Subgroups — C₃×#10613998 #14319906

Order 1920.

2176 conjugacy classes of subgroups.

The subgroup lattice has 456 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×C₅×#117	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65276	C₂	1	4	yes	maximal, complemented
5	C₃×#65244	C₂	1	2	yes	maximal
6	C₃×#65232	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#685	C₂	1	4	yes	maximal, complemented
8	#10613998	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	4	no	—
13	C₂²×C₃×C₄×D₅	—	2	4	no	—
14	C₂²×C₃×C₄×D₅	C₄	1	8	yes	complemented
15	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
16	C₂²×C₃×C₄×D₅	C₂²	1	2	yes	—
17	C₃×C₅×#117	—	2	4	no	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
19	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
21	C₂×C₃×C₂²⋊Dic₅	C₂²	1	2	yes	—
22	C₂×C₃×#685	C₂²	1	8	yes	—
23	C₃×#4072	—	2	4	no	—
24	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
25	C₂×C₃×C₄×Dic₅	C₂²	1	2	yes	complemented
26	C₃×#3963	C₂²	1	8	yes	complemented
27	C₃×#2280	—	5	1	no	maximal, Hall
28	C₂³×C₄×D₅	C₂×C₃	1	1	yes	characteristic
29	C₂×C₅×#117	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#4072	C₂×C₃	1	1	yes	characteristic, complemented
31	#65276	C₂×C₃	1	4	yes	complemented
32	#65244	C₂×C₃	1	2	yes	—
33	#65232	C₂×C₃	1	2	yes	complemented
34	C₄×#685	C₂×C₃	1	4	yes	complemented
35	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
36	C₂³×C₃×D₅	—	2	2	no	—
37	C₂³×C₃×D₅	—	2	2	no	—
38	C₂³×C₃×D₅	—	2	8	no	—
39	C₂³×C₃×D₅	C₂×C₄	1	4	yes	—
40	C₂³×C₃×D₅	C₂³	1	2	yes	—
41	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
42	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
43	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
44	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
45	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂²×C₃×Dic₅	—	2	2	no	—
48	C₂²×C₃×Dic₅	—	2	2	no	—
49	C₂²×C₃×Dic₅	C₂×C₄	1	4	yes	—
50	C₂²×C₃×Dic₅	C₂³	1	4	yes	—
51	C₂²×C₃×Dic₅	C₂³	1	2	yes	—
52	C₂×C₃×C₄×D₅	—	2	32	no	—
53	C₂×C₃×C₄×D₅	—	2	4	no	—
54	C₂×C₃×C₄×D₅	—	2	4	no	—
55	C₂×C₃×C₄×D₅	—	2	4	no	—
56	C₂×C₃×C₄×D₅	—	2	4	no	—
57	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
58	C₂×C₃×C₄×D₅	C₂×C₄	1	8	yes	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
61	C₃×C₄²×C₅	—	2	4	no	—
62	C₃×C₂²⋊Dic₅	—	2	4	no	—
63	C₃×#685	—	2	16	no	—
64	C₃×C₄⋊Dic₅	—	2	4	no	—
65	C₃×C₄×Dic₅	—	2	4	no	—
66	C₂⁴×C₃×C₄	—	5	1	no	—
67	C₂×C₃×#117	—	5	1	no	—
68	C₂×C₃×#117	D₅	1	1	yes	characteristic, complemented
69	C₃×#381	—	5	2	no	—
70	C₃×#380	—	5	4	no	—
71	C₃×#379	—	5	2	no	—
72	C₃×C₄×C₂²⋊C₄	—	5	4	no	—
73	C₂⁴×D₅	C₂²×C₃	1	1	yes	characteristic
74	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
75	C₂³×Dic₅	C₂²×C₃	1	1	yes	characteristic
76	C₂²×C₄×D₅	—	2	4	no	—
77	C₂²×C₄×D₅	—	2	4	no	—
78	C₂²×C₄×D₅	C₃×C₄	1	8	yes	complemented
