Subgroups — C₃×#10615499 #14412550

Order 1920.

1544 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×C₃×#709	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₃×C₅×M₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4072	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65422	C₂	1	4	yes	maximal, complemented
5	C₃×#65420	C₂	1	2	yes	maximal, complemented
6	C₃×#65409	C₂	1	2	yes	maximal, complemented
7	C₃×#65402	C₂	1	4	yes	maximal, complemented
8	#10615499	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₂²⋊D₅	—	2	1	no	—
11	C₂×C₃×#709	—	2	4	no	—
12	C₂×C₃×#709	—	2	1	no	—
13	C₂×C₃×#709	—	2	1	no	—
14	C₂×C₃×#709	C₄	1	8	yes	complemented
15	C₂×C₃×#709	C₂²	1	2	yes	—
16	C₂×C₃×#709	C₂²	1	2	yes	—
17	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
18	C₂²×C₃×C₄×D₅	—	2	1	no	—
19	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×M₁₆	—	2	4	no	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
22	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	complemented
23	C₂²×C₃×C₅×C₈	C₂²	1	2	yes	complemented
24	C₂×C₃×C₂²⋊Dic₅	—	2	1	no	—
25	C₃×#4072	—	2	1	no	—
26	C₃×#4072	—	2	1	no	—
27	C₃×#4072	C₂²	1	2	yes	—
28	C₃×#4072	C₂²	1	2	yes	complemented
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	2	yes	complemented
30	C₂×C₃×C₄×Dic₅	—	2	1	no	—
31	C₃×#3953	C₂²	1	8	yes	complemented
32	C₃×#3948	C₂²	1	8	yes	complemented
33	C₃×#2896	—	5	1	no	maximal, Hall
34	C₂²×#709	C₂×C₃	1	1	yes	characteristic
35	C₂²×C₅×M₁₆	C₂×C₃	1	1	yes	characteristic, complemented
36	C₂×#4072	C₂×C₃	1	1	yes	characteristic, complemented
37	#65422	C₂×C₃	1	4	yes	complemented
38	#65420	C₂×C₃	1	2	yes	complemented
39	#65409	C₂×C₃	1	2	yes	complemented
40	#65402	C₂×C₃	1	4	yes	complemented
41	C₂⁴×C₃×C₅	D₄	1	1	yes	characteristic
42	C₂³×C₃×D₅	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	—
44	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
45	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
46	C₂²×C₃×C₄×C₅	D₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	D₄	1	4	yes	—
48	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₂²⋊D₅	—	2	8	no	—
52	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
53	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
54	C₂²×C₃×Dic₅	—	2	1	no	—
55	C₂²×C₃×Dic₅	—	2	2	no	—
56	C₃×#709	—	2	8	no	—
57	C₃×#709	—	2	8	no	—
58	C₃×#709	—	2	4	no	—
59	C₃×#709	—	2	4	no	—
60	C₃×#709	C₂×C₄	1	8	yes	—
61	C₃×#709	C₂×C₄	1	8	yes	complemented
62	C₂×C₃×D₂₀	—	2	1	no	—
63	C₂×C₃×D₂₀	—	2	2	no	—
64	C₂×C₃×D₂₀	C₂×C₄	1	4	yes	complemented
65	C₂×C₃×D₂₀	C₂³	1	2	yes	—
66	C₂×C₃×C₄×D₅	—	2	8	no	—
67	C₂×C₃×C₄×D₅	—	2	2	no	—
68	C₂×C₃×C₄×D₅	—	2	2	no	—
69	C₂×C₃×Dic₁₀	—	2	1	no	—
70	C₂×C₃×Dic₁₀	—	2	2	no	—
71	C₂×C₃×Dic₁₀	C₂×C₄	1	4	yes	complemented
72	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
73	C₃×C₅×M₁₆	—	2	4	no	—
