Subgroups — C₃×#10605781 #14319909

Order 1920.

2176 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	C₂³×C₃×C₄×D₅	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×#4023	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#381	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65500	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65244	C₂	1	2	yes	maximal
6	C₃×#64956	C₂	1	4	yes	maximal, complemented
7	C₃×#64955	C₂	1	4	yes	maximal, complemented
8	#10605781	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂³×C₃×Dic₅	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₄×D₅	—	2	8	no	—
13	C₂²×C₃×C₄×D₅	C₄	1	8	yes	complemented
14	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
15	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
17	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
18	C₂×C₃×#685	C₂²	1	8	yes	—
19	C₂×C₃×#683	C₂²	1	4	yes	complemented
20	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	complemented
21	C₃×#4023	—	2	8	no	—
22	C₃×C₅×#95	C₂²	1	4	yes	complemented
23	C₃×#3963	C₂²	1	4	yes	complemented
24	C₃×#2280	—	5	1	no	maximal, Hall
25	C₂³×C₄×D₅	C₂×C₃	1	1	yes	characteristic
26	C₂×#4023	C₂×C₃	1	2	yes	complemented
27	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
28	#65500	C₂×C₃	1	1	yes	characteristic, complemented
29	#65244	C₂×C₃	1	2	yes	—
30	#64956	C₂×C₃	1	4	yes	complemented
31	#64955	C₂×C₃	1	4	yes	complemented
32	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
33	C₂³×C₃×D₅	—	2	4	no	—
34	C₂³×C₃×D₅	—	2	8	no	—
35	C₂³×C₃×D₅	C₂×C₄	1	4	yes	—
36	C₂³×C₃×D₅	C₂³	1	2	yes	—
37	C₂²×C₃×C₄×C₅	—	2	4	no	—
38	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
39	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
40	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
41	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
42	C₂²×C₃×Dic₅	D₄	1	8	yes	—
43	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
44	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	C₂³	1	1	yes	characteristic
46	C₂×C₃×C₄×D₅	—	2	32	no	—
47	C₂×C₃×C₄×D₅	—	2	8	no	—
48	C₂×C₃×C₄×D₅	—	2	8	no	—
49	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
50	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
51	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
52	C₃×C₂²⋊Dic₅	—	2	4	no	—
53	C₃×#685	—	2	16	no	—
54	C₃×#683	—	2	8	no	—
55	C₃×C₄×Dic₅	—	2	8	no	—
56	C₂⁴×C₃×C₄	—	5	1	no	—
57	C₂×C₃×#117	—	5	2	no	—
58	C₃×#381	—	5	1	no	—
59	C₃×#381	D₅	1	1	yes	characteristic, complemented
60	C₃×#380	—	5	4	no	—
61	C₃×#379	—	5	2	no	—
62	C₃×C₄×C₂²⋊C₄	—	5	4	no	—
63	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
64	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
65	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
66	C₂²×C₄×D₅	—	2	8	no	—
67	C₂²×C₄×D₅	C₃×C₄	1	8	yes	complemented
68	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
