Subgroups — C₃×#10605850 #14322384

Order 1920.

2320 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	C₂³×C₃×D₂₀	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×D₅×C₂²⋊C₄	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, complemented
6	C₃×#64954	C₂	1	8	yes	maximal, complemented
7	#10605850	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
9	C₂⁴×C₃×D₅	C₂²	1	1	yes	characteristic
10	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
11	C₂²×C₃×D₂₀	—	2	8	no	—
12	C₂²×C₃×D₂₀	C₄	1	8	yes	complemented
13	C₂²×C₃×D₂₀	C₂²	1	4	yes	—
14	C₂²×C₃×C₄×D₅	C₂²	1	4	yes	complemented
15	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
16	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#685	C₂²	1	4	yes	complemented
18	C₂×C₃×#685	C₂²	1	8	yes	complemented
19	C₃×D₅×C₂²⋊C₄	—	2	8	no	—
20	C₃×C₅×#95	C₂²	1	4	yes	complemented
21	C₃×#3963	C₂²	1	4	yes	complemented
22	C₃×#2308	—	5	1	no	maximal, Hall
23	C₂³×D₂₀	C₂×C₃	1	1	yes	characteristic
24	C₂×D₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
25	C₅×#381	C₂×C₃	1	1	yes	characteristic, complemented
26	#65500	C₂×C₃	1	1	yes	characteristic, complemented
27	#65244	C₂×C₃	1	2	yes	complemented
28	#64954	C₂×C₃	1	8	yes	complemented
29	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
30	C₂³×C₃×D₅	—	2	4	no	—
31	C₂³×C₃×D₅	—	4	4	no	—
32	C₂³×C₃×D₅	—	4	4	no	—
33	C₂³×C₃×D₅	C₂×C₄	1	4	yes	—
34	C₂³×C₃×D₅	C₂×C₄	1	4	yes	complemented
35	C₂³×C₃×D₅	D₄	1	8	yes	—
36	C₂³×C₃×D₅	C₂³	1	2	yes	—
37	C₂³×C₃×D₅	C₂³	1	2	yes	—
38	C₂²×C₃×C₄×C₅	—	2	4	no	—
39	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
40	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
41	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
42	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
43	C₂×C₃×D₂₀	—	2	32	no	—
44	C₂×C₃×D₂₀	—	2	8	no	—
45	C₂×C₃×D₂₀	—	2	8	no	—
46	C₂×C₃×D₂₀	C₂×C₄	1	16	yes	complemented
47	C₂×C₃×C₄×D₅	—	2	8	no	—
48	C₂×C₃×C₄×D₅	—	4	8	no	—
49	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
50	C₃×C₂²⋊Dic₅	—	2	4	no	—
51	C₃×#685	—	2	8	no	—
52	C₃×#685	—	4	8	no	—
53	C₂³×C₃×D₄	—	5	1	no	—
54	C₂²×C₃×C₂²⋊C₄	—	5	2	no	—
55	C₃×#386	—	5	8	no	—
56	C₃×#381	—	5	1	no	—
57	C₃×#381	D₅	1	1	yes	characteristic, complemented
58	C₃×#379	—	5	2	no	—
59	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
60	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
61	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
62	C₂²×D₂₀	—	2	8	no	—
63	C₂²×D₂₀	C₃×C₄	1	8	yes	complemented
64	C₂²×D₂₀	C₂²×C₃	1	4	yes	—
65	C₂²×C₄×D₅	C₂²×C₃	1	4	yes	complemented
66	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
67	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
68	C₂×#685	C₂²×C₃	1	4	yes	complemented
69	C₂×#685	C₂²×C₃	1	8	yes	complemented
70	D₅×C₂²⋊C₄	—	2	8	no	—
