Subgroups — C₃×#10605582 #14330632

Order 1920.

1376 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4099	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#379	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65536	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65246	C₂	1	3	yes	maximal, complemented
5	C₃×#65245	C₂	1	3	yes	maximal, complemented
6	C₃×#65234	C₂	1	3	yes	maximal, complemented
7	C₃×#65233	C₂	1	3	yes	maximal, complemented
8	#10605582	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁵×C₃×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₂²⋊D₅	C₂²	1	3	yes	—
11	C₂²×C₃×C₄×D₅	C₂²	1	1	yes	characteristic, complemented
12	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	3	yes	—
14	C₃×#4099	C₄	1	8	yes	complemented
15	C₂×C₃×C₂²⋊Dic₅	C₂²	1	3	yes	—
16	C₂×C₃×C₂²⋊Dic₅	C₂²	1	3	yes	—
17	C₂×C₃×C₂²⋊Dic₅	C₂²	1	3	yes	—
18	C₂×C₃×#685	C₂²	1	3	yes	complemented
19	C₂×C₃×#683	C₂²	1	3	yes	complemented
20	C₂×C₃×C₄×Dic₅	C₂²	1	3	yes	complemented
21	C₃×#3963	C₂²	1	3	yes	complemented
22	C₃×#3963	C₂²	1	3	yes	complemented
23	C₃×#2375	—	5	1	no	maximal, Hall
24	C₂×#4099	C₂×C₃	1	1	yes	characteristic
25	C₅×#379	C₂×C₃	1	1	yes	characteristic, complemented
26	#65536	C₂×C₃	1	1	yes	characteristic, complemented
27	#65246	C₂×C₃	1	3	yes	complemented
28	#65245	C₂×C₃	1	3	yes	complemented
29	#65234	C₂×C₃	1	3	yes	complemented
30	#65233	C₂×C₃	1	3	yes	complemented
31	C₂⁴×C₃×C₅	—	4	3	no	—
32	C₂⁴×C₃×C₅	—	4	3	no	—
33	C₂⁴×C₃×C₅	C₂×C₄	1	4	yes	complemented
34	C₂⁴×C₃×C₅	C₂³	1	3	yes	—
35	C₂³×C₃×D₅	C₂³	1	1	yes	characteristic
36	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
37	C₂²×C₃×C₄×C₅	C₂³	1	3	yes	—
38	C₂×C₃×C₂²⋊D₅	—	4	3	no	—
39	C₂×C₃×C₂²⋊D₅	—	4	3	no	—
40	C₂×C₃×C₂²⋊D₅	C₂×C₄	1	12	yes	—
41	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
42	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
43	C₂²×C₃×Dic₅	C₂³	1	3	yes	—
44	C₂×C₃×C₄×D₅	—	4	3	no	—
45	C₃×C₅×C₂²⋊C₄	—	4	3	no	—
46	C₃×C₅×C₂²⋊C₄	—	4	3	no	—
47	C₃×C₂²⋊Dic₅	—	4	3	no	—
48	C₃×C₂²⋊Dic₅	—	4	3	no	—
49	C₃×C₂²⋊Dic₅	C₂×C₄	1	12	yes	complemented
50	C₃×#685	—	4	3	no	—
51	C₃×#683	—	4	3	no	—
52	C₃×C₄×Dic₅	—	4	3	no	—
53	C₂×C₃×#120	—	5	1	no	—