69	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
70	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
71	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
72	C₂×#685	C₂²×C₃	1	8	yes	—
73	C₂×#683	C₂²×C₃	1	4	yes	complemented
74	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	complemented
75	#4023	—	2	8	no	—
76	C₅×#95	C₂²×C₃	1	4	yes	complemented
77	#3963	C₂²×C₃	1	4	yes	complemented
78	#2280	—	5	1	no	Sylow
79	C₂³×C₃×C₅	—	2	4	no	—
80	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
81	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
82	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
83	C₂²×C₃×D₅	—	2	32	no	—
84	C₂²×C₃×D₅	—	2	8	no	—
85	C₂²×C₃×D₅	—	2	4	no	—
86	C₂²×C₃×D₅	—	2	4	no	—
87	C₂²×C₃×D₅	—	2	16	no	—
88	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
89	C₂²×C₃×D₅	#41	1	8	yes	—
90	C₂×C₃×C₄×C₅	—	2	8	no	—
91	C₂×C₃×C₄×C₅	—	2	4	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	8	no	—
94	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
95	C₂×C₃×Dic₅	—	2	4	no	—
96	C₂×C₃×Dic₅	—	2	8	no	—
97	C₂×C₃×Dic₅	C₂²⋊C₄	1	16	yes	complemented
98	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
99	C₂×C₃×Dic₅	C₂²×C₄	1	2	yes	—
100	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
101	C₂×C₃×Dic₅	C₂×D₄	1	4	yes	—
102	C₃×C₄×D₅	—	2	16	no	—
103	C₃×C₄×D₅	—	2	16	no	—
104	C₂⁵×C₃	—	5	1	no	—
105	C₂³×C₃×C₄	—	5	1	no	—
106	C₂³×C₃×C₄	—	5	8	no	—
107	C₂³×C₃×C₄	—	5	2	no	—
108	C₂³×C₃×C₄	—	5	2	no	—
109	C₂³×C₃×C₄	—	10	8	no	—
110	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
111	C₃×#117	—	10	8	no	—
112	C₂×C₃×C₄⋊C₄	—	5	4	no	—
113	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
114	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
115	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
116	C₂×C₃×C₄²	—	5	4	no	—
117	C₃×#95	—	5	4	no	—
118	C₃×#95	C₂×D₅	1	4	yes	complemented
119	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
120	C₂³×D₅	—	2	4	no	—
121	C₂³×D₅	—	2	8	no	—
122	C₂³×D₅	C₂×C₃×C₄	1	4	yes	—
123	C₂³×D₅	C₂³×C₃	1	2	yes	—
124	C₂²×C₄×C₅	—	2	4	no	—
125	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
126	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
127	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
128	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
129	C₂²×Dic₅	C₃×D₄	1	8	yes	—
130	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
131	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
132	C₂²×Dic₅	C₂³×C₃	1	1	yes	characteristic
133	C₂×C₄×D₅	—	2	32	no	—
134	C₂×C₄×D₅	—	2	8	no	—
135	C₂×C₄×D₅	—	2	8	no	—
136	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
137	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
138	C₅×C₂²⋊C₄	—	2	4	no	—
139	C₂²⋊Dic₅	—	2	4	no	—
140	#685	—	2	16	no	—
141	#683	—	2	8	no	—
142	C₄×Dic₅	—	2	8	no	—
143	C₂⁴×C₄	—	5	1	no	—
144	C₂×#117	—	5	2	no	—
145	#381	—	5	1	no	—
