Subgroups — C₃×C₅×#1855 #14274889

Order 1920.

556 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#108	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#407	C₂	1	1	yes	maximal, characteristic
4	C₂×C₃×C₅×C₂²⋊C₈	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#341	C₂	1	2	yes	maximal, complemented
6	C₅×#1855	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
7	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
8	C₂×C₃×C₅×M₁₆	—	2	1	no	—
9	C₂×C₃×C₅×M₁₆	—	2	4	no	—
10	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
13	C₂²×C₃×C₅×C₈	—	2	1	no	—
14	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	—
15	C₃×C₅×#108	—	2	4	no	—
16	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
17	C₃×C₅×C₂²⋊C₈	—	2	1	no	—
18	C₃×C₅×C₂²⋊C₈	C₄	1	2	yes	—
19	C₃×C₅×C₂²⋊C₈	C₄	1	2	yes	—
20	C₃×#1855	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
21	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic
22	C₂×C₅×#108	C₂×C₃	1	2	yes	complemented
23	C₅×#407	C₂×C₃	1	1	yes	characteristic
24	C₂×C₅×C₂²⋊C₈	C₂×C₃	1	1	yes	characteristic
25	C₅×#341	C₂×C₃	1	2	yes	complemented
26	C₂⁴×C₃×C₅	Q₈	1	1	yes	characteristic
27	C₂²×C₃×C₄×C₅	—	2	2	no	—
28	C₂²×C₃×C₄×C₅	—	2	2	no	—
29	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
30	C₂²×C₃×C₄×C₅	C₂×C₄	1	1	yes	characteristic
31	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
32	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
33	C₂²×C₃×C₄×C₅	Q₈	1	1	yes	characteristic
34	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
35	C₃×C₅×M₁₆	—	2	4	no	—
36	C₃×C₅×M₁₆	—	2	2	no	—
37	C₃×C₅×M₁₆	—	2	2	no	—
38	C₃×C₅×M₁₆	—	2	2	no	—
39	C₃×C₅×M₁₆	D₄	1	4	yes	—
40	C₂×C₃×C₅×C₈	—	2	4	no	—
41	C₂×C₃×C₅×C₈	—	2	2	no	—
42	C₂×C₃×C₅×C₈	—	2	2	no	—
43	C₂×C₃×C₅×C₈	—	2	2	no	—
44	C₂×C₃×C₅×C₈	—	2	1	no	—
45	C₂×C₃×C₅×C₈	—	2	1	no	—
46	C₂×C₃×C₅×C₈	C₂×C₄	1	4	yes	—
47	C₂²×C₃×M₁₆	C₂×C₅	1	1	yes	characteristic
48	C₂×C₃×#108	C₂×C₅	1	2	yes	complemented
49	C₃×#407	C₂×C₅	1	1	yes	characteristic
50	C₂×C₃×C₂²⋊C₈	C₂×C₅	1	1	yes	characteristic
51	C₃×#341	C₂×C₅	1	2	yes	complemented
52	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
53	C₂×C₅×M₁₆	—	2	1	no	—
54	C₂×C₅×M₁₆	—	2	4	no	—
55	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
56	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
57	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
58	C₂²×C₅×C₈	—	2	1	no	—
59	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	—
60	C₅×#108	—	2	4	no	—
61	C₅×C₂²⋊C₈	—	2	1	no	—
62	C₅×C₂²⋊C₈	—	2	1	no	—
63	C₅×C₂²⋊C₈	C₃×C₄	1	2	yes	—
64	C₅×C₂²⋊C₈	C₃×C₄	1	2	yes	—
65	#1855	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