54	C₃×#390	—	5	3	no	—
55	C₃×#388	—	5	3	no	—
56	C₃×#388	—	5	3	no	—
57	C₃×#386	—	5	3	no	—
58	C₃×#379	—	5	1	no	—
59	C₃×#379	D₅	1	1	yes	characteristic, complemented
60	C₂⁵×C₅	C₂²×C₃	1	1	yes	characteristic
61	C₂²×C₂²⋊D₅	C₂²×C₃	1	3	yes	—
62	C₂²×C₄×D₅	C₂²×C₃	1	1	yes	characteristic, complemented
63	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
64	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	3	yes	—
65	#4099	C₃×C₄	1	8	yes	complemented
66	C₂×C₂²⋊Dic₅	C₂²×C₃	1	3	yes	—
67	C₂×C₂²⋊Dic₅	C₂²×C₃	1	3	yes	—
68	C₂×C₂²⋊Dic₅	C₂²×C₃	1	3	yes	—
69	C₂×#685	C₂²×C₃	1	3	yes	complemented
70	C₂×#683	C₂²×C₃	1	3	yes	complemented
71	C₂×C₄×Dic₅	C₂²×C₃	1	3	yes	complemented
72	#3963	C₂²×C₃	1	3	yes	complemented
73	#3963	C₂²×C₃	1	3	yes	complemented
74	#2375	—	5	1	no	Sylow
75	C₂³×C₃×C₅	—	2	3	no	—
76	C₂³×C₃×C₅	—	2	3	no	—
77	C₂³×C₃×C₅	—	2	3	no	—
78	C₂³×C₃×C₅	—	2	3	no	—
79	C₂³×C₃×C₅	—	2	3	no	—
80	C₂³×C₃×C₅	—	2	3	no	—
81	C₂³×C₃×C₅	—	4	12	no	—
82	C₂³×C₃×C₅	—	4	12	no	—
83	C₂³×C₃×C₅	—	4	4	no	—
84	C₂³×C₃×C₅	C₂²×C₄	1	6	yes	—
85	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
86	C₂²×C₃×D₅	—	2	3	no	—
87	C₂²×C₃×D₅	—	2	3	no	—
88	C₂²×C₃×D₅	C₂²×C₄	1	2	yes	—
89	C₂×C₃×C₄×C₅	—	2	3	no	—
90	C₂×C₃×C₄×C₅	—	2	3	no	—
91	C₂×C₃×C₄×C₅	—	2	3	no	—
92	C₂×C₃×C₄×C₅	—	2	3	no	—
93	C₃×C₂²⋊D₅	—	4	12	no	—
94	C₂×C₃×Dic₅	—	2	3	no	—
95	C₂×C₃×Dic₅	—	2	3	no	—
96	C₂×C₃×Dic₅	—	2	3	no	—
97	C₂×C₃×Dic₅	—	2	3	no	—
98	C₂×C₃×Dic₅	—	2	3	no	—
99	C₂×C₃×Dic₅	—	2	3	no	—
100	C₂×C₃×Dic₅	C₂²×C₄	1	6	yes	—
101	C₃×C₄×D₅	—	4	4	no	—
102	C₂⁵×C₃	C₂×D₅	1	1	yes	characteristic
103	C₂²×C₃×D₄	—	5	3	no	—
104	C₂³×C₃×C₄	—	5	1	no	—
105	C₃×#120	—	5	8	no	—
106	C₂×C₃×C₄⋊C₄	—	5	3	no	—
107	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
108	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
109	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
110	C₂×C₃×C₂²⋊C₄	—	5	3	no	—
111	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	3	yes	—
112	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	3	yes	—
113	C₂×C₃×C₄²	—	5	3	no	—
114	C₃×#95	—	5	3	no	—
115	C₃×#95	—	5	3	no	—
116	C₂⁴×C₅	—	4	3	no	—
117	C₂⁴×C₅	—	4	3	no	—
118	C₂⁴×C₅	C₂×C₃×C₄	1	4	yes	complemented
119	C₂⁴×C₅	C₂³×C₃	1	3	yes	—