74	C₃×C₅×M₁₆	—	2	4	no	—
75	C₂×C₃×C₅×C₈	—	2	4	no	—
76	C₂×C₃×C₅×C₈	C₂³	1	4	yes	—
77	C₃×C₂²⋊Dic₅	—	2	2	no	—
78	C₃×C₂²⋊Dic₅	—	2	2	no	—
79	C₃×C₄⋊Dic₅	—	2	2	no	—
80	C₃×C₄⋊Dic₅	C₂³	1	4	yes	—
81	C₃×C₄×Dic₅	—	2	2	no	—
82	C₃×C₄×Dic₅	—	2	2	no	—
83	C₂²×C₃×#41	—	5	1	no	—
84	C₂²×C₃×M₁₆	D₅	1	1	yes	characteristic, complemented
85	C₂×C₃×#117	—	5	1	no	—
86	C₃×#419	—	5	2	no	—
87	C₃×#418	—	5	2	no	—
88	C₃×#417	—	5	4	no	—
89	C₃×#416	—	5	4	no	—
90	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
91	C₂²×C₂²⋊D₅	—	2	1	no	—
92	C₂×#709	—	2	1	no	—
93	C₂×#709	—	2	1	no	—
94	C₂×#709	—	2	4	no	—
95	C₂×#709	C₃×C₄	1	8	yes	complemented
96	C₂×#709	C₂²×C₃	1	2	yes	—
97	C₂×#709	C₂²×C₃	1	2	yes	—
98	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
99	C₂²×C₄×D₅	—	2	1	no	—
100	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
101	C₂×C₅×M₁₆	—	2	4	no	—
102	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
103	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	complemented
104	C₂²×C₅×C₈	C₂²×C₃	1	2	yes	complemented
105	C₂×C₂²⋊Dic₅	—	2	1	no	—
106	#4072	—	2	1	no	—
107	#4072	—	2	1	no	—
108	#4072	C₂²×C₃	1	2	yes	—
109	#4072	C₂²×C₃	1	2	yes	complemented
110	C₂×C₄⋊Dic₅	C₂²×C₃	1	2	yes	complemented
111	C₂×C₄×Dic₅	—	2	1	no	—
112	#3953	C₂²×C₃	1	8	yes	complemented
113	#3948	C₂²×C₃	1	8	yes	complemented
114	#2896	—	5	1	no	Sylow
115	C₂³×C₃×C₅	—	4	2	no	—
116	C₂³×C₃×C₅	C₂²⋊C₄	1	4	yes	—
117	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
118	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
119	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
120	C₂²×C₃×D₅	—	2	4	no	—
121	C₂²×C₃×D₅	—	2	2	no	—
122	C₂²×C₃×D₅	—	4	4	no	—
123	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
124	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
125	C₂×C₃×C₄×C₅	C₂²⋊C₄	1	4	yes	—
126	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
127	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
128	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
129	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
130	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
131	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
132	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
134	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₃×C₂²⋊D₅	—	2	8	no	—
137	C₃×C₂²⋊D₅	—	2	8	no	—
138	C₂×C₃×Dic₅	—	2	4	no	—
139	C₂×C₃×Dic₅	—	2	2	no	—
140	C₂×C₃×Dic₅	—	2	4	no	—
141	C₂×C₃×Dic₅	—	4	4	no	—
142	C₃×D₂₀	—	2	4	no	—
143	C₃×D₂₀	—	2	2	no	—
144	C₃×D₂₀	C₂²×C₄	1	4	yes	—
145	C₃×C₄×D₅	—	2	8	no	—
146	C₃×C₄×D₅	—	2	8	no	—
147	C₃×Dic₁₀	—	2	4	no	—
148	C₃×Dic₁₀	—	2	2	no	—
149	C₃×Dic₁₀	C₂²×C₄	1	4	yes	—
150	C₃×C₅×C₈	—	2	4	no	—
151	C₂×C₃×#41	—	5	8	no	—
152	C₂×C₃×#41	—	5	2	no	—
153	C₂×C₃×#41	—	5	2	no	—
154	C₂×C₃×#41	—	10	1	no	—
155	C₂×C₃×#41	—	10	1	no	—
156	C₂×C₃×#41	—	10	4	no	—