66	C₂³×C₃×C₅	—	2	2	no	—
67	C₂³×C₃×C₅	—	2	2	no	—
68	C₂³×C₃×C₅	—	4	1	no	—
69	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
70	C₂³×C₃×C₅	C₄⋊C₄	1	1	yes	characteristic
71	C₂³×C₃×C₅	C₂×Q₈	1	1	yes	characteristic
72	C₂×C₃×C₄×C₅	—	2	2	no	—
73	C₂×C₃×C₄×C₅	—	2	2	no	—
74	C₂×C₃×C₄×C₅	—	2	2	no	—
75	C₂×C₃×C₄×C₅	—	2	1	no	—
76	C₂×C₃×C₄×C₅	—	2	1	no	—
77	C₂×C₃×C₄×C₅	—	2	1	no	—
78	C₂×C₃×C₄×C₅	—	2	1	no	—
79	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
80	C₂×C₃×C₄×C₅	C₄⋊C₄	1	1	yes	characteristic
81	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
82	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
83	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
84	C₂×C₃×C₄×C₅	#41	1	2	yes	—
85	C₃×C₅×C₈	—	2	4	no	—
86	C₃×C₅×C₈	—	2	4	no	—
87	C₃×C₅×C₈	—	4	1	no	—
88	C₃×C₅×C₈	—	4	1	no	—
89	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
90	C₂×C₃×M₁₆	—	2	1	no	—
91	C₂×C₃×M₁₆	—	2	4	no	—
92	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
93	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
94	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
95	C₂²×C₃×C₈	—	2	1	no	—
96	C₂²×C₃×C₈	C₂²×C₅	1	2	yes	—
97	C₃×#108	—	2	4	no	—
98	C₃×C₂²⋊C₈	—	2	1	no	—
99	C₃×C₂²⋊C₈	—	2	1	no	—
100	C₃×C₂²⋊C₈	C₄×C₅	1	2	yes	—
101	C₃×C₂²⋊C₈	C₄×C₅	1	2	yes	—
102	C₂⁴×C₅	C₃×Q₈	1	1	yes	characteristic
103	C₂²×C₄×C₅	—	2	2	no	—
104	C₂²×C₄×C₅	—	2	2	no	—
105	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
106	C₂²×C₄×C₅	C₂×C₃×C₄	1	1	yes	characteristic
107	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
108	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
109	C₂²×C₄×C₅	C₃×Q₈	1	1	yes	characteristic
110	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
111	C₅×M₁₆	—	2	4	no	—
112	C₅×M₁₆	—	2	2	no	—
113	C₅×M₁₆	—	2	2	no	—
114	C₅×M₁₆	—	2	2	no	—
115	C₅×M₁₆	C₃×D₄	1	4	yes	—
116	C₂×C₅×C₈	—	2	4	no	—
117	C₂×C₅×C₈	—	2	2	no	—
118	C₂×C₅×C₈	—	2	2	no	—
119	C₂×C₅×C₈	—	2	2	no	—
120	C₂×C₅×C₈	—	2	1	no	—
121	C₂×C₅×C₈	—	2	1	no	—
122	C₂×C₅×C₈	C₂×C₃×C₄	1	4	yes	—
123	C₂²×M₁₆	C₂×C₃×C₅	1	1	yes	characteristic
124	C₂×#108	C₂×C₃×C₅	1	2	yes	complemented
125	#407	C₂×C₃×C₅	1	1	yes	characteristic
126	C₂×C₂²⋊C₈	C₂×C₃×C₅	1	1	yes	characteristic
127	#341	C₂×C₃×C₅	1	2	yes	complemented
128	C₂²×C₃×C₅	—	2	1	no	—
129	C₂²×C₃×C₅	—	2	1	no	—
130	C₂²×C₃×C₅	—	2	1	no	—
131	C₂²×C₃×C₅	—	2	1	no	—
132	C₂²×C₃×C₅	—	2	1	no	—
133	C₂²×C₃×C₅	—	2	1	no	—
134	C₂²×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×C₅	—	4	4	no	—
136	C₂²×C₃×C₅	#108	1	2	yes	complemented
137	C₂²×C₃×C₅	C₂×C₄⋊C₄	1	1	yes	characteristic
138	C₂²×C₃×C₅	C₂²⋊Q₈	1	2	yes	—
139	C₃×C₄×C₅	—	2	1	no	—
