Subgroups — C₃×#10605735 #14322594

Order 1920.

1344 conjugacy classes of subgroups.

The subgroup lattice has 432 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#685	C₂	1	1	yes	maximal, characteristic
2	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65501	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65279	C₂	1	4	yes	maximal, complemented
5	C₃×#65244	C₂	1	2	yes	maximal
6	C₃×C₂²⋊C₄×Dic₅	C₂	1	2	yes	maximal, complemented
7	C₃×#64959	C₂	1	4	yes	maximal, complemented
8	#10605735	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	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
13	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
14	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
15	C₂×C₃×#685	C₄	1	8	yes	complemented
16	C₂×C₃×#685	C₂²	1	4	yes	—
17	C₂×C₃×#685	C₂²	1	4	yes	—
18	C₂×C₃×#685	C₂²	1	2	yes	—
19	C₂×C₃×#685	C₂²	1	2	yes	—
20	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
21	C₂×C₃×C₄×Dic₅	C₂²	1	4	yes	complemented
22	C₃×C₅×#95	C₂²	1	2	yes	complemented
23	C₃×#3963	C₂²	1	4	yes	complemented
24	C₃×#3963	C₂²	1	2	yes	complemented
25	C₃×#2312	—	5	1	no	maximal, Hall
26	C₂²×#685	C₂×C₃	1	1	yes	characteristic
27	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
28	#65501	C₂×C₃	1	1	yes	characteristic, complemented
29	#65279	C₂×C₃	1	4	yes	complemented
30	#65244	C₂×C₃	1	2	yes	—
31	C₂²⋊C₄×Dic₅	C₂×C₃	1	2	yes	complemented
32	#64959	C₂×C₃	1	4	yes	complemented
33	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
34	C₂³×C₃×D₅	—	2	2	no	—
35	C₂³×C₃×D₅	—	2	2	no	—
36	C₂³×C₃×D₅	—	4	2	no	—
37	C₂³×C₃×D₅	—	4	2	no	—
38	C₂³×C₃×D₅	C₂×C₄	1	4	yes	—
39	C₂³×C₃×D₅	C₂³	1	2	yes	—
40	C₂²×C₃×C₄×C₅	—	4	2	no	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
45	C₂²×C₃×Dic₅	—	4	2	no	—
46	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
47	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
48	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
49	C₃×C₅×C₄⋊C₄	—	4	2	no	—
50	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
51	C₃×C₂²⋊Dic₅	—	2	4	no	—
52	C₃×#685	—	4	4	no	—
53	C₃×#685	—	4	4	no	—
54	C₃×#685	C₂×C₄	1	8	yes	—
55	C₃×#685	C₂×C₄	1	8	yes	—
56	C₃×C₄⋊Dic₅	—	4	2	no	—
57	C₃×C₄×Dic₅	—	4	4	no	—
58	C₂²×C₃×C₂²⋊C₄	—	5	1	no	—
59	C₃×#388	—	5	4	no	—
60	C₃×#388	—	5	4	no	—
61	C₃×#380	—	5	1	no	—
62	C₃×#380	D₅	1	1	yes	characteristic, complemented
63	C₃×#379	—	5	2	no	—
64	C₃×C₄×C₂²⋊C₄	—	5	2	no	—
65	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
66	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
67	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
68	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
69	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
70	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
71	C₂×#685	C₃×C₄	1	8	yes	complemented
72	C₂×#685	C₂²×C₃	1	4	yes	—
73	C₂×#685	C₂²×C₃	1	4	yes	—
74	C₂×#685	C₂²×C₃	1	2	yes	—
75	C₂×#685	C₂²×C₃	1	2	yes	—
76	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
77	C₂×C₄×Dic₅	C₂²×C₃	1	4	yes	complemented
78	C₅×#95	C₂²×C₃	1	2	yes	complemented
79	#3963	C₂²×C₃	1	4	yes	complemented
80	#3963	C₂²×C₃	1	2	yes	complemented
81	#2312	—	5	1	no	Sylow
82	C₂³×C₃×C₅	—	2	2	no	—
83	C₂³×C₃×C₅	—	2	2	no	—
84	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
85	C₂³×C₃×C₅	#41	1	2	yes	—
86	C₂³×C₃×C₅	#41	1	2	yes	—
87	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
88	C₂²×C₃×D₅	—	2	8	no	—
89	C₂²×C₃×D₅	—	2	2	no	—
90	C₂²×C₃×D₅	—	2	2	no	—
91	C₂²×C₃×D₅	—	2	4	no	—
92	C₂²×C₃×D₅	—	2	4	no	—
93	C₂²×C₃×D₅	—	4	4	no	—