71	C₅×#95	C₂²×C₃	1	4	yes	complemented
72	#3963	C₂²×C₃	1	4	yes	complemented
73	#2308	—	5	1	no	Sylow
74	C₂³×C₃×C₅	—	2	4	no	—
75	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
76	C₂³×C₃×C₅	C₂×D₄	1	4	yes	—
77	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
78	C₂²×C₃×D₅	—	2	8	no	—
79	C₂²×C₃×D₅	—	2	8	no	—
80	C₂²×C₃×D₅	—	2	4	no	—
81	C₂²×C₃×D₅	—	2	8	no	—
82	C₂²×C₃×D₅	—	4	8	no	—
83	C₂²×C₃×D₅	—	4	8	no	—
84	C₂²×C₃×D₅	—	4	16	no	—
85	C₂²×C₃×D₅	—	4	16	no	—
86	C₂²×C₃×D₅	C₂²⋊C₄	1	16	yes	complemented
87	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
88	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
89	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
90	C₂²×C₃×D₅	C₂×D₄	1	4	yes	—
91	C₂×C₃×C₄×C₅	—	2	8	no	—
92	C₂×C₃×C₄×C₅	—	2	4	no	—
93	C₂×C₃×C₄×C₅	—	2	4	no	—
94	C₂×C₃×C₄×C₅	—	2	8	no	—
95	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
96	C₂×C₃×Dic₅	—	2	4	no	—
97	C₂×C₃×Dic₅	—	2	8	no	—
98	C₃×D₂₀	—	2	32	no	—
99	C₃×C₄×D₅	—	4	16	no	—
100	C₂⁵×C₃	—	5	1	no	—
101	C₂⁵×C₃	—	5	1	no	—
102	C₂²×C₃×D₄	—	5	8	no	—
103	C₂²×C₃×D₄	—	5	4	no	—
104	C₂²×C₃×D₄	—	10	8	no	—
105	C₂³×C₃×C₄	—	5	4	no	—
106	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
107	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
108	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
109	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
110	C₂×C₃×C₂²⋊C₄	—	10	8	no	—
111	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
112	C₃×#95	—	5	4	no	—
113	C₃×#95	C₂×D₅	1	4	yes	complemented
114	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
115	C₂³×D₅	—	2	4	no	—
116	C₂³×D₅	—	4	4	no	—
117	C₂³×D₅	—	4	4	no	—
118	C₂³×D₅	C₂×C₃×C₄	1	4	yes	—
119	C₂³×D₅	C₂×C₃×C₄	1	4	yes	complemented
120	C₂³×D₅	C₃×D₄	1	8	yes	—
121	C₂³×D₅	C₂³×C₃	1	2	yes	—
122	C₂³×D₅	C₂³×C₃	1	2	yes	—
123	C₂²×C₄×C₅	—	2	4	no	—
124	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
125	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
126	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
127	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
128	C₂×D₂₀	—	2	32	no	—
129	C₂×D₂₀	—	2	8	no	—
130	C₂×D₂₀	—	2	8	no	—
131	C₂×D₂₀	C₂×C₃×C₄	1	16	yes	complemented
132	C₂×C₄×D₅	—	2	8	no	—
133	C₂×C₄×D₅	—	4	8	no	—
134	C₅×C₂²⋊C₄	—	2	4	no	—
135	C₂²⋊Dic₅	—	2	4	no	—
136	#685	—	2	8	no	—
137	#685	—	4	8	no	—
138	C₂³×D₄	—	5	1	no	—
139	C₂²×C₂²⋊C₄	—	5	2	no	—
140	#386	—	5	8	no	—
141	#381	—	5	1	no	—
142	#381	C₃×D₅	1	1	yes	characteristic, complemented
143	#379	—	5	2	no	—
144	C₂²×C₃×C₅	—	2	4	no	—
145	C₂²×C₃×C₅	—	2	8	no	—
146	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
147	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
148	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
149	C₂²×C₃×C₅	H(5,𝔽₂)	1	4	yes	—