140	C₃×C₄×C₅	—	2	1	no	—
141	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
142	C₃×C₄×C₅	#120	1	1	yes	characteristic
143	C₃×C₄×C₅	#123	1	1	yes	characteristic
144	C₂⁴×C₃	C₅×Q₈	1	1	yes	characteristic
145	C₂²×C₃×C₄	—	2	2	no	—
146	C₂²×C₃×C₄	—	2	2	no	—
147	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
148	C₂²×C₃×C₄	C₂×C₄×C₅	1	1	yes	characteristic
149	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
150	C₂²×C₃×C₄	C₅×D₄	1	1	yes	characteristic
151	C₂²×C₃×C₄	C₅×Q₈	1	1	yes	characteristic
152	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
153	C₃×M₁₆	—	2	4	no	—
154	C₃×M₁₆	—	2	2	no	—
155	C₃×M₁₆	—	2	2	no	—
156	C₃×M₁₆	—	2	2	no	—
157	C₃×M₁₆	C₅×D₄	1	4	yes	—
158	C₂×C₃×C₈	—	2	4	no	—
159	C₂×C₃×C₈	—	2	2	no	—
160	C₂×C₃×C₈	—	2	2	no	—
161	C₂×C₃×C₈	—	2	2	no	—
162	C₂×C₃×C₈	—	2	1	no	—
163	C₂×C₃×C₈	—	2	1	no	—
164	C₂×C₃×C₈	C₂×C₄×C₅	1	4	yes	—
165	C₂³×C₅	—	2	2	no	—
166	C₂³×C₅	—	2	2	no	—
167	C₂³×C₅	—	4	1	no	—
168	C₂³×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
169	C₂³×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
170	C₂³×C₅	C₂×C₃×Q₈	1	1	yes	characteristic
171	C₂×C₄×C₅	—	2	2	no	—
172	C₂×C₄×C₅	—	2	2	no	—
173	C₂×C₄×C₅	—	2	2	no	—
174	C₂×C₄×C₅	—	2	1	no	—
175	C₂×C₄×C₅	—	2	1	no	—
176	C₂×C₄×C₅	—	2	1	no	—
177	C₂×C₄×C₅	—	2	1	no	—
178	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
179	C₂×C₄×C₅	C₃×C₄⋊C₄	1	1	yes	characteristic
180	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
181	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
182	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
183	C₂×C₄×C₅	C₃×#41	1	2	yes	—
184	C₅×C₈	—	2	4	no	—
185	C₅×C₈	—	2	4	no	—
186	C₅×C₈	—	4	1	no	—
187	C₅×C₈	—	4	1	no	—
188	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
189	C₂×M₁₆	—	2	1	no	—
190	C₂×M₁₆	—	2	4	no	—
191	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
192	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
193	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
194	C₂²×C₈	—	2	1	no	—
195	C₂²×C₈	C₂²×C₃×C₅	1	2	yes	—
196	#108	—	2	4	no	—
197	C₂²⋊C₈	—	2	1	no	—
198	C₂²⋊C₈	—	2	1	no	—
199	C₂²⋊C₈	C₃×C₄×C₅	1	2	yes	—
200	C₂²⋊C₈	C₃×C₄×C₅	1	2	yes	—
201	C₂×C₃×C₅	—	2	2	no	—
202	C₂×C₃×C₅	—	2	2	no	—
203	C₂×C₃×C₅	—	4	1	no	—
204	C₂×C₃×C₅	#385	1	1	yes	characteristic
205	C₂×C₃×C₅	C₂×#108	1	1	yes	characteristic
206	C₂×C₃×C₅	#430	1	1	yes	characteristic
207	C₂³×C₃	—	2	2	no	—
208	C₂³×C₃	—	2	2	no	—
209	C₂³×C₃	—	4	1	no	—
210	C₂³×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
211	C₂³×C₃	C₅×C₄⋊C₄	1	1	yes	characteristic
212	C₂³×C₃	C₂×C₅×Q₈	1	1	yes	characteristic
213	C₂×C₃×C₄	—	2	2	no	—
214	C₂×C₃×C₄	—	2	2	no	—
