Subgroups — C₃×#10611452 #14417627

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 492 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic
2	C₃×#65908	C₂	1	2	yes	maximal, complemented
3	C₃×C₄×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×Q₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65315	C₂	1	2	yes	maximal, complemented
6	C₃×D₅×#107	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65161	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65106	C₂	1	2	yes	maximal, complemented
9	C₃×#65092	C₂	1	2	yes	maximal, complemented
10	C₃×C₄×D₄₀	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64978	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611452	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#688	C₂²	1	2	yes	—
18	C₃×#4065	C₄	1	8	yes	complemented
19	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×#676	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4039	—	2	2	no	—
23	C₃×#4039	C₂²	1	2	yes	—
24	C₃×D₅×C₄⋊C₄	—	2	2	no	—
25	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₄×D₂₀	—	2	2	no	—
27	C₃×C₄×D₂₀	C₂²	1	2	yes	—
28	C₃×#4018	—	2	2	no	—
29	C₃×#4018	C₂²	1	1	yes	characteristic
30	C₃×C₅×#107	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3950	C₂²	1	1	yes	characteristic
36	C₃×#3947	C₂²	1	1	yes	characteristic
37	C₃×C₈×Dic₅	C₂²	1	1	yes	characteristic
38	C₃×#3941	C₂²	1	2	yes	—
39	C₃×#3939	C₂²	1	2	yes	—
40	C₃×#3935	C₂²	1	1	yes	characteristic