146	#381	C₃×D₅	1	1	yes	characteristic, complemented
147	#380	—	5	4	no	—
148	#379	—	5	2	no	—
149	C₄×C₂²⋊C₄	—	5	4	no	—
150	C₂²×C₃×C₅	—	2	4	no	—
151	C₂²×C₃×C₅	—	2	8	no	—
152	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
153	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
154	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
155	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
156	C₂×C₃×D₅	—	2	32	no	—
157	C₂×C₃×D₅	—	2	4	no	—
158	C₂×C₃×D₅	—	2	4	no	—
159	C₂×C₃×D₅	—	2	16	no	—
160	C₂×C₃×D₅	#117	1	8	yes	complemented
161	C₃×C₄×C₅	—	2	4	no	—
162	C₃×C₄×C₅	—	4	4	no	—
163	C₃×Dic₅	—	4	4	no	—
164	C₃×Dic₅	C₂×C₂²⋊C₄	1	4	yes	—
165	C₃×Dic₅	C₂×C₂²⋊C₄	1	4	yes	—
166	C₂⁴×C₃	—	5	2	no	—
167	C₂⁴×C₃	—	5	4	no	—
168	C₂⁴×C₃	—	10	8	no	—
169	C₂⁴×C₃	—	10	4	no	—
170	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
171	C₂²×C₃×C₄	—	2	4	no	—
172	C₂²×C₃×C₄	—	5	4	no	—
173	C₂²×C₃×C₄	—	5	8	no	—
174	C₂²×C₃×C₄	—	5	1	no	—
175	C₂²×C₃×C₄	—	5	1	no	—
176	C₂²×C₃×C₄	—	5	8	no	—
177	C₂²×C₃×C₄	—	5	8	no	—
178	C₂²×C₃×C₄	—	5	4	no	—
179	C₂²×C₃×C₄	—	10	8	no	—
180	C₂²×C₃×C₄	—	10	8	no	—
181	C₂²×C₃×C₄	—	10	32	no	—
182	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
183	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
184	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
185	C₃×C₄⋊C₄	—	10	8	no	—
186	C₃×C₂²⋊C₄	—	2	4	no	—
187	C₃×C₂²⋊C₄	—	10	16	no	—
188	C₃×C₂²⋊C₄	—	10	4	no	—
189	C₃×C₄²	—	10	8	no	—
190	C₂³×C₅	—	2	4	no	—
191	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
192	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
193	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
194	C₂²×D₅	—	2	32	no	—
195	C₂²×D₅	—	2	8	no	—
196	C₂²×D₅	—	2	4	no	—
197	C₂²×D₅	—	2	4	no	—
198	C₂²×D₅	—	2	16	no	—
199	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
200	C₂²×D₅	C₃×#41	1	8	yes	—
201	C₂×C₄×C₅	—	2	8	no	—
202	C₂×C₄×C₅	—	2	4	no	—
203	C₂×C₄×C₅	—	2	4	no	—
204	C₂×C₄×C₅	—	2	8	no	—
205	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
206	C₂×Dic₅	—	2	4	no	—
207	C₂×Dic₅	—	2	8	no	—
208	C₂×Dic₅	C₃×C₂²⋊C₄	1	16	yes	complemented
209	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
210	C₂×Dic₅	C₂²×C₃×C₄	1	2	yes	—
211	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
212	C₂×Dic₅	C₂×C₃×D₄	1	4	yes	—
213	C₄×D₅	—	2	16	no	—
214	C₄×D₅	—	2	16	no	—
215	C₂⁵	—	5	1	no	—
216	C₂³×C₄	—	5	1	no	—
217	C₂³×C₄	—	5	8	no	—
218	C₂³×C₄	—	5	2	no	—
219	C₂³×C₄	—	5	2	no	—
220	C₂³×C₄	—	10	8	no	—
221	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
222	#117	—	10	8	no	—
223	C₂×C₄⋊C₄	—	5	4	no	—
224	C₂×C₂²⋊C₄	—	5	2	no	—
225	C₂×C₂²⋊C₄	—	5	8	no	—
226	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
227	C₂×C₄²	—	5	4	no	—
228	#95	—	5	4	no	—
229	#95	C₂×C₃×D₅	1	4	yes	complemented
230	C₂×C₃×C₅	—	2	4	no	—
231	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
232	C₂×C₃×C₅	C₂×#117	1	2	yes	—
233	C₂×C₃×C₅	#525	1	4	yes	—