215	C₂×C₃×C₄	—	2	2	no	—
216	C₂×C₃×C₄	—	2	1	no	—
217	C₂×C₃×C₄	—	2	1	no	—
218	C₂×C₃×C₄	—	2	1	no	—
219	C₂×C₃×C₄	—	2	1	no	—
220	C₂×C₃×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
221	C₂×C₃×C₄	C₅×C₄⋊C₄	1	1	yes	characteristic
222	C₂×C₃×C₄	C₂²×C₄×C₅	1	1	yes	characteristic
223	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
224	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
225	C₂×C₃×C₄	C₅×#41	1	2	yes	—
226	C₃×C₈	—	2	4	no	—
227	C₃×C₈	—	2	4	no	—
228	C₃×C₈	—	4	1	no	—
229	C₃×C₈	—	4	1	no	—
230	C₂²×C₅	—	2	1	no	—
231	C₂²×C₅	—	2	1	no	—
232	C₂²×C₅	—	2	1	no	—
233	C₂²×C₅	—	2	1	no	—
234	C₂²×C₅	—	2	1	no	—
235	C₂²×C₅	—	2	1	no	—
236	C₂²×C₅	—	2	1	no	—
237	C₂²×C₅	—	4	4	no	—
238	C₂²×C₅	C₃×#108	1	2	yes	complemented
239	C₂²×C₅	C₂×C₃×C₄⋊C₄	1	1	yes	characteristic
240	C₂²×C₅	C₃×C₂²⋊Q₈	1	2	yes	—
241	C₄×C₅	—	2	1	no	—
242	C₄×C₅	—	2	1	no	—
243	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
244	C₄×C₅	C₃×#120	1	1	yes	characteristic
245	C₄×C₅	C₃×#123	1	1	yes	characteristic
246	C₂⁴	C₃×C₅×Q₈	1	1	yes	characteristic
247	C₂²×C₄	—	2	2	no	—
248	C₂²×C₄	—	2	2	no	—
249	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
250	C₂²×C₄	C₂×C₃×C₄×C₅	1	1	yes	characteristic
251	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
252	C₂²×C₄	C₃×C₅×D₄	1	1	yes	characteristic
253	C₂²×C₄	C₃×C₅×Q₈	1	1	yes	characteristic
254	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
255	M₁₆	—	2	4	no	—
256	M₁₆	—	2	2	no	—
257	M₁₆	—	2	2	no	—
258	M₁₆	—	2	2	no	—
259	M₁₆	C₃×C₅×D₄	1	4	yes	—
260	C₂×C₈	—	2	4	no	—
261	C₂×C₈	—	2	2	no	—
262	C₂×C₈	—	2	2	no	—
263	C₂×C₈	—	2	2	no	—
264	C₂×C₈	—	2	1	no	—
265	C₂×C₈	—	2	1	no	—
266	C₂×C₈	C₂×C₃×C₄×C₅	1	4	yes	—
267	C₃×C₅	#1855	1	1	yes	characteristic, direct product factor, Hall
268	C₂²×C₃	—	2	1	no	—
269	C₂²×C₃	—	2	1	no	—
270	C₂²×C₃	—	2	1	no	—
271	C₂²×C₃	—	2	1	no	—
272	C₂²×C₃	—	2	1	no	—
273	C₂²×C₃	—	2	1	no	—
274	C₂²×C₃	—	2	1	no	—
275	C₂²×C₃	—	4	4	no	—
276	C₂²×C₃	C₅×#108	1	2	yes	complemented
277	C₂²×C₃	C₂×C₅×C₄⋊C₄	1	1	yes	characteristic
278	C₂²×C₃	C₅×C₂²⋊Q₈	1	2	yes	—
279	C₃×C₄	—	2	1	no	—
280	C₃×C₄	—	2	1	no	—
281	C₃×C₄	C₄×C₅×D₄	1	2	yes	—
282	C₃×C₄	C₅×#120	1	1	yes	characteristic
283	C₃×C₄	C₅×#123	1	1	yes	characteristic
284	C₂×C₅	—	2	2	no	—
285	C₂×C₅	—	2	2	no	—
286	C₂×C₅	—	4	1	no	—
287	C₂×C₅	C₃×#385	1	1	yes	characteristic
288	C₂×C₅	C₂×C₃×#108	1	1	yes	characteristic
289	C₂×C₅	C₃×#430	1	1	yes	characteristic
290	C₂³	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	4	1	no	—
293	C₂³	C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
294	C₂³	C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