94	C₂²×C₃×D₅	—	4	4	no	—
95	C₂²×C₃×D₅	—	4	8	no	—
96	C₂²×C₃×D₅	—	4	8	no	—
97	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
98	C₂×C₃×C₄×C₅	—	2	2	no	—
99	C₂×C₃×C₄×C₅	—	2	2	no	—
100	C₂×C₃×C₄×C₅	—	2	4	no	—
101	C₂×C₃×C₄×C₅	—	2	4	no	—
102	C₂×C₃×C₄×C₅	—	2	4	no	—
103	C₂×C₃×C₄×C₅	—	4	4	no	—
104	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
105	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
106	C₂×C₃×Dic₅	—	2	4	no	—
107	C₂×C₃×Dic₅	—	2	4	no	—
108	C₂×C₃×Dic₅	—	2	4	no	—
109	C₂×C₃×Dic₅	—	2	4	no	—
110	C₂×C₃×Dic₅	—	4	4	no	—
111	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
112	C₂⁵×C₃	—	5	1	no	—
113	C₂³×C₃×C₄	—	5	1	no	—
114	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
115	C₂×C₃×C₄⋊C₄	—	5	2	no	—
116	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
117	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
118	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
119	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
120	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
121	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
122	C₂×C₃×C₂²⋊C₄	—	5	4	no	—
123	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
124	C₂×C₃×C₄²	—	5	4	no	—
125	C₃×#95	—	5	4	no	—
126	C₃×#95	—	5	2	no	—
127	C₃×#95	C₂×D₅	1	2	yes	complemented
128	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
129	C₂³×D₅	—	2	2	no	—
130	C₂³×D₅	—	2	2	no	—
131	C₂³×D₅	—	4	2	no	—
132	C₂³×D₅	—	4	2	no	—
133	C₂³×D₅	C₂×C₃×C₄	1	4	yes	—
134	C₂³×D₅	C₂³×C₃	1	2	yes	—
135	C₂²×C₄×C₅	—	4	2	no	—
136	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
137	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
138	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
139	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
140	C₂²×Dic₅	—	4	2	no	—
141	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
142	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
143	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
144	C₅×C₄⋊C₄	—	4	2	no	—
145	C₅×C₂²⋊C₄	—	2	4	no	—
146	C₂²⋊Dic₅	—	2	4	no	—
147	#685	—	4	4	no	—
148	#685	—	4	4	no	—
149	#685	C₂×C₃×C₄	1	8	yes	—
150	#685	C₂×C₃×C₄	1	8	yes	—
151	C₄⋊Dic₅	—	4	2	no	—
152	C₄×Dic₅	—	4	4	no	—
153	C₂²×C₂²⋊C₄	—	5	1	no	—
154	#388	—	5	4	no	—
155	#388	—	5	4	no	—
156	#380	—	5	1	no	—
157	#380	C₃×D₅	1	1	yes	characteristic, complemented
158	#379	—	5	2	no	—
159	C₄×C₂²⋊C₄	—	5	2	no	—
160	C₂²×C₃×C₅	—	2	2	no	—
161	C₂²×C₃×C₅	—	2	2	no	—
162	C₂²×C₃×C₅	—	2	4	no	—
163	C₂²×C₃×C₅	—	2	4	no	—
164	C₂²×C₃×C₅	#117	1	4	yes	—
165	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
166	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
167	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
168	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
169	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
170	C₂×C₃×D₅	—	2	4	no	—
171	C₂×C₃×D₅	—	2	4	no	—
172	C₂×C₃×D₅	—	2	4	no	—
173	C₂×C₃×D₅	—	4	16	no	—
174	C₂×C₃×D₅	—	4	4	no	—
175	C₂×C₃×D₅	—	4	4	no	—
176	C₃×C₄×C₅	—	2	2	no	—
177	C₃×C₄×C₅	—	2	2	no	—
178	C₃×C₄×C₅	—	4	4	no	—
179	C₃×Dic₅	—	2	4	no	—
180	C₃×Dic₅	—	4	4	no	—
181	C₂⁴×C₃	—	5	2	no	—
182	C₂⁴×C₃	—	5	4	no	—
183	C₂⁴×C₃	—	10	2	no	—
184	C₂⁴×C₃	—	10	2	no	—
185	C₂⁴×C₃	—	20	2	no	—
186	C₂⁴×C₃	—	20	2	no	—
187	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
188	C₂²×C₃×C₄	—	4	2	no	—
189	C₂²×C₃×C₄	—	5	2	no	—
190	C₂²×C₃×C₄	—	5	4	no	—
191	C₂²×C₃×C₄	—	5	4	no	—
192	C₂²×C₃×C₄	—	20	2	no	—
193	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
194	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