157	C₂²×C₃×Q₈	—	5	1	no	—
158	C₂²×C₃×D₄	—	5	1	no	—
159	C₂²×C₃×D₄	—	10	1	no	—
160	C₂³×C₃×C₄	—	10	1	no	—
161	C₂³×C₃×C₄	C₂×D₅	1	1	yes	characteristic
162	C₂×C₃×M₁₆	—	2	4	no	—
163	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	—
164	C₂×C₃×M₁₆	C₂×D₅	1	2	yes	complemented
165	C₂²×C₃×C₈	C₂×D₅	1	2	yes	complemented
166	C₃×#117	—	5	2	no	—
167	C₃×#117	—	5	2	no	—
168	C₃×#117	—	10	1	no	—
169	C₃×#117	—	10	1	no	—
170	C₂×C₃×C₄⋊C₄	—	5	2	no	—
171	C₂×C₃×C₂²⋊C₄	—	10	1	no	—
172	C₂×C₃×C₄²	—	10	1	no	—
173	C₃×#103	—	5	8	no	—
174	C₃×#102	—	5	8	no	—
175	C₂⁴×C₅	C₃×D₄	1	1	yes	characteristic
176	C₂³×D₅	—	2	1	no	—
177	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
178	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
179	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
180	C₂²×C₄×C₅	C₃×D₄	1	1	yes	characteristic
181	C₂²×C₄×C₅	C₃×D₄	1	4	yes	—
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
184	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₂×C₂²⋊D₅	—	2	8	no	—
186	C₂×C₂²⋊D₅	—	2	2	no	—
187	C₂×C₂²⋊D₅	—	2	2	no	—
188	C₂²×Dic₅	—	2	1	no	—
189	C₂²×Dic₅	—	2	2	no	—
190	#709	—	2	8	no	—
191	#709	—	2	8	no	—
192	#709	—	2	4	no	—
193	#709	—	2	4	no	—
194	#709	C₂×C₃×C₄	1	8	yes	—
195	#709	C₂×C₃×C₄	1	8	yes	complemented
196	C₂×D₂₀	—	2	1	no	—
197	C₂×D₂₀	—	2	2	no	—
198	C₂×D₂₀	C₂×C₃×C₄	1	4	yes	complemented
199	C₂×D₂₀	C₂³×C₃	1	2	yes	—
200	C₂×C₄×D₅	—	2	8	no	—
201	C₂×C₄×D₅	—	2	2	no	—
202	C₂×C₄×D₅	—	2	2	no	—
203	C₂×Dic₁₀	—	2	1	no	—
204	C₂×Dic₁₀	—	2	2	no	—
205	C₂×Dic₁₀	C₂×C₃×C₄	1	4	yes	complemented
206	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
207	C₅×M₁₆	—	2	4	no	—
208	C₅×M₁₆	—	2	4	no	—
209	C₂×C₅×C₈	—	2	4	no	—
210	C₂×C₅×C₈	C₂³×C₃	1	4	yes	—
211	C₂²⋊Dic₅	—	2	2	no	—
212	C₂²⋊Dic₅	—	2	2	no	—
213	C₄⋊Dic₅	—	2	2	no	—
214	C₄⋊Dic₅	C₂³×C₃	1	4	yes	—
215	C₄×Dic₅	—	2	2	no	—
216	C₄×Dic₅	—	2	2	no	—
217	C₂²×#41	—	5	1	no	—
218	C₂²×M₁₆	C₃×D₅	1	1	yes	characteristic, complemented
219	C₂×#117	—	5	1	no	—
220	#419	—	5	2	no	—
221	#418	—	5	2	no	—
222	#417	—	5	4	no	—
223	#416	—	5	4	no	—
224	C₂²×C₃×C₅	—	2	2	no	—
225	C₂²×C₃×C₅	—	2	2	no	—
226	C₂²×C₃×C₅	—	2	2	no	—
227	C₂²×C₃×C₅	—	4	4	no	—
228	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
229	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	2	yes	—
231	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
232	C₂×C₃×D₅	—	2	4	no	—
233	C₂×C₃×D₅	—	4	8	no	—
234	C₂×C₃×D₅	—	4	4	no	—
235	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
236	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
237	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	2	yes	—
238	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
239	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
240	C₃×Dic₅	—	2	4	no	—
241	C₃×Dic₅	—	4	4	no	—
242	C₂⁴×C₃	—	10	1	no	—
243	C₂⁴×C₃	D₂₀	1	1	yes	characteristic