79	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
80	C₂²×C₄×D₅	C₂²×C₃	1	2	yes	—
81	C₅×#117	—	2	4	no	—
82	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
83	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
84	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
85	C₂×C₂²⋊Dic₅	C₂²×C₃	1	2	yes	—
86	C₂×#685	C₂²×C₃	1	8	yes	—
87	#4072	—	2	4	no	—
88	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
89	C₂×C₄×Dic₅	C₂²×C₃	1	2	yes	complemented
90	#3963	C₂²×C₃	1	8	yes	complemented
91	#2280	—	5	1	no	Sylow
92	C₂³×C₃×C₅	—	2	4	no	—
93	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
94	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
95	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
96	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
97	C₂²×C₃×D₅	—	2	16	no	—
98	C₂²×C₃×D₅	—	2	16	no	—
99	C₂²×C₃×D₅	—	2	8	no	—
100	C₂²×C₃×D₅	—	2	2	no	—
101	C₂²×C₃×D₅	—	2	2	no	—
102	C₂²×C₃×D₅	—	2	4	no	—
103	C₂²×C₃×D₅	—	2	16	no	—
104	C₂²×C₃×D₅	C₂²×C₄	1	4	yes	—
105	C₂²×C₃×D₅	#41	1	8	yes	—
106	C₂×C₃×C₄×C₅	—	2	4	no	—
107	C₂×C₃×C₄×C₅	—	2	8	no	—
108	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	16	yes	complemented
109	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
110	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
112	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×Dic₅	—	2	8	no	—
116	C₂×C₃×Dic₅	—	2	2	no	—
117	C₂×C₃×Dic₅	—	2	2	no	—
118	C₂×C₃×Dic₅	—	2	4	no	—
119	C₂×C₃×Dic₅	—	2	8	no	—
120	C₂×C₃×Dic₅	C₂²×C₄	1	4	yes	—
121	C₃×C₄×D₅	—	2	16	no	—
122	C₃×C₄×D₅	—	2	16	no	—
123	C₂⁵×C₃	—	5	1	no	—
124	C₂³×C₃×C₄	—	5	1	no	—
125	C₂³×C₃×C₄	—	5	8	no	—
126	C₂³×C₃×C₄	—	5	2	no	—
127	C₂³×C₃×C₄	—	5	2	no	—
128	C₂³×C₃×C₄	—	10	4	no	—
129	C₂³×C₃×C₄	—	10	4	no	—
130	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
131	C₃×#117	—	2	4	no	—
132	C₃×#117	—	10	4	no	—
133	C₂×C₃×C₄⋊C₄	—	5	2	no	—
134	C₂×C₃×C₄⋊C₄	C₂×D₅	1	2	yes	complemented
135	C₂×C₃×C₂²⋊C₄	—	5	2	no	—
136	C₂×C₃×C₂²⋊C₄	—	5	8	no	—
137	C₂×C₃×C₂²⋊C₄	C₂×D₅	1	2	yes	—
138	C₂×C₃×C₄²	—	5	2	no	—
139	C₂×C₃×C₄²	C₂×D₅	1	2	yes	complemented
140	C₃×#95	—	5	8	no	—
141	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
142	C₂³×D₅	—	2	2	no	—
143	C₂³×D₅	—	2	2	no	—
144	C₂³×D₅	—	2	8	no	—
145	C₂³×D₅	C₂×C₃×C₄	1	4	yes	—
146	C₂³×D₅	C₂³×C₃	1	2	yes	—
147	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
148	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
149	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
150	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
151	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
152	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
153	C₂²×Dic₅	—	2	2	no	—
154	C₂²×Dic₅	—	2	2	no	—
155	C₂²×Dic₅	C₂×C₃×C₄	1	4	yes	—
156	C₂²×Dic₅	C₂³×C₃	1	4	yes	—
157	C₂²×Dic₅	C₂³×C₃	1	2	yes	—
158	C₂×C₄×D₅	—	2	32	no	—