120	C₂³×D₅	C₂³×C₃	1	1	yes	characteristic
121	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
122	C₂²×C₄×C₅	C₂³×C₃	1	3	yes	—
123	C₂×C₂²⋊D₅	—	4	3	no	—
124	C₂×C₂²⋊D₅	—	4	3	no	—
125	C₂×C₂²⋊D₅	C₂×C₃×C₄	1	12	yes	—
126	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
127	C₂²×Dic₅	C₂³×C₃	1	3	yes	—
128	C₂²×Dic₅	C₂³×C₃	1	3	yes	—
129	C₂×C₄×D₅	—	4	3	no	—
130	C₅×C₂²⋊C₄	—	4	3	no	—
131	C₅×C₂²⋊C₄	—	4	3	no	—
132	C₂²⋊Dic₅	—	4	3	no	—
133	C₂²⋊Dic₅	—	4	3	no	—
134	C₂²⋊Dic₅	C₂×C₃×C₄	1	12	yes	complemented
135	#685	—	4	3	no	—
136	#683	—	4	3	no	—
137	C₄×Dic₅	—	4	3	no	—
138	C₂×#120	—	5	1	no	—
139	#390	—	5	3	no	—
140	#388	—	5	3	no	—
141	#388	—	5	3	no	—
142	#386	—	5	3	no	—
143	#379	—	5	1	no	—
144	#379	C₃×D₅	1	1	yes	characteristic, complemented
145	C₂²×C₃×C₅	—	2	6	no	—
146	C₂²×C₃×C₅	—	2	6	no	—
147	C₂²×C₃×C₅	—	2	6	no	—
148	C₂²×C₃×C₅	—	4	16	no	—
149	C₂²×C₃×C₅	—	4	3	no	—
150	C₂²×C₃×C₅	—	4	3	no	—
151	C₂²×C₃×C₅	—	4	3	no	—
152	C₂²×C₃×C₅	—	4	3	no	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	H(5,𝔽₂)	1	3	yes	—
155	C₂²×C₃×C₅	H(5,𝔽₂)	1	3	yes	—
156	C₂×C₃×D₅	—	2	6	no	—
157	C₂×C₃×D₅	—	4	3	no	—
158	C₂×C₃×D₅	—	4	1	no	—
159	C₃×C₄×C₅	—	4	3	no	—
160	C₃×C₄×C₅	—	4	1	no	—
161	C₃×Dic₅	—	2	6	no	—
162	C₃×Dic₅	—	4	3	no	—
163	C₃×Dic₅	—	4	1	no	—
164	C₂⁴×C₃	—	4	3	no	—
165	C₂⁴×C₃	—	4	3	no	—
166	C₂⁴×C₃	—	5	1	no	—
167	C₂⁴×C₃	C₄×D₅	1	4	yes	complemented
168	C₂⁴×C₃	C₂²×D₅	1	3	yes	—
169	C₂×C₃×D₄	—	5	12	no	—
170	C₂×C₃×D₄	—	20	3	no	—
171	C₂×C₃×D₄	—	20	3	no	—
172	C₂²×C₃×C₄	—	5	3	no	—
173	C₂²×C₃×C₄	—	5	1	no	—
174	C₂²×C₃×C₄	—	5	3	no	—
175	C₂²×C₃×C₄	—	20	3	no	—
176	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
177	C₂²×C₃×C₄	C₂²×D₅	1	3	yes	—
178	C₃×C₄⋊C₄	—	20	3	no	—
179	C₃×C₂²⋊C₄	—	4	3	no	—
180	C₃×C₂²⋊C₄	—	4	3	no	—
181	C₃×C₂²⋊C₄	—	5	12	no	—
182	C₃×C₂²⋊C₄	—	20	3	no	—
183	C₃×C₂²⋊C₄	—	20	3	no	—
184	C₃×C₂²⋊C₄	—	20	3	no	—
185	C₃×C₄²	—	20	3	no	—
186	C₂³×C₅	—	2	3	no	—
187	C₂³×C₅	—	2	3	no	—
188	C₂³×C₅	—	2	3	no	—
189	C₂³×C₅	—	2	3	no	—
190	C₂³×C₅	—	2	3	no	—
191	C₂³×C₅	—	2	3	no	—
192	C₂³×C₅	—	4	12	no	—
193	C₂³×C₅	—	4	12	no	—
194	C₂³×C₅	—	4	4	no	—
195	C₂³×C₅	C₂²×C₃×C₄	1	6	yes	—
196	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