244	C₃×#41	—	5	8	no	—
245	C₃×#41	—	5	8	no	—
246	C₃×#41	—	10	8	no	—
247	C₃×#41	—	10	8	no	—
248	C₃×#41	—	10	4	no	—
249	C₃×#41	—	10	4	no	—
250	C₂×C₃×Q₈	—	5	4	no	—
251	C₂×C₃×Q₈	—	5	2	no	—
252	C₂×C₃×Q₈	—	10	1	no	—
253	C₂×C₃×Q₈	—	10	2	no	—
254	C₂×C₃×D₄	—	5	4	no	—
255	C₂×C₃×D₄	—	5	2	no	—
256	C₂×C₃×D₄	—	10	8	no	—
257	C₂×C₃×D₄	—	10	2	no	—
258	C₂×C₃×D₄	—	10	2	no	—
259	C₂×C₃×D₄	—	10	1	no	—
260	C₂×C₃×D₄	—	10	2	no	—
261	C₂²×C₃×C₄	—	10	1	no	—
262	C₂²×C₃×C₄	—	10	8	no	—
263	C₂²×C₃×C₄	—	10	2	no	—
264	C₂²×C₃×C₄	—	10	2	no	—
265	C₂²×C₃×C₄	—	10	2	no	—
266	C₂²×C₃×C₄	C₄×D₅	1	4	yes	—
267	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
268	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
269	C₂²×C₃×C₄	D₂₀	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂²⋊D₅	1	4	yes	—
271	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
273	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
274	C₃×M₁₆	—	2	4	no	—
275	C₃×M₁₆	—	2	4	no	—
276	C₂×C₃×C₈	—	2	4	no	—
277	C₂×C₃×C₈	C₂²×D₅	1	4	yes	—
278	C₃×C₄⋊C₄	—	5	4	no	—
279	C₃×C₄⋊C₄	—	10	2	no	—
280	C₃×C₂²⋊C₄	—	10	2	no	—
281	C₃×C₂²⋊C₄	—	10	2	no	—
282	C₃×C₄²	—	10	2	no	—
283	C₃×C₄²	—	10	2	no	—
284	C₂³×C₅	—	4	2	no	—
285	C₂³×C₅	C₃×C₂²⋊C₄	1	4	yes	—
286	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
287	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂²×D₅	—	2	4	no	—
290	C₂²×D₅	—	2	2	no	—
291	C₂²×D₅	—	4	4	no	—
292	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
293	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
294	C₂×C₄×C₅	C₃×C₂²⋊C₄	1	4	yes	—
295	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
296	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
297	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
301	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
302	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
303	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
304	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
305	C₂²⋊D₅	—	2	8	no	—
306	C₂²⋊D₅	—	2	8	no	—
307	C₂×Dic₅	—	2	4	no	—
308	C₂×Dic₅	—	2	2	no	—
309	C₂×Dic₅	—	2	4	no	—
310	C₂×Dic₅	—	4	4	no	—
311	D₂₀	—	2	4	no	—
312	D₂₀	—	2	2	no	—
313	D₂₀	C₂²×C₃×C₄	1	4	yes	—
314	C₄×D₅	—	2	8	no	—
315	C₄×D₅	—	2	8	no	—
316	Dic₁₀	—	2	4	no	—
317	Dic₁₀	—	2	2	no	—
318	Dic₁₀	C₂²×C₃×C₄	1	4	yes	—
319	C₅×C₈	—	2	4	no	—
320	C₂×#41	—	5	8	no	—
321	C₂×#41	—	5	2	no	—
322	C₂×#41	—	5	2	no	—
323	C₂×#41	—	10	1	no	—
324	C₂×#41	—	10	1	no	—
325	C₂×#41	—	10	4	no	—
326	C₂²×Q₈	—	5	1	no	—
327	C₂²×D₄	—	5	1	no	—
328	C₂²×D₄	—	10	1	no	—
329	C₂³×C₄	—	10	1	no	—
330	C₂³×C₄	C₂×C₃×D₅	1	1	yes	characteristic
331	C₂×M₁₆	—	2	4	no	—
332	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	—
333	C₂×M₁₆	C₂×C₃×D₅	1	2	yes	complemented
334	C₂²×C₈	C₂×C₃×D₅	1	2	yes	complemented
335	#117	—	5	2	no	—
336	#117	—	5	2	no	—
337	#117	—	10	1	no	—
