3×C5×#2127 #14275161

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2127 #14275161