197	C₂²×D₅	—	2	3	no	—
198	C₂²×D₅	—	2	3	no	—
199	C₂²×D₅	C₂²×C₃×C₄	1	2	yes	—
200	C₂×C₄×C₅	—	2	3	no	—
201	C₂×C₄×C₅	—	2	3	no	—
202	C₂×C₄×C₅	—	2	3	no	—
203	C₂×C₄×C₅	—	2	3	no	—
204	C₂²⋊D₅	—	4	12	no	—
205	C₂×Dic₅	—	2	3	no	—
206	C₂×Dic₅	—	2	3	no	—
207	C₂×Dic₅	—	2	3	no	—
208	C₂×Dic₅	—	2	3	no	—
209	C₂×Dic₅	—	2	3	no	—
210	C₂×Dic₅	—	2	3	no	—
211	C₂×Dic₅	C₂²×C₃×C₄	1	6	yes	—
212	C₄×D₅	—	4	4	no	—
213	C₂⁵	C₂×C₃×D₅	1	1	yes	characteristic
214	C₂²×D₄	—	5	3	no	—
215	C₂³×C₄	—	5	1	no	—
216	#120	—	5	8	no	—
217	C₂×C₄⋊C₄	—	5	3	no	—
218	C₂×C₂²⋊C₄	—	5	3	no	—
219	C₂×C₂²⋊C₄	—	5	3	no	—
220	C₂×C₂²⋊C₄	—	5	3	no	—
221	C₂×C₂²⋊C₄	—	5	3	no	—
222	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	3	yes	—
223	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	3	yes	—
224	C₂×C₄²	—	5	3	no	—
225	#95	—	5	3	no	—
226	#95	—	5	3	no	—
227	C₂×C₃×C₅	—	4	6	no	—
228	C₂×C₃×C₅	#518	1	3	yes	—
229	C₂×C₃×C₅	#560	1	3	yes	—
230	C₂×C₃×C₅	H(3,𝔽₄)	1	1	yes	characteristic
231	C₃×D₅	—	4	2	no	—
232	C₂³×C₃	—	2	3	no	—
233	C₂³×C₃	—	2	3	no	—
234	C₂³×C₃	—	2	3	no	—
235	C₂³×C₃	—	2	3	no	—
236	C₂³×C₃	—	2	3	no	—
237	C₂³×C₃	—	2	3	no	—
238	C₂³×C₃	—	4	12	no	—
239	C₂³×C₃	—	4	4	no	—
240	C₂³×C₃	—	4	12	no	—
241	C₂³×C₃	—	5	2	no	—
242	C₂³×C₃	—	10	3	no	—
243	C₂³×C₃	—	10	3	no	—
244	C₂³×C₃	C₂×C₄×D₅	1	6	yes	—
245	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
246	C₃×D₄	—	20	12	no	—
247	C₂×C₃×C₄	—	2	3	no	—
248	C₂×C₃×C₄	—	2	3	no	—
249	C₂×C₃×C₄	—	2	3	no	—
250	C₂×C₃×C₄	—	2	3	no	—
251	C₂×C₃×C₄	—	5	6	no	—
252	C₂×C₃×C₄	—	10	3	no	—
253	C₂×C₃×C₄	—	10	3	no	—
254	C₂×C₃×C₄	—	10	3	no	—
255	C₂×C₃×C₄	—	10	3	no	—
256	C₂×C₃×C₄	—	10	3	no	—
257	C₂×C₃×C₄	—	10	3	no	—
258	C₂×C₃×C₄	—	20	4	no	—
259	C₂²×C₅	—	2	6	no	—
260	C₂²×C₅	—	2	6	no	—
261	C₂²×C₅	—	2	6	no	—
262	C₂²×C₅	—	4	16	no	—
263	C₂²×C₅	—	4	3	no	—
264	C₂²×C₅	—	4	3	no	—
265	C₂²×C₅	—	4	3	no	—
266	C₂²×C₅	—	4	3	no	—
267	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
268	C₂²×C₅	C₃×H(5,𝔽₂)	1	3	yes	—
269	C₂²×C₅	C₃×H(5,𝔽₂)	1	3	yes	—
270	C₂×D₅	—	2	6	no	—
271	C₂×D₅	—	4	3	no	—
272	C₂×D₅	—	4	1	no	—
273	C₄×C₅	—	4	3	no	—
274	C₄×C₅	—	4	1	no	—
275	Dic₅	—	2	6	no	—
276	Dic₅	—	4	3	no	—
277	Dic₅	—	4	1	no	—
278	C₂⁴	—	4	3	no	—
279	C₂⁴	—	4	3	no	—