195	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
196	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
197	C₃×C₄⋊C₄	—	4	2	no	—
198	C₃×C₄⋊C₄	—	20	2	no	—
199	C₃×C₂²⋊C₄	—	2	4	no	—
200	C₃×C₂²⋊C₄	—	5	8	no	—
201	C₃×C₂²⋊C₄	—	5	8	no	—
202	C₃×C₂²⋊C₄	—	10	4	no	—
203	C₃×C₂²⋊C₄	—	20	4	no	—
204	C₃×C₂²⋊C₄	—	20	4	no	—
205	C₃×C₄²	—	20	4	no	—
206	C₂³×C₅	—	2	2	no	—
207	C₂³×C₅	—	2	2	no	—
208	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
209	C₂³×C₅	C₃×#41	1	2	yes	—
210	C₂³×C₅	C₃×#41	1	2	yes	—
211	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
212	C₂²×D₅	—	2	8	no	—
213	C₂²×D₅	—	2	2	no	—
214	C₂²×D₅	—	2	2	no	—
215	C₂²×D₅	—	2	4	no	—
216	C₂²×D₅	—	2	4	no	—
217	C₂²×D₅	—	4	4	no	—
218	C₂²×D₅	—	4	4	no	—
219	C₂²×D₅	—	4	8	no	—
220	C₂²×D₅	—	4	8	no	—
221	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
222	C₂×C₄×C₅	—	2	2	no	—
223	C₂×C₄×C₅	—	2	2	no	—
224	C₂×C₄×C₅	—	2	4	no	—
225	C₂×C₄×C₅	—	2	4	no	—
226	C₂×C₄×C₅	—	2	4	no	—
227	C₂×C₄×C₅	—	4	4	no	—
228	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
229	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
230	C₂×Dic₅	—	2	4	no	—
231	C₂×Dic₅	—	2	4	no	—
232	C₂×Dic₅	—	2	4	no	—
233	C₂×Dic₅	—	2	4	no	—
234	C₂×Dic₅	—	4	4	no	—
235	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
236	C₂⁵	—	5	1	no	—
237	C₂³×C₄	—	5	1	no	—
238	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
239	C₂×C₄⋊C₄	—	5	2	no	—
240	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
241	C₂×C₂²⋊C₄	—	5	8	no	—
242	C₂×C₂²⋊C₄	—	5	2	no	—
243	C₂×C₂²⋊C₄	—	5	2	no	—
244	C₂×C₂²⋊C₄	—	5	2	no	—
245	C₂×C₂²⋊C₄	—	5	4	no	—
246	C₂×C₂²⋊C₄	—	5	4	no	—
247	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
248	C₂×C₄²	—	5	4	no	—
249	#95	—	5	4	no	—
250	#95	—	5	2	no	—
251	#95	C₂×C₃×D₅	1	2	yes	complemented
252	C₂×C₃×C₅	—	2	4	no	—
253	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
254	C₂×C₃×C₅	#518	1	1	yes	characteristic
255	C₂×C₃×C₅	#518	1	1	yes	characteristic
256	C₂×C₃×C₅	#538	1	2	yes	—
257	C₂×C₃×C₅	#538	1	2	yes	—
258	C₃×D₅	—	4	4	no	—
259	C₂³×C₃	—	2	2	no	—
260	C₂³×C₃	—	2	2	no	—
261	C₂³×C₃	—	5	4	no	—
262	C₂³×C₃	—	10	2	no	—
263	C₂³×C₃	—	10	4	no	—
264	C₂³×C₃	—	10	2	no	—
265	C₂³×C₃	—	10	4	no	—
266	C₂³×C₃	—	10	8	no	—
267	C₂³×C₃	—	20	4	no	—
268	C₂³×C₃	—	20	4	no	—
269	C₂³×C₃	—	20	8	no	—
270	C₂³×C₃	—	20	8	no	—
271	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
272	C₂³×C₃	#711	1	2	yes	—
273	C₂³×C₃	#713	1	2	yes	—
274	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
275	C₂×C₃×C₄	—	2	2	no	—
276	C₂×C₃×C₄	—	2	2	no	—
277	C₂×C₃×C₄	—	2	4	no	—
278	C₂×C₃×C₄	—	2	4	no	—
279	C₂×C₃×C₄	—	2	4	no	—
280	C₂×C₃×C₄	—	4	4	no	—
281	C₂×C₃×C₄	—	5	4	no	—
282	C₂×C₃×C₄	—	10	4	no	—
283	C₂×C₃×C₄	—	10	4	no	—
284	C₂×C₃×C₄	—	10	4	no	—
285	C₂×C₃×C₄	—	10	4	no	—
286	C₂×C₃×C₄	—	20	4	no	—
287	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
288	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
289	C₂²×C₅	—	2	2	no	—
290	C₂²×C₅	—	2	2	no	—
291	C₂²×C₅	—	2	4	no	—
292	C₂²×C₅	—	2	4	no	—
293	C₂²×C₅	C₃×#117	1	4	yes	—
294	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
295	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
296	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
297	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
298	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
299	C₂×D₅	—	2	4	no	—
300	C₂×D₅	—	2	4	no	—
301	C₂×D₅	—	2	4	no	—
302	C₂×D₅	—	4	16	no	—
303	C₂×D₅	—	4	4	no	—
304	C₂×D₅	—	4	4	no	—
305	C₄×C₅	—	2	2	no	—
306	C₄×C₅	—	2	2	no	—
307	C₄×C₅	—	4	4	no	—