159	C₂×C₄×D₅	—	2	4	no	—
160	C₂×C₄×D₅	—	2	4	no	—
161	C₂×C₄×D₅	—	2	4	no	—
162	C₂×C₄×D₅	—	2	4	no	—
163	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
164	C₂×C₄×D₅	C₂×C₃×C₄	1	8	yes	—
165	C₅×C₄⋊C₄	—	2	4	no	—
166	C₅×C₂²⋊C₄	—	2	4	no	—
167	C₄²×C₅	—	2	4	no	—
168	C₂²⋊Dic₅	—	2	4	no	—
169	#685	—	2	16	no	—
170	C₄⋊Dic₅	—	2	4	no	—
171	C₄×Dic₅	—	2	4	no	—
172	C₂⁴×C₄	—	5	1	no	—
173	C₂×#117	—	5	1	no	—
174	C₂×#117	C₃×D₅	1	1	yes	characteristic, complemented
175	#381	—	5	2	no	—
176	#380	—	5	4	no	—
177	#379	—	5	2	no	—
178	C₄×C₂²⋊C₄	—	5	4	no	—
179	C₂²×C₃×C₅	—	2	4	no	—
180	C₂²×C₃×C₅	—	2	4	no	—
181	C₂²×C₃×C₅	—	2	4	no	—
182	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	4	yes	—
183	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
184	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
186	C₂²×C₃×C₅	C₂×#41	1	4	yes	—
187	C₂×C₃×D₅	—	2	32	no	—
188	C₂×C₃×D₅	—	2	4	no	—
189	C₂×C₃×D₅	—	2	4	no	—
190	C₂×C₃×D₅	—	2	8	no	—
191	C₂×C₃×D₅	—	2	8	no	—
192	C₂×C₃×D₅	#117	1	8	yes	complemented
193	C₃×C₄×C₅	—	4	4	no	—
194	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
195	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	—
196	C₃×Dic₅	—	2	4	no	—
197	C₃×Dic₅	—	4	4	no	—
198	C₂⁴×C₃	—	5	2	no	—
199	C₂⁴×C₃	—	5	4	no	—
200	C₂⁴×C₃	—	10	8	no	—
201	C₂⁴×C₃	—	10	2	no	—
202	C₂⁴×C₃	—	10	2	no	—
203	C₂⁴×C₃	C₂²×D₅	1	1	yes	characteristic
204	C₂²×C₃×C₄	—	5	4	no	—
205	C₂²×C₃×C₄	—	5	2	no	—
206	C₂²×C₃×C₄	—	5	8	no	—
207	C₂²×C₃×C₄	—	5	8	no	—
208	C₂²×C₃×C₄	—	5	4	no	—
209	C₂²×C₃×C₄	—	10	2	no	—
210	C₂²×C₃×C₄	—	10	2	no	—
211	C₂²×C₃×C₄	—	10	32	no	—
212	C₂²×C₃×C₄	—	10	4	no	—
213	C₂²×C₃×C₄	—	10	4	no	—
214	C₂²×C₃×C₄	—	10	4	no	—
215	C₂²×C₃×C₄	—	10	4	no	—
216	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
217	C₂²×C₃×C₄	D₂₀	1	4	yes	—
218	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
219	C₂²×C₃×C₄	C₂²×D₅	1	4	yes	—
220	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
222	C₃×C₄⋊C₄	—	2	4	no	—
223	C₃×C₄⋊C₄	—	10	4	no	—
224	C₃×C₂²⋊C₄	—	2	4	no	—
225	C₃×C₂²⋊C₄	—	10	16	no	—
226	C₃×C₂²⋊C₄	—	10	4	no	—
227	C₃×C₄²	—	2	4	no	—
228	C₃×C₄²	—	10	4	no	—
229	C₂³×C₅	—	2	4	no	—
230	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
231	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
232	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
233	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
234	C₂²×D₅	—	2	16	no	—
235	C₂²×D₅	—	2	16	no	—
236	C₂²×D₅	—	2	8	no	—
237	C₂²×D₅	—	2	2	no	—
238	C₂²×D₅	—	2	2	no	—
239	C₂²×D₅	—	2	4	no	—
240	C₂²×D₅	—	2	16	no	—
241	C₂²×D₅	C₂²×C₃×C₄	1	4	yes	—
242	C₂²×D₅	C₃×#41	1	8	yes	—
243	C₂×C₄×C₅	—	2	4	no	—
244	C₂×C₄×C₅	—	2	8	no	—
245	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	16	yes	complemented
246	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
247	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