280	C₂⁴	—	5	1	no	—
281	C₂⁴	C₃×C₄×D₅	1	4	yes	complemented
282	C₂⁴	C₂²×C₃×D₅	1	3	yes	—
283	C₂×D₄	—	5	12	no	—
284	C₂×D₄	—	20	3	no	—
285	C₂×D₄	—	20	3	no	—
286	C₂²×C₄	—	5	3	no	—
287	C₂²×C₄	—	5	1	no	—
288	C₂²×C₄	—	5	3	no	—
289	C₂²×C₄	—	20	3	no	—
290	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
291	C₂²×C₄	C₂²×C₃×D₅	1	3	yes	—
292	C₄⋊C₄	—	20	3	no	—
293	C₂²⋊C₄	—	4	3	no	—
294	C₂²⋊C₄	—	4	3	no	—
295	C₂²⋊C₄	—	5	12	no	—
296	C₂²⋊C₄	—	20	3	no	—
297	C₂²⋊C₄	—	20	3	no	—
298	C₂²⋊C₄	—	20	3	no	—
299	C₄²	—	20	3	no	—
300	C₃×C₅	#2375	1	1	yes	characteristic, complemented, Hall
301	C₂²×C₃	—	2	6	no	—
302	C₂²×C₃	—	2	6	no	—
303	C₂²×C₃	—	2	6	no	—
304	C₂²×C₃	—	4	16	no	—
305	C₂²×C₃	—	4	3	no	—
306	C₂²×C₃	—	4	3	no	—
307	C₂²×C₃	—	4	3	no	—
308	C₂²×C₃	—	4	3	no	—
309	C₂²×C₃	—	10	6	no	—
310	C₂²×C₃	—	20	1	no	—
311	C₂²×C₃	—	20	3	no	—
312	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
313	C₂²×C₃	#4144	1	3	yes	—
314	C₂²×C₃	#4144	1	3	yes	—
315	C₃×C₄	—	4	1	no	—
316	C₃×C₄	—	4	3	no	—
317	C₃×C₄	—	10	6	no	—
318	C₃×C₄	—	20	1	no	—
319	C₃×C₄	—	20	3	no	—
320	C₂×C₅	—	4	6	no	—
321	C₂×C₅	C₃×#518	1	3	yes	—
322	C₂×C₅	C₃×#560	1	3	yes	—
323	C₂×C₅	C₃×H(3,𝔽₄)	1	1	yes	characteristic
324	D₅	—	4	2	no	—
325	C₂³	—	2	3	no	—
326	C₂³	—	2	3	no	—
327	C₂³	—	2	3	no	—
328	C₂³	—	2	3	no	—
329	C₂³	—	2	3	no	—
330	C₂³	—	2	3	no	—
331	C₂³	—	4	12	no	—
332	C₂³	—	4	4	no	—
333	C₂³	—	4	12	no	—
334	C₂³	—	5	2	no	—
335	C₂³	—	10	3	no	—
336	C₂³	—	10	3	no	—
337	C₂³	C₂×C₃×C₄×D₅	1	6	yes	—
338	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
339	D₄	—	20	12	no	—
340	C₂×C₄	—	2	3	no	—
341	C₂×C₄	—	2	3	no	—
342	C₂×C₄	—	2	3	no	—
343	C₂×C₄	—	2	3	no	—
344	C₂×C₄	—	5	6	no	—
345	C₂×C₄	—	10	3	no	—
346	C₂×C₄	—	10	3	no	—
347	C₂×C₄	—	10	3	no	—
348	C₂×C₄	—	10	3	no	—
349	C₂×C₄	—	10	3	no	—
350	C₂×C₄	—	10	3	no	—
351	C₂×C₄	—	20	4	no	—
352	C₂×C₃	—	4	6	no	—
353	C₂×C₃	—	20	2	no	—
354	C₂×C₃	#65820	1	3	yes	—
355	C₂×C₃	#65928	1	1	yes	characteristic
356	C₂×C₃	#65929	1	3	yes	—
357	C₅	C₃×#2375	1	1	yes	characteristic, complemented, Sylow
358	C₂²	—	2	6	no	—
359	C₂²	—	2	6	no	—
360	C₂²	—	2	6	no	—
361	C₂²	—	4	16	no	—
362	C₂²	—	4	3	no	—
363	C₂²	—	4	3	no	—
364	C₂²	—	4	3	no	—
365	C₂²	—	4	3	no	—