295	C₂³	C₂×C₃×C₅×Q₈	1	1	yes	characteristic
296	C₂×C₄	—	2	2	no	—
297	C₂×C₄	—	2	2	no	—
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	1	no	—
300	C₂×C₄	—	2	1	no	—
301	C₂×C₄	—	2	1	no	—
302	C₂×C₄	—	2	1	no	—
303	C₂×C₄	C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
304	C₂×C₄	C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
305	C₂×C₄	C₂²×C₃×C₄×C₅	1	1	yes	characteristic
306	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
307	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
308	C₂×C₄	C₃×C₅×#41	1	2	yes	—
309	C₈	—	2	4	no	—
310	C₈	—	2	4	no	—
311	C₈	—	4	1	no	—
312	C₈	—	4	1	no	—
313	C₂×C₃	—	2	2	no	—
314	C₂×C₃	—	2	2	no	—
315	C₂×C₃	—	4	1	no	—
316	C₂×C₃	C₅×#385	1	1	yes	characteristic
317	C₂×C₃	C₂×C₅×#108	1	1	yes	characteristic
318	C₂×C₃	C₅×#430	1	1	yes	characteristic
319	C₅	C₃×#1855	1	1	yes	characteristic, direct product factor, Sylow
320	C₂²	—	2	1	no	—
321	C₂²	—	2	1	no	—
322	C₂²	—	2	1	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	1	no	—
327	C₂²	—	4	4	no	—
328	C₂²	C₃×C₅×#108	1	2	yes	complemented
329	C₂²	C₂×C₃×C₅×C₄⋊C₄	1	1	yes	characteristic
330	C₂²	C₃×C₅×C₂²⋊Q₈	1	2	yes	—
331	C₄	—	2	1	no	—
332	C₄	—	2	1	no	—
333	C₄	C₃×C₄×C₅×D₄	1	2	yes	—
334	C₄	C₃×C₅×#120	1	1	yes	characteristic
335	C₄	C₃×C₅×#123	1	1	yes	characteristic
336	C₃	C₅×#1855	1	1	yes	characteristic, direct product factor, Sylow
337	C₂	—	2	2	no	—
338	C₂	—	2	2	no	—
339	C₂	—	4	1	no	—
340	C₂	C₃×C₅×#385	1	1	yes	characteristic
341	C₂	C₂×C₃×C₅×#108	1	1	yes	characteristic
342	C₂	C₃×C₅×#430	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄×C₅	C₂×D₄
commutator	C₂×C₄	C₂²×C₃×C₄×C₅
Frattini, cosocle	C₂²×C₄	C₂³×C₃×C₅
socle	C₂²×C₃×C₅	C₂×C₄⋊C₄
prime radical	C₂⁴×C₃×C₅	Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₃×C₄×C₅ ◁ C₂³×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#108	C₂	semidirect
5. C₃×C₅×#341	C₂	semidirect
6. C₅×#1855	C₃	direct (N × H)
20. C₃×#1855	C₅	direct (N × H)
22. C₂×C₅×#108	C₂×C₃	semidirect
25. C₅×#341	C₂×C₃	semidirect
48. C₂×C₃×#108	C₂×C₅	semidirect
51. C₃×#341	C₂×C₅	semidirect
65. #1855	C₃×C₅	direct (N × H)
124. C₂×#108	C₂×C₃×C₅	semidirect
127. #341	C₂×C₃×C₅	semidirect
136. C₂²×C₃×C₅	#108	semidirect
238. C₂²×C₅	C₃×#108	semidirect
267. C₃×C₅	#1855	direct (N × H)
276. C₂²×C₃	C₅×#108	semidirect
319. C₅	C₃×#1855	direct (N × H)
328. C₂²	C₃×C₅×#108	semidirect
336. C₃	C₅×#1855	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×C₃×C₅×M₁₆	2
C₂×C₃×C₅×#108	2
C₃×C₅×#407	2
C₂×C₃×C₅×C₂²⋊C₈	2
C₃×C₅×#341	2
C₅×#1855	3
C₃×#1855	5

Subgroups — C3×C5×#1855 #14274889

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#1855 #14274889