248	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
249	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
250	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
251	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
252	C₂×Dic₅	—	2	8	no	—
253	C₂×Dic₅	—	2	2	no	—
254	C₂×Dic₅	—	2	2	no	—
255	C₂×Dic₅	—	2	4	no	—
256	C₂×Dic₅	—	2	8	no	—
257	C₂×Dic₅	C₂²×C₃×C₄	1	4	yes	—
258	C₄×D₅	—	2	16	no	—
259	C₄×D₅	—	2	16	no	—
260	C₂⁵	—	5	1	no	—
261	C₂³×C₄	—	5	1	no	—
262	C₂³×C₄	—	5	8	no	—
263	C₂³×C₄	—	5	2	no	—
264	C₂³×C₄	—	5	2	no	—
265	C₂³×C₄	—	10	4	no	—
266	C₂³×C₄	—	10	4	no	—
267	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
268	#117	—	2	4	no	—
269	#117	—	10	4	no	—
270	C₂×C₄⋊C₄	—	5	2	no	—
271	C₂×C₄⋊C₄	C₂×C₃×D₅	1	2	yes	complemented
272	C₂×C₂²⋊C₄	—	5	2	no	—
273	C₂×C₂²⋊C₄	—	5	8	no	—
274	C₂×C₂²⋊C₄	C₂×C₃×D₅	1	2	yes	—
275	C₂×C₄²	—	5	2	no	—
276	C₂×C₄²	C₂×C₃×D₅	1	2	yes	complemented
277	#95	—	5	8	no	—
278	C₂×C₃×C₅	—	2	4	no	—
279	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
280	C₂×C₃×C₅	C₂×#117	1	2	yes	—
281	C₂×C₃×C₅	#525	1	2	yes	—
282	C₂×C₃×C₅	#525	1	2	yes	—
283	C₃×D₅	—	2	8	no	—
284	C₂³×C₃	—	2	4	no	—
285	C₂³×C₃	—	5	4	no	—
286	C₂³×C₃	—	5	8	no	—
287	C₂³×C₃	—	10	16	no	—
288	C₂³×C₃	—	10	16	no	—
289	C₂³×C₃	—	10	16	no	—
290	C₂³×C₃	—	10	2	no	—
291	C₂³×C₃	—	10	4	no	—
292	C₂³×C₃	—	10	2	no	—
293	C₂³×C₃	—	10	8	no	—
294	C₂³×C₃	C₂×C₄×D₅	1	2	yes	—
295	C₂³×C₃	C₂×D₂₀	1	2	yes	—
296	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
297	C₂³×C₃	C₂³×D₅	1	1	yes	characteristic
298	C₂×C₃×C₄	—	2	8	no	—
299	C₂×C₃×C₄	—	2	4	no	—
300	C₂×C₃×C₄	—	5	4	no	—
301	C₂×C₃×C₄	—	10	2	no	—
302	C₂×C₃×C₄	—	10	2	no	—
303	C₂×C₃×C₄	—	10	8	no	—
304	C₂×C₃×C₄	—	10	16	no	—
305	C₂×C₃×C₄	—	10	16	no	—
306	C₂×C₃×C₄	—	10	4	no	—
307	C₂×C₃×C₄	—	10	8	no	—
308	C₂×C₃×C₄	#685	1	16	yes	complemented
309	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
310	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
311	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
312	C₂×C₃×C₄	C₂×D₂₀	1	2	yes	—
313	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
314	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
315	C₂²×C₅	—	2	4	no	—
316	C₂²×C₅	—	2	4	no	—
317	C₂²×C₅	—	2	4	no	—
318	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
319	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
320	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
321	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₂²×C₅	C₂×C₃×#41	1	4	yes	—
323	C₂×D₅	—	2	32	no	—
324	C₂×D₅	—	2	4	no	—
325	C₂×D₅	—	2	4	no	—
326	C₂×D₅	—	2	8	no	—
327	C₂×D₅	—	2	8	no	—
328	C₂×D₅	C₃×#117	1	8	yes	complemented
329	C₄×C₅	—	4	4	no	—
330	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
331	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	—
332	Dic₅	—	2	4	no	—
333	Dic₅	—	4	4	no	—