338	#117	—	10	1	no	—
339	C₂×C₄⋊C₄	—	5	2	no	—
340	C₂×C₂²⋊C₄	—	10	1	no	—
341	C₂×C₄²	—	10	1	no	—
342	#103	—	5	8	no	—
343	#102	—	5	8	no	—
344	C₂×C₃×C₅	—	2	2	no	—
345	C₂×C₃×C₅	—	2	2	no	—
346	C₂×C₃×C₅	—	2	2	no	—
347	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
348	C₂×C₃×C₅	#575	1	2	yes	—
349	C₃×D₅	—	4	4	no	—
350	C₂³×C₃	—	4	2	no	—
351	C₂³×C₃	—	10	2	no	—
352	C₂³×C₃	—	10	4	no	—
353	C₂³×C₃	—	20	4	no	—
354	C₂³×C₃	#685	1	4	yes	—
355	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
356	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
357	C₂³×C₃	C₂×D₂₀	1	1	yes	characteristic
358	C₃×Q₈	—	5	4	no	—
359	C₃×Q₈	—	10	2	no	—
360	C₃×Q₈	—	10	4	no	—
361	C₃×D₄	—	5	4	no	—
362	C₃×D₄	—	10	8	no	—
363	C₃×D₄	—	10	8	no	—
364	C₃×D₄	—	10	2	no	—
365	C₃×D₄	—	10	4	no	—
366	C₂×C₃×C₄	—	10	2	no	—
367	C₂×C₃×C₄	—	10	4	no	—
368	C₂×C₃×C₄	—	10	8	no	—
369	C₂×C₃×C₄	—	10	8	no	—
370	C₂×C₃×C₄	—	10	4	no	—
371	C₂×C₃×C₄	—	20	4	no	—
372	C₂×C₃×C₄	#685	1	4	yes	—
373	C₂×C₃×C₄	#685	1	4	yes	—
374	C₂×C₃×C₄	#685	1	4	yes	—
375	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
376	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
377	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
378	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
379	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
380	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
381	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
382	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
383	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
384	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
385	C₃×C₈	—	2	4	no	—
386	C₂²×C₅	—	2	2	no	—
387	C₂²×C₅	—	2	2	no	—
388	C₂²×C₅	—	2	2	no	—
389	C₂²×C₅	—	4	4	no	—
390	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
391	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
392	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
393	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
394	C₂×D₅	—	2	4	no	—
395	C₂×D₅	—	4	8	no	—
396	C₂×D₅	—	4	4	no	—
397	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
398	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
399	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	2	yes	—
400	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
401	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
402	Dic₅	—	2	4	no	—
403	Dic₅	—	4	4	no	—
404	C₂⁴	—	10	1	no	—
405	C₂⁴	C₃×D₂₀	1	1	yes	characteristic
406	#41	—	5	8	no	—
407	#41	—	5	8	no	—
408	#41	—	10	8	no	—
409	#41	—	10	8	no	—
410	#41	—	10	4	no	—
411	#41	—	10	4	no	—
412	C₂×Q₈	—	5	4	no	—
413	C₂×Q₈	—	5	2	no	—
414	C₂×Q₈	—	10	1	no	—
415	C₂×Q₈	—	10	2	no	—
416	C₂×D₄	—	5	4	no	—
417	C₂×D₄	—	5	2	no	—
418	C₂×D₄	—	10	8	no	—
419	C₂×D₄	—	10	2	no	—
420	C₂×D₄	—	10	2	no	—
421	C₂×D₄	—	10	1	no	—
422	C₂×D₄	—	10	2	no	—