308	Dic₅	—	2	4	no	—
309	Dic₅	—	4	4	no	—
310	C₂⁴	—	5	2	no	—
311	C₂⁴	—	5	4	no	—
312	C₂⁴	—	10	2	no	—
313	C₂⁴	—	10	2	no	—
314	C₂⁴	—	20	2	no	—
315	C₂⁴	—	20	2	no	—
316	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
317	C₂²×C₄	—	4	2	no	—
318	C₂²×C₄	—	5	2	no	—
319	C₂²×C₄	—	5	4	no	—
320	C₂²×C₄	—	5	4	no	—
321	C₂²×C₄	—	20	2	no	—
322	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
323	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
324	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
325	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
326	C₄⋊C₄	—	4	2	no	—
327	C₄⋊C₄	—	20	2	no	—
328	C₂²⋊C₄	—	2	4	no	—
329	C₂²⋊C₄	—	5	8	no	—
330	C₂²⋊C₄	—	5	8	no	—
331	C₂²⋊C₄	—	10	4	no	—
332	C₂²⋊C₄	—	20	4	no	—
333	C₂²⋊C₄	—	20	4	no	—
334	C₄²	—	20	4	no	—
335	C₃×C₅	#2312	1	1	yes	characteristic, complemented, Hall
336	C₂²×C₃	—	2	2	no	—
337	C₂²×C₃	—	2	2	no	—
338	C₂²×C₃	—	2	4	no	—
339	C₂²×C₃	—	2	4	no	—
340	C₂²×C₃	—	10	4	no	—
341	C₂²×C₃	—	10	4	no	—
342	C₂²×C₃	—	10	4	no	—
343	C₂²×C₃	—	20	16	no	—
344	C₂²×C₃	—	20	4	no	—
345	C₂²×C₃	—	20	4	no	—
346	C₂²×C₃	#4038	1	4	yes	—
347	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
348	C₂²×C₃	C₂×#711	1	1	yes	characteristic
349	C₂²×C₃	#4144	1	2	yes	—
350	C₂²×C₃	C₂×#713	1	1	yes	characteristic
351	C₂²×C₃	#4149	1	2	yes	—
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	2	2	no	—
354	C₃×C₄	—	4	4	no	—
355	C₃×C₄	—	10	4	no	—
356	C₃×C₄	—	20	4	no	—
357	C₂×C₅	—	2	4	no	—
358	C₂×C₅	C₂×C₃×#117	1	1	yes	characteristic
359	C₂×C₅	C₃×#518	1	1	yes	characteristic
360	C₂×C₅	C₃×#518	1	1	yes	characteristic
361	C₂×C₅	C₃×#538	1	2	yes	—
362	C₂×C₅	C₃×#538	1	2	yes	—
363	D₅	—	4	4	no	—
364	C₂³	—	2	2	no	—
365	C₂³	—	2	2	no	—
366	C₂³	—	5	4	no	—
367	C₂³	—	10	2	no	—
368	C₂³	—	10	4	no	—
369	C₂³	—	10	2	no	—
370	C₂³	—	10	4	no	—
371	C₂³	—	10	8	no	—
372	C₂³	—	20	4	no	—
373	C₂³	—	20	4	no	—
374	C₂³	—	20	8	no	—
375	C₂³	—	20	8	no	—
376	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
377	C₂³	C₃×#711	1	2	yes	—
378	C₂³	C₃×#713	1	2	yes	—
379	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
380	C₂×C₄	—	2	2	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	4	4	no	—
386	C₂×C₄	—	5	4	no	—
387	C₂×C₄	—	10	4	no	—
388	C₂×C₄	—	10	4	no	—
389	C₂×C₄	—	10	4	no	—
390	C₂×C₄	—	10	4	no	—
391	C₂×C₄	—	20	4	no	—
392	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
393	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
394	C₂×C₃	—	2	4	no	—
395	C₂×C₃	—	20	4	no	—
396	C₂×C₃	#65820	1	1	yes	characteristic
397	C₂×C₃	C₂×#4038	1	1	yes	characteristic
398	C₂×C₃	#65855	1	1	yes	characteristic
399	C₂×C₃	#65951	1	2	yes	—
400	C₂×C₃	#65978	1	2	yes	—
401	C₅	C₃×#2312	1	1	yes	characteristic, complemented, Sylow
402	C₂²	—	2	2	no	—
403	C₂²	—	2	4	no	—
404	C₂²	—	2	4	no	—
405	C₂²	—	2	2	no	—
406	C₂²	—	10	4	no	—
407	C₂²	—	10	4	no	—
408	C₂²	—	10	4	no	—
409	C₂²	—	20	16	no	—
410	C₂²	—	20	4	no	—
411	C₂²	—	20	4	no	—
412	C₂²	C₃×#4038	1	4	yes	—
413	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
414	C₂²	C₂×C₃×#711	1	1	yes	characteristic
415	C₂²	C₃×#4144	1	2	yes	—
416	C₂²	C₂×C₃×#713	1	1	yes	characteristic
417	C₂²	C₃×#4149	1	2	yes	—
418	C₄	—	2	2	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	4	no	—
421	C₄	—	10	4	no	—
422	C₄	—	20	4	no	—
423	C₃	#10605735	1	1	yes	characteristic, direct product factor, Sylow
424	C₂	—	2	4	no	—
425	C₂	—	20	4	no	—
426	C₂	C₃×#65820	1	1	yes	characteristic
427	C₂	C₂×C₃×#4038	1	1	yes	characteristic
428	C₂	C₃×#65855	1	1	yes	characteristic
429	C₂	C₃×#65951	1	2	yes	—
430	C₂	C₃×#65978	1	2	yes	—