334	C₂⁴	—	5	2	no	—
335	C₂⁴	—	5	4	no	—
336	C₂⁴	—	10	8	no	—
337	C₂⁴	—	10	2	no	—
338	C₂⁴	—	10	2	no	—
339	C₂⁴	C₂²×C₃×D₅	1	1	yes	characteristic
340	C₂²×C₄	—	5	4	no	—
341	C₂²×C₄	—	5	2	no	—
342	C₂²×C₄	—	5	8	no	—
343	C₂²×C₄	—	5	8	no	—
344	C₂²×C₄	—	5	4	no	—
345	C₂²×C₄	—	10	2	no	—
346	C₂²×C₄	—	10	2	no	—
347	C₂²×C₄	—	10	32	no	—
348	C₂²×C₄	—	10	4	no	—
349	C₂²×C₄	—	10	4	no	—
350	C₂²×C₄	—	10	4	no	—
351	C₂²×C₄	—	10	4	no	—
352	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
353	C₂²×C₄	C₃×D₂₀	1	4	yes	—
354	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
355	C₂²×C₄	C₂²×C₃×D₅	1	4	yes	—
356	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
357	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
358	C₄⋊C₄	—	2	4	no	—
359	C₄⋊C₄	—	10	4	no	—
360	C₂²⋊C₄	—	2	4	no	—
361	C₂²⋊C₄	—	10	16	no	—
362	C₂²⋊C₄	—	10	4	no	—
363	C₄²	—	2	4	no	—
364	C₄²	—	10	4	no	—
365	C₃×C₅	#2280	1	1	yes	characteristic, complemented, Hall
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	4	no	—
368	C₂²×C₃	—	2	4	no	—
369	C₂²×C₃	—	5	8	no	—
370	C₂²×C₃	—	10	32	no	—
371	C₂²×C₃	—	10	4	no	—
372	C₂²×C₃	—	10	8	no	—
373	C₂²×C₃	—	10	4	no	—
374	C₂²×C₃	—	10	8	no	—
375	C₂²×C₃	C₂×#685	1	4	yes	—
376	C₂²×C₃	C₂²×C₄×D₅	1	1	yes	characteristic
377	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
378	C₂²×C₃	D₅×#41	1	4	yes	—
379	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
380	C₃×C₄	—	4	4	no	—
381	C₃×C₄	—	10	4	no	—
382	C₃×C₄	—	20	4	no	—
383	C₃×C₄	C₂×#685	1	4	yes	—
384	C₃×C₄	C₂×#685	1	4	yes	—
385	C₂×C₅	—	2	4	no	—
386	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
387	C₂×C₅	C₂×C₃×#117	1	2	yes	—
388	C₂×C₅	C₃×#525	1	2	yes	—
389	C₂×C₅	C₃×#525	1	2	yes	—
390	D₅	—	2	8	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	5	4	no	—
393	C₂³	—	5	8	no	—
394	C₂³	—	10	16	no	—
395	C₂³	—	10	16	no	—
396	C₂³	—	10	16	no	—
397	C₂³	—	10	2	no	—
398	C₂³	—	10	4	no	—
399	C₂³	—	10	2	no	—
400	C₂³	—	10	8	no	—
401	C₂³	C₂×C₃×C₄×D₅	1	2	yes	—
402	C₂³	C₂×C₃×D₂₀	1	2	yes	—
403	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
404	C₂³	C₂³×C₃×D₅	1	1	yes	characteristic
405	C₂×C₄	—	2	8	no	—
406	C₂×C₄	—	2	4	no	—
407	C₂×C₄	—	5	4	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	10	8	no	—
411	C₂×C₄	—	10	16	no	—
412	C₂×C₄	—	10	16	no	—
413	C₂×C₄	—	10	4	no	—
414	C₂×C₄	—	10	8	no	—
415	C₂×C₄	C₃×#685	1	16	yes	complemented
416	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
417	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
418	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
419	C₂×C₄	C₂×C₃×D₂₀	1	2	yes	—
420	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
421	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
422	C₂×C₃	—	2	4	no	—
423	C₂×C₃	—	10	8	no	—
424	C₂×C₃	D₅×#117	1	2	yes	—
425	C₂×C₃	#65858	1	2	yes	—
426	C₂×C₃	C₂²×#685	1	1	yes	characteristic