366	C₂²	—	10	6	no	—
367	C₂²	—	20	1	no	—
368	C₂²	—	20	3	no	—
369	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
370	C₂²	C₃×#4144	1	3	yes	—
371	C₂²	C₃×#4144	1	3	yes	—
372	C₄	—	4	1	no	—
373	C₄	—	4	3	no	—
374	C₄	—	10	6	no	—
375	C₄	—	20	1	no	—
376	C₄	—	20	3	no	—
377	C₃	#10605582	1	1	yes	characteristic, direct product factor, Sylow
378	C₂	—	4	6	no	—
379	C₂	—	20	2	no	—
380	C₂	C₃×#65820	1	3	yes	—
381	C₂	C₃×#65928	1	1	yes	characteristic
382	C₂	C₃×#65929	1	3	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#379	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂×C₃×#4099	C₂
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#379	D₅
hypocenter	C₅	C₃×#2375
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#379

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#379	C₂	semidirect
3. C₃×#65536	C₂	semidirect
4. C₃×#65246	C₂	semidirect
5. C₃×#65245	C₂	semidirect
6. C₃×#65234	C₂	semidirect
7. C₃×#65233	C₂	semidirect
8. #10605582	C₃	direct (N × H)
11. C₂²×C₃×C₄×D₅	C₂²	semidirect
14. C₃×#4099	C₄	semidirect
18. C₂×C₃×#685	C₂²	semidirect
19. C₂×C₃×#683	C₂²	semidirect
20. C₂×C₃×C₄×Dic₅	C₂²	semidirect
21. C₃×#3963	C₂²	semidirect
22. C₃×#3963	C₂²	semidirect
25. C₅×#379	C₂×C₃	semidirect
26. #65536	C₂×C₃	semidirect
27. #65246	C₂×C₃	semidirect
28. #65245	C₂×C₃	semidirect
29. #65234	C₂×C₃	semidirect
30. #65233	C₂×C₃	semidirect
33. C₂⁴×C₃×C₅	C₂×C₄	semidirect
49. C₃×C₂²⋊Dic₅	C₂×C₄	semidirect
59. C₃×#379	D₅	semidirect
62. C₂²×C₄×D₅	C₂²×C₃	semidirect
65. #4099	C₃×C₄	semidirect
69. C₂×#685	C₂²×C₃	semidirect
70. C₂×#683	C₂²×C₃	semidirect
71. C₂×C₄×Dic₅	C₂²×C₃	semidirect
72. #3963	C₂²×C₃	semidirect
73. #3963	C₂²×C₃	semidirect
118. C₂⁴×C₅	C₂×C₃×C₄	semidirect
134. C₂²⋊Dic₅	C₂×C₃×C₄	semidirect
144. #379	C₃×D₅	semidirect
167. C₂⁴×C₃	C₄×D₅	semidirect
281. C₂⁴	C₃×C₄×D₅	semidirect
300. C₃×C₅	#2375	semidirect
357. C₅	C₃×#2375	semidirect
377. C₃	#10605582	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×#4099	2
C₃×C₅×#379	2
C₃×#65536	2
C₃×#65246	2
C₃×#65245	2
C₃×#65234	2
C₃×#65233	2
#10605582	3
C₃×#2375	5

Subgroups — C3×#10605582 #14330632

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605582 #14330632