150	C₂×C₃×D₅	—	2	8	no	—
151	C₂×C₃×D₅	—	2	8	no	—
152	C₂×C₃×D₅	—	2	8	no	—
153	C₂×C₃×D₅	—	2	4	no	—
154	C₂×C₃×D₅	—	2	8	no	—
155	C₂×C₃×D₅	—	4	16	no	—
156	C₂×C₃×D₅	—	4	16	no	—
157	C₂×C₃×D₅	—	4	8	no	—
158	C₂×C₃×D₅	C₂×C₂²⋊C₄	1	8	yes	—
159	C₃×C₄×C₅	—	2	4	no	—
160	C₃×C₄×C₅	—	4	4	no	—
161	C₃×Dic₅	—	4	4	no	—
162	C₂⁴×C₃	—	5	2	no	—
163	C₂⁴×C₃	—	5	4	no	—
164	C₂⁴×C₃	—	5	8	no	—
165	C₂⁴×C₃	—	5	2	no	—
166	C₂⁴×C₃	—	5	4	no	—
167	C₂⁴×C₃	—	10	4	no	—
168	C₂⁴×C₃	—	20	4	no	—
169	C₂⁴×C₃	—	20	4	no	—
170	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
171	C₂×C₃×D₄	—	5	16	no	—
172	C₂×C₃×D₄	—	10	8	no	—
173	C₂×C₃×D₄	—	10	8	no	—
174	C₂×C₃×D₄	—	10	32	no	—
175	C₂²×C₃×C₄	—	2	4	no	—
176	C₂²×C₃×C₄	—	5	4	no	—
177	C₂²×C₃×C₄	—	10	8	no	—
178	C₂²×C₃×C₄	—	20	8	no	—
179	C₂²×C₃×C₄	C₄×D₅	1	4	yes	complemented
180	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
181	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
182	C₃×C₂²⋊C₄	—	2	4	no	—
183	C₃×C₂²⋊C₄	—	10	8	no	—
184	C₃×C₂²⋊C₄	—	10	4	no	—
185	C₃×C₂²⋊C₄	—	20	8	no	—
186	C₂³×C₅	—	2	4	no	—
187	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
188	C₂³×C₅	C₂×C₃×D₄	1	4	yes	—
189	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
190	C₂²×D₅	—	2	8	no	—
191	C₂²×D₅	—	2	8	no	—
192	C₂²×D₅	—	2	4	no	—
193	C₂²×D₅	—	2	8	no	—
194	C₂²×D₅	—	4	8	no	—
195	C₂²×D₅	—	4	8	no	—
196	C₂²×D₅	—	4	16	no	—
197	C₂²×D₅	—	4	16	no	—
198	C₂²×D₅	C₃×C₂²⋊C₄	1	16	yes	complemented
199	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
200	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
201	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
202	C₂²×D₅	C₂×C₃×D₄	1	4	yes	—
203	C₂×C₄×C₅	—	2	8	no	—
204	C₂×C₄×C₅	—	2	4	no	—
205	C₂×C₄×C₅	—	2	4	no	—
206	C₂×C₄×C₅	—	2	8	no	—
207	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
208	C₂×Dic₅	—	2	4	no	—
209	C₂×Dic₅	—	2	8	no	—
210	D₂₀	—	2	32	no	—
211	C₄×D₅	—	4	16	no	—
212	C₂⁵	—	5	1	no	—
213	C₂⁵	—	5	1	no	—
214	C₂²×D₄	—	5	8	no	—
215	C₂²×D₄	—	5	4	no	—
216	C₂²×D₄	—	10	8	no	—
217	C₂³×C₄	—	5	4	no	—
218	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
219	C₂×C₂²⋊C₄	—	5	2	no	—
220	C₂×C₂²⋊C₄	—	5	4	no	—
221	C₂×C₂²⋊C₄	—	5	8	no	—
222	C₂×C₂²⋊C₄	—	10	8	no	—
223	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
224	#95	—	5	4	no	—
225	#95	C₂×C₃×D₅	1	4	yes	complemented
226	C₂×C₃×C₅	—	2	4	no	—
227	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×C₃×C₅	#518	1	2	yes	—
229	C₂×C₃×C₅	#534	1	4	yes	—
230	C₃×D₅	—	2	8	no	—
231	C₃×D₅	—	4	4	no	—
232	C₂³×C₃	—	2	4	no	—
233	C₂³×C₃	—	5	4	no	—
234	C₂³×C₃	—	5	4	no	—
235	C₂³×C₃	—	5	4	no	—
236	C₂³×C₃	—	5	16	no	—
237	C₂³×C₃	—	5	4	no	—
238	C₂³×C₃	—	10	8	no	—
239	C₂³×C₃	—	10	4	no	—
240	C₂³×C₃	—	10	8	no	—
241	C₂³×C₃	—	10	8	no	—
242	C₂³×C₃	—	20	8	no	—
243	C₂³×C₃	—	20	8	no	—
244	C₂³×C₃	—	20	16	no	—