427	C₂×C₃	#66162	1	2	yes	—
428	C₅	C₃×#2280	1	1	yes	characteristic, complemented, Sylow
429	C₂²	—	2	4	no	—
430	C₂²	—	2	4	no	—
431	C₂²	—	2	4	no	—
432	C₂²	—	5	8	no	—
433	C₂²	—	10	32	no	—
434	C₂²	—	10	4	no	—
435	C₂²	—	10	8	no	—
436	C₂²	—	10	4	no	—
437	C₂²	—	10	8	no	—
438	C₂²	C₂×C₃×#685	1	4	yes	—
439	C₂²	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
440	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
441	C₂²	C₃×D₅×#41	1	4	yes	—
442	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
443	C₄	—	4	4	no	—
444	C₄	—	10	4	no	—
445	C₄	—	20	4	no	—
446	C₄	C₂×C₃×#685	1	4	yes	—
447	C₄	C₂×C₃×#685	1	4	yes	—
448	C₃	#10613998	1	1	yes	characteristic, direct product factor, Sylow
449	C₂	—	2	4	no	—
450	C₂	—	10	8	no	—
451	C₂	C₃×D₅×#117	1	2	yes	—
452	C₂	C₃×#65858	1	2	yes	—
453	C₂	C₂²×C₃×#685	1	1	yes	characteristic
454	C₂	C₃×#66162	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃×C₄	C₂²×D₅
commutator	C₂²×C₅	C₂³×C₃×C₄
Frattini	C₂³	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#117	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₃×D₅	C₂²
cosocle	C₂³×C₅	C₂⁴×C₃
hypercenter	C₂×C₃×#117	D₅
hypocenter	C₅	C₃×#2280
LCS	G ▷ C₂²×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#117

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#117	C₂	semidirect
3. C₂×C₃×#4072	C₂	semidirect
4. C₃×#65276	C₂	semidirect
6. C₃×#65232	C₂	semidirect
7. C₃×C₄×#685	C₂	semidirect
8. #10613998	C₃	direct (N × H)
14. C₂²×C₃×C₄×D₅	C₄	semidirect
18. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
20. C₂×C₃×C₄²×C₅	C₂²	semidirect
24. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
25. C₂×C₃×C₄×Dic₅	C₂²	semidirect
26. C₃×#3963	C₂²	semidirect
29. C₂×C₅×#117	C₂×C₃	semidirect
30. C₂×#4072	C₂×C₃	semidirect
31. #65276	C₂×C₃	semidirect
33. #65232	C₂×C₃	semidirect
34. C₄×#685	C₂×C₃	semidirect
68. C₂×C₃×#117	D₅	semidirect
78. C₂²×C₄×D₅	C₃×C₄	semidirect
82. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
84. C₂×C₄²×C₅	C₂²×C₃	semidirect
88. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
89. C₂×C₄×Dic₅	C₂²×C₃	semidirect
90. #3963	C₂²×C₃	semidirect
108. C₂×C₃×C₄×C₅	C₂²⋊C₄	semidirect
134. C₂×C₃×C₄⋊C₄	C₂×D₅	semidirect
139. C₂×C₃×C₄²	C₂×D₅	semidirect
174. C₂×#117	C₃×D₅	semidirect
192. C₂×C₃×D₅	#117	semidirect
245. C₂×C₄×C₅	C₃×C₂²⋊C₄	semidirect
271. C₂×C₄⋊C₄	C₂×C₃×D₅	semidirect
276. C₂×C₄²	C₂×C₃×D₅	semidirect
308. C₂×C₃×C₄	#685	semidirect
328. C₂×D₅	C₃×#117	semidirect
365. C₃×C₅	#2280	semidirect
415. C₂×C₄	C₃×#685	semidirect
428. C₅	C₃×#2280	semidirect
448. C₃	#10613998	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×C₅×#117	2
C₂×C₃×#4072	2
C₃×#65276	2
C₃×#65244	2
C₃×#65232	2
C₃×C₄×#685	2
#10613998	3
C₃×#2280	5

Subgroups — C3×#10613998 #14319906

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613998 #14319906