	subgroup	G/H
center	C₂³×C₃	C₂³×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₃×C₅×#380	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×D₅	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₃×#380	D₅
hypocenter	C₅	C₃×#2312
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂³×C₃ ◁ C₃×#380

Complements

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

N	H ≅ G/N	type
2. C₃×C₅×#380	C₂	semidirect
3. C₃×#65501	C₂	semidirect
4. C₃×#65279	C₂	semidirect
6. C₃×C₂²⋊C₄×Dic₅	C₂	semidirect
7. C₃×#64959	C₂	semidirect
8. #10605735	C₃	direct (N × H)
12. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
15. C₂×C₃×#685	C₄	semidirect
20. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
21. C₂×C₃×C₄×Dic₅	C₂²	semidirect
22. C₃×C₅×#95	C₂²	semidirect
23. C₃×#3963	C₂²	semidirect
24. C₃×#3963	C₂²	semidirect
27. C₅×#380	C₂×C₃	semidirect
28. #65501	C₂×C₃	semidirect
29. #65279	C₂×C₃	semidirect
31. C₂²⋊C₄×Dic₅	C₂×C₃	semidirect
32. #64959	C₂×C₃	semidirect
62. C₃×#380	D₅	semidirect
68. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
71. C₂×#685	C₃×C₄	semidirect
76. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
77. C₂×C₄×Dic₅	C₂²×C₃	semidirect
78. C₅×#95	C₂²×C₃	semidirect
79. #3963	C₂²×C₃	semidirect
80. #3963	C₂²×C₃	semidirect
116. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
127. C₃×#95	C₂×D₅	semidirect
157. #380	C₃×D₅	semidirect
240. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
251. #95	C₂×C₃×D₅	semidirect
335. C₃×C₅	#2312	semidirect
401. C₅	C₃×#2312	semidirect
423. C₃	#10605735	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×#685	2
C₃×C₅×#380	2
C₃×#65501	2
C₃×#65279	2
C₃×#65244	2
C₃×C₂²⋊C₄×Dic₅	2
C₃×#64959	2
#10605735	3
C₃×#2312	5

Subgroups — C3×#10605735 #14322594

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10605735 #14322594