245	C₂³×C₃	—	20	16	no	—
246	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
247	C₂³×C₃	D₄×D₅	1	4	yes	—
248	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
249	C₃×D₄	—	10	32	no	—
250	C₂×C₃×C₄	—	2	4	no	—
251	C₂×C₃×C₄	—	2	8	no	—
252	C₂×C₃×C₄	—	2	4	no	—
253	C₂×C₃×C₄	—	2	8	no	—
254	C₂×C₃×C₄	—	10	4	no	—
255	C₂×C₃×C₄	—	10	8	no	—
256	C₂×C₃×C₄	—	20	16	no	—
257	C₂×C₃×C₄	C₂×C₄×D₅	1	4	yes	—
258	C₂²×C₅	—	2	4	no	—
259	C₂²×C₅	—	2	8	no	—
260	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
261	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
262	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
263	C₂²×C₅	C₃×H(5,𝔽₂)	1	4	yes	—
264	C₂×D₅	—	2	8	no	—
265	C₂×D₅	—	2	8	no	—
266	C₂×D₅	—	2	8	no	—
267	C₂×D₅	—	2	4	no	—
268	C₂×D₅	—	2	8	no	—
269	C₂×D₅	—	4	16	no	—
270	C₂×D₅	—	4	16	no	—
271	C₂×D₅	—	4	8	no	—
272	C₂×D₅	C₂×C₃×C₂²⋊C₄	1	8	yes	—
273	C₄×C₅	—	2	4	no	—
274	C₄×C₅	—	4	4	no	—
275	Dic₅	—	4	4	no	—
276	C₂⁴	—	5	2	no	—
277	C₂⁴	—	5	4	no	—
278	C₂⁴	—	5	8	no	—
279	C₂⁴	—	5	2	no	—
280	C₂⁴	—	5	4	no	—
281	C₂⁴	—	10	4	no	—
282	C₂⁴	—	20	4	no	—
283	C₂⁴	—	20	4	no	—
284	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
285	C₂×D₄	—	5	16	no	—
286	C₂×D₄	—	10	8	no	—
287	C₂×D₄	—	10	8	no	—
288	C₂×D₄	—	10	32	no	—
289	C₂²×C₄	—	2	4	no	—
290	C₂²×C₄	—	5	4	no	—
291	C₂²×C₄	—	10	8	no	—
292	C₂²×C₄	—	20	8	no	—
293	C₂²×C₄	C₃×C₄×D₅	1	4	yes	complemented
294	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
295	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
296	C₂²⋊C₄	—	2	4	no	—
297	C₂²⋊C₄	—	10	8	no	—
298	C₂²⋊C₄	—	10	4	no	—
299	C₂²⋊C₄	—	20	8	no	—
300	C₃×C₅	#2308	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	8	no	—
305	C₂²×C₃	—	10	8	no	—
306	C₂²×C₃	—	10	8	no	—
307	C₂²×C₃	—	10	4	no	—
308	C₂²×C₃	—	10	8	no	—
309	C₂²×C₃	—	20	16	no	—
310	C₂²×C₃	—	20	16	no	—
311	C₂²×C₃	—	20	8	no	—
312	C₂²×C₃	D₅×C₂²⋊C₄	1	4	yes	—
313	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
314	C₂²×C₃	C₂×D₄×D₅	1	2	yes	—
315	C₂²×C₃	#4149	1	4	yes	—
316	C₃×C₄	—	2	4	no	—
317	C₃×C₄	—	4	4	no	—
318	C₃×C₄	—	20	4	no	—
319	C₂×C₅	—	2	4	no	—
320	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
321	C₂×C₅	C₃×#518	1	2	yes	—
322	C₂×C₅	C₃×#534	1	4	yes	—
323	D₅	—	2	8	no	—
324	D₅	—	4	4	no	—
325	C₂³	—	2	4	no	—
326	C₂³	—	5	4	no	—
327	C₂³	—	5	4	no	—
328	C₂³	—	5	4	no	—
329	C₂³	—	5	16	no	—
330	C₂³	—	5	4	no	—
331	C₂³	—	10	8	no	—
332	C₂³	—	10	4	no	—
333	C₂³	—	10	8	no	—
334	C₂³	—	10	8	no	—
335	C₂³	—	20	8	no	—
336	C₂³	—	20	8	no	—
337	C₂³	—	20	16	no	—
338	C₂³	—	20	16	no	—
339	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
340	C₂³	C₃×D₄×D₅	1	4	yes	—
341	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
342	D₄	—	10	32	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	8	no	—
345	C₂×C₄	—	2	4	no	—