234	C₃×D₅	—	2	8	no	—
235	C₂³×C₃	—	2	4	no	—
236	C₂³×C₃	—	5	4	no	—
237	C₂³×C₃	—	5	8	no	—
238	C₂³×C₃	—	10	16	no	—
239	C₂³×C₃	—	10	32	no	—
240	C₂³×C₃	—	10	4	no	—
241	C₂³×C₃	—	10	4	no	—
242	C₂³×C₃	—	10	8	no	—
243	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
244	C₂³×C₃	D₄×D₅	1	4	yes	—
245	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
246	C₂×C₃×C₄	—	2	4	no	—
247	C₂×C₃×C₄	—	2	8	no	—
248	C₂×C₃×C₄	—	2	4	no	—
249	C₂×C₃×C₄	—	2	8	no	—
250	C₂×C₃×C₄	—	5	2	no	—
251	C₂×C₃×C₄	—	5	2	no	—
252	C₂×C₃×C₄	—	5	4	no	—
253	C₂×C₃×C₄	—	5	4	no	—
254	C₂×C₃×C₄	—	5	16	no	—
255	C₂×C₃×C₄	—	10	16	no	—
256	C₂×C₃×C₄	—	10	16	no	—
257	C₂×C₃×C₄	—	10	4	no	—
258	C₂×C₃×C₄	—	10	8	no	—
259	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
260	C₂²×C₅	—	2	4	no	—
261	C₂²×C₅	—	2	8	no	—
262	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
263	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
264	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
265	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
266	C₂×D₅	—	2	32	no	—
267	C₂×D₅	—	2	4	no	—
268	C₂×D₅	—	2	4	no	—
269	C₂×D₅	—	2	16	no	—
270	C₂×D₅	C₃×#117	1	8	yes	complemented
271	C₄×C₅	—	2	4	no	—
272	C₄×C₅	—	4	4	no	—
273	Dic₅	—	4	4	no	—
274	Dic₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
275	Dic₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
276	C₂⁴	—	5	2	no	—
277	C₂⁴	—	5	4	no	—
278	C₂⁴	—	10	8	no	—
279	C₂⁴	—	10	4	no	—
280	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
281	C₂²×C₄	—	2	4	no	—
282	C₂²×C₄	—	5	4	no	—
283	C₂²×C₄	—	5	8	no	—
284	C₂²×C₄	—	5	1	no	—
285	C₂²×C₄	—	5	1	no	—
286	C₂²×C₄	—	5	8	no	—
287	C₂²×C₄	—	5	8	no	—
288	C₂²×C₄	—	5	4	no	—
289	C₂²×C₄	—	10	8	no	—
290	C₂²×C₄	—	10	8	no	—
291	C₂²×C₄	—	10	32	no	—
292	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
293	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
294	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
295	C₄⋊C₄	—	10	8	no	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	10	16	no	—
298	C₂²⋊C₄	—	10	4	no	—
299	C₄²	—	10	8	no	—
300	C₃×C₅	#2280	1	1	yes	characteristic, complemented, Hall
301	C₂²×C₃	—	2	4	no	—
302	C₂²×C₃	—	2	8	no	—
303	C₂²×C₃	—	5	8	no	—
304	C₂²×C₃	—	10	32	no	—
305	C₂²×C₃	—	10	4	no	—
306	C₂²×C₃	—	10	4	no	—
307	C₂²×C₃	—	10	16	no	—
308	C₂²×C₃	D₅×C₂²⋊C₄	1	4	yes	—
309	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
310	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
311	C₂²×C₃	D₅×#41	1	4	yes	—
312	C₃×C₄	—	2	4	no	—
313	C₃×C₄	—	4	4	no	—
314	C₃×C₄	—	5	4	no	—
315	C₃×C₄	—	5	4	no	—
316	C₃×C₄	—	20	4	no	—
317	C₂×C₅	—	2	4	no	—
318	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
319	C₂×C₅	C₂×C₃×#117	1	2	yes	—
320	C₂×C₅	C₃×#525	1	4	yes	—
321	D₅	—	2	8	no	—
322	C₂³	—	2	4	no	—
323	C₂³	—	5	4	no	—
324	C₂³	—	5	8	no	—
325	C₂³	—	10	16	no	—
326	C₂³	—	10	32	no	—
327	C₂³	—	10	4	no	—
328	C₂³	—	10	4	no	—
329	C₂³	—	10	8	no	—