423	C₂²×C₄	—	10	1	no	—
424	C₂²×C₄	—	10	8	no	—
425	C₂²×C₄	—	10	2	no	—
426	C₂²×C₄	—	10	2	no	—
427	C₂²×C₄	—	10	2	no	—
428	C₂²×C₄	C₃×C₄×D₅	1	4	yes	—
429	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
430	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
431	C₂²×C₄	C₃×D₂₀	1	1	yes	characteristic
432	C₂²×C₄	C₃×C₂²⋊D₅	1	4	yes	—
433	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
435	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
436	M₁₆	—	2	4	no	—
437	M₁₆	—	2	4	no	—
438	C₂×C₈	—	2	4	no	—
439	C₂×C₈	C₂²×C₃×D₅	1	4	yes	—
440	C₄⋊C₄	—	5	4	no	—
441	C₄⋊C₄	—	10	2	no	—
442	C₂²⋊C₄	—	10	2	no	—
443	C₂²⋊C₄	—	10	2	no	—
444	C₄²	—	10	2	no	—
445	C₄²	—	10	2	no	—
446	C₃×C₅	#2896	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	2	2	no	—
449	C₂²×C₃	—	2	2	no	—
450	C₂²×C₃	—	4	4	no	—
451	C₂²×C₃	—	10	4	no	—
452	C₂²×C₃	—	20	8	no	—
453	C₂²×C₃	—	20	4	no	—
454	C₂²×C₃	C₂×#685	1	2	yes	—
455	C₂²×C₃	C₂×#685	1	2	yes	—
456	C₂²×C₃	C₂×#685	1	2	yes	—
457	C₂²×C₃	C₂²×D₂₀	1	1	yes	characteristic
458	C₃×C₄	—	10	4	no	—
459	C₃×C₄	—	20	4	no	—
460	C₃×C₄	C₂×#685	1	2	yes	—
461	C₃×C₄	C₂×#685	1	2	yes	—
462	C₃×C₄	C₂×#685	1	2	yes	—
463	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
464	C₃×C₄	C₂²×C₂²⋊D₅	1	1	yes	characteristic
465	C₂×C₅	—	2	2	no	—
466	C₂×C₅	—	2	2	no	—
467	C₂×C₅	—	2	2	no	—
468	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
469	C₂×C₅	C₃×#575	1	2	yes	—
470	D₅	—	4	4	no	—
471	C₂³	—	4	2	no	—
472	C₂³	—	10	2	no	—
473	C₂³	—	10	4	no	—
474	C₂³	—	20	4	no	—
475	C₂³	C₃×#685	1	4	yes	—
476	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
477	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
478	C₂³	C₂×C₃×D₂₀	1	1	yes	characteristic
479	Q₈	—	5	4	no	—
480	Q₈	—	10	2	no	—
481	Q₈	—	10	4	no	—
482	D₄	—	5	4	no	—
483	D₄	—	10	8	no	—
484	D₄	—	10	8	no	—
485	D₄	—	10	2	no	—
486	D₄	—	10	4	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	10	4	no	—
489	C₂×C₄	—	10	8	no	—
490	C₂×C₄	—	10	8	no	—
491	C₂×C₄	—	10	4	no	—
492	C₂×C₄	—	20	4	no	—
493	C₂×C₄	C₃×#685	1	4	yes	—
494	C₂×C₄	C₃×#685	1	4	yes	—
495	C₂×C₄	C₃×#685	1	4	yes	—
496	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
497	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
498	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
499	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
500	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
501	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
502	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
503	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
504	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
505	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
506	C₈	—	2	4	no	—
507	C₂×C₃	—	2	2	no	—
508	C₂×C₃	—	2	2	no	—
509	C₂×C₃	—	2	2	no	—
510	C₂×C₃	—	20	4	no	—
511	C₂×C₃	#66082	1	2	yes	—