346	C₂×C₄	—	2	8	no	—
347	C₂×C₄	—	10	4	no	—
348	C₂×C₄	—	10	8	no	—
349	C₂×C₄	—	20	16	no	—
350	C₂×C₄	C₂×C₃×C₄×D₅	1	4	yes	—
351	C₂×C₃	—	2	4	no	—
352	C₂×C₃	—	10	8	no	—
353	C₂×C₃	—	20	4	no	—
354	C₂×C₃	C₂×D₅×C₂²⋊C₄	1	1	yes	characteristic
355	C₂×C₃	#65855	1	2	yes	—
356	C₂×C₃	#65987	1	4	yes	—
357	C₅	C₃×#2308	1	1	yes	characteristic, complemented, Sylow
358	C₂²	—	2	4	no	—
359	C₂²	—	2	8	no	—
360	C₂²	—	5	8	no	—
361	C₂²	—	10	8	no	—
362	C₂²	—	10	8	no	—
363	C₂²	—	10	8	no	—
364	C₂²	—	10	8	no	—
365	C₂²	—	10	4	no	—
366	C₂²	—	20	16	no	—
367	C₂²	—	20	16	no	—
368	C₂²	—	20	8	no	—
369	C₂²	C₃×D₅×C₂²⋊C₄	1	4	yes	—
370	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
371	C₂²	C₂×C₃×D₄×D₅	1	2	yes	—
372	C₂²	C₃×#4149	1	4	yes	—
373	C₄	—	2	4	no	—
374	C₄	—	4	4	no	—
375	C₄	—	20	4	no	—
376	C₃	#10605850	1	1	yes	characteristic, direct product factor, Sylow
377	C₂	—	2	4	no	—
378	C₂	—	10	8	no	—
379	C₂	—	20	4	no	—
380	C₂	C₂×C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
381	C₂	C₃×#65855	1	2	yes	—
382	C₂	C₃×#65987	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	C₂³×C₃×D₂₀	C₂
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#381	D₅
hypocenter	C₅	C₃×#2308
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×D₅×C₂²⋊C₄	C₂	semidirect
3. C₃×C₅×#381	C₂	semidirect
4. C₃×#65500	C₂	semidirect
5. C₃×#65244	C₂	semidirect
6. C₃×#64954	C₂	semidirect
7. #10605850	C₃	direct (N × H)
12. C₂²×C₃×D₂₀	C₄	semidirect
14. C₂²×C₃×C₄×D₅	C₂²	semidirect
17. C₂×C₃×#685	C₂²	semidirect
18. C₂×C₃×#685	C₂²	semidirect
20. C₃×C₅×#95	C₂²	semidirect
21. C₃×#3963	C₂²	semidirect
24. C₂×D₅×C₂²⋊C₄	C₂×C₃	semidirect
25. C₅×#381	C₂×C₃	semidirect
26. #65500	C₂×C₃	semidirect
27. #65244	C₂×C₃	semidirect
28. #64954	C₂×C₃	semidirect
34. C₂³×C₃×D₅	C₂×C₄	semidirect
39. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
46. C₂×C₃×D₂₀	C₂×C₄	semidirect
57. C₃×#381	D₅	semidirect
63. C₂²×D₂₀	C₃×C₄	semidirect
65. C₂²×C₄×D₅	C₂²×C₃	semidirect
68. C₂×#685	C₂²×C₃	semidirect
69. C₂×#685	C₂²×C₃	semidirect
71. C₅×#95	C₂²×C₃	semidirect
72. #3963	C₂²×C₃	semidirect
86. C₂²×C₃×D₅	C₂²⋊C₄	semidirect
113. C₃×#95	C₂×D₅	semidirect
119. C₂³×D₅	C₂×C₃×C₄	semidirect
124. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
131. C₂×D₂₀	C₂×C₃×C₄	semidirect
142. #381	C₃×D₅	semidirect
179. C₂²×C₃×C₄	C₄×D₅	semidirect
198. C₂²×D₅	C₃×C₂²⋊C₄	semidirect
225. #95	C₂×C₃×D₅	semidirect
293. C₂²×C₄	C₃×C₄×D₅	semidirect
300. C₃×C₅	#2308	semidirect
357. C₅	C₃×#2308	semidirect
376. C₃	#10605850	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×D₂₀	2
C₂×C₃×D₅×C₂²⋊C₄	2
C₃×C₅×#381	2
C₃×#65500	2
C₃×#65244	2
C₃×#64954	2
#10605850	3
C₃×#2308	5

Subgroups — C3×#10605850 #14322384

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605850 #14322384