330	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
331	C₂³	C₃×D₄×D₅	1	4	yes	—
332	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
333	C₂×C₄	—	2	4	no	—
334	C₂×C₄	—	2	8	no	—
335	C₂×C₄	—	2	4	no	—
336	C₂×C₄	—	2	8	no	—
337	C₂×C₄	—	5	2	no	—
338	C₂×C₄	—	5	2	no	—
339	C₂×C₄	—	5	4	no	—
340	C₂×C₄	—	5	4	no	—
341	C₂×C₄	—	5	16	no	—
342	C₂×C₄	—	10	16	no	—
343	C₂×C₄	—	10	16	no	—
344	C₂×C₄	—	10	4	no	—
345	C₂×C₄	—	10	8	no	—
346	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
347	C₂×C₃	—	2	4	no	—
348	C₂×C₃	—	10	8	no	—
349	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
350	C₂×C₃	D₅×#117	1	2	yes	—
351	C₂×C₃	#65990	1	4	yes	—
352	C₅	C₃×#2280	1	1	yes	characteristic, complemented, Sylow
353	C₂²	—	2	4	no	—
354	C₂²	—	2	8	no	—
355	C₂²	—	5	8	no	—
356	C₂²	—	10	32	no	—
357	C₂²	—	10	4	no	—
358	C₂²	—	10	16	no	—
359	C₂²	—	10	4	no	—
360	C₂²	C₃×D₅×C₂²⋊C₄	1	4	yes	—
361	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
362	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
363	C₂²	C₃×D₅×#41	1	4	yes	—
364	C₄	—	2	4	no	—
365	C₄	—	4	4	no	—
366	C₄	—	5	4	no	—
367	C₄	—	5	4	no	—
368	C₄	—	20	4	no	—
369	C₃	#10605781	1	1	yes	characteristic, direct product factor, Sylow
370	C₂	—	2	4	no	—
371	C₂	—	10	8	no	—
372	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
373	C₂	C₃×D₅×#117	1	2	yes	—
374	C₂	C₃×#65990	1	4	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#381	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×D₅	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#381	D₅
hypocenter	C₅	C₃×#2280
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#381

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×#4023	C₂	semidirect
3. C₃×C₅×#381	C₂	semidirect
4. C₃×#65500	C₂	semidirect
6. C₃×#64956	C₂	semidirect
7. C₃×#64955	C₂	semidirect
8. #10605781	C₃	direct (N × H)
13. C₂²×C₃×C₄×D₅	C₄	semidirect
19. C₂×C₃×#683	C₂²	semidirect
20. C₂×C₃×C₄×Dic₅	C₂²	semidirect
22. C₃×C₅×#95	C₂²	semidirect
23. C₃×#3963	C₂²	semidirect
26. C₂×#4023	C₂×C₃	semidirect
27. C₅×#381	C₂×C₃	semidirect
28. #65500	C₂×C₃	semidirect
30. #64956	C₂×C₃	semidirect
31. #64955	C₂×C₃	semidirect
59. C₃×#381	D₅	semidirect
67. C₂²×C₄×D₅	C₃×C₄	semidirect
73. C₂×#683	C₂²×C₃	semidirect
74. C₂×C₄×Dic₅	C₂²×C₃	semidirect
76. C₅×#95	C₂²×C₃	semidirect
77. #3963	C₂²×C₃	semidirect
97. C₂×C₃×Dic₅	C₂²⋊C₄	semidirect
118. C₃×#95	C₂×D₅	semidirect
146. #381	C₃×D₅	semidirect
160. C₂×C₃×D₅	#117	semidirect
208. C₂×Dic₅	C₃×C₂²⋊C₄	semidirect
229. #95	C₂×C₃×D₅	semidirect
270. C₂×D₅	C₃×#117	semidirect
300. C₃×C₅	#2280	semidirect
352. C₅	C₃×#2280	semidirect
369. C₃	#10605781	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×C₃×C₄×D₅	2
C₂×C₃×#4023	2
C₃×C₅×#381	2
C₃×#65500	2
C₃×#65244	2
C₃×#64956	2
C₃×#64955	2
#10605781	3
C₃×#2280	5

Subgroups — C3×#10605781 #14319909

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605781 #14319909