512	C₂×C₃	C₂²×#685	1	1	yes	characteristic
513	C₅	C₃×#2896	1	1	yes	characteristic, complemented, Sylow
514	C₂²	—	2	2	no	—
515	C₂²	—	2	2	no	—
516	C₂²	—	2	2	no	—
517	C₂²	—	4	4	no	—
518	C₂²	—	10	4	no	—
519	C₂²	—	20	8	no	—
520	C₂²	—	20	4	no	—
521	C₂²	C₂×C₃×#685	1	2	yes	—
522	C₂²	C₂×C₃×#685	1	2	yes	—
523	C₂²	C₂×C₃×#685	1	2	yes	—
524	C₂²	C₂²×C₃×D₂₀	1	1	yes	characteristic
525	C₄	—	10	4	no	—
526	C₄	—	20	4	no	—
527	C₄	C₂×C₃×#685	1	2	yes	—
528	C₄	C₂×C₃×#685	1	2	yes	—
529	C₄	C₂×C₃×#685	1	2	yes	—
530	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
531	C₄	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
532	C₃	#10615499	1	1	yes	characteristic, direct product factor, Sylow
533	C₂	—	2	2	no	—
534	C₂	—	2	2	no	—
535	C₂	—	2	2	no	—
536	C₂	—	20	4	no	—
537	C₂	C₃×#66082	1	2	yes	—
538	C₂	C₂²×C₃×#685	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃×C₄	C₂×D₂₀
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂²×C₃×C₅×M₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂²×C₃×#709	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₂²×C₃×M₁₆	D₅
hypocenter	C₅	C₃×#2896
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂³×C₃×C₄ ◁ C₂²×C₃×M₁₆

Complements

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

N	H ≅ G/N	type
2. C₂²×C₃×C₅×M₁₆	C₂	semidirect
3. C₂×C₃×#4072	C₂	semidirect
4. C₃×#65422	C₂	semidirect
5. C₃×#65420	C₂	semidirect
6. C₃×#65409	C₂	semidirect
7. C₃×#65402	C₂	semidirect
8. #10615499	C₃	direct (N × H)
14. C₂×C₃×#709	C₄	semidirect
22. C₂×C₃×C₅×M₁₆	C₂²	semidirect
23. C₂²×C₃×C₅×C₈	C₂²	semidirect
28. C₃×#4072	C₂²	semidirect
29. C₂×C₃×C₄⋊Dic₅	C₂²	semidirect
31. C₃×#3953	C₂²	semidirect
32. C₃×#3948	C₂²	semidirect
35. C₂²×C₅×M₁₆	C₂×C₃	semidirect
36. C₂×#4072	C₂×C₃	semidirect
37. #65422	C₂×C₃	semidirect
38. #65420	C₂×C₃	semidirect
39. #65409	C₂×C₃	semidirect
40. #65402	C₂×C₃	semidirect
61. C₃×#709	C₂×C₄	semidirect
64. C₂×C₃×D₂₀	C₂×C₄	semidirect
71. C₂×C₃×Dic₁₀	C₂×C₄	semidirect
84. C₂²×C₃×M₁₆	D₅	semidirect
95. C₂×#709	C₃×C₄	semidirect
103. C₂×C₅×M₁₆	C₂²×C₃	semidirect
104. C₂²×C₅×C₈	C₂²×C₃	semidirect
109. #4072	C₂²×C₃	semidirect
110. C₂×C₄⋊Dic₅	C₂²×C₃	semidirect
112. #3953	C₂²×C₃	semidirect
113. #3948	C₂²×C₃	semidirect
164. C₂×C₃×M₁₆	C₂×D₅	semidirect
165. C₂²×C₃×C₈	C₂×D₅	semidirect
195. #709	C₂×C₃×C₄	semidirect
198. C₂×D₂₀	C₂×C₃×C₄	semidirect
205. C₂×Dic₁₀	C₂×C₃×C₄	semidirect
218. C₂²×M₁₆	C₃×D₅	semidirect
333. C₂×M₁₆	C₂×C₃×D₅	semidirect
334. C₂²×C₈	C₂×C₃×D₅	semidirect
446. C₃×C₅	#2896	semidirect
513. C₅	C₃×#2896	semidirect
532. C₃	#10615499	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×#709	2
C₂²×C₃×C₅×M₁₆	2
C₂×C₃×#4072	2
C₃×#65422	2
C₃×#65420	2
C₃×#65409	2
C₃×#65402	2
#10615499	3
C₃×#2896	5

Subgroups — C3×#10615499 #14412550

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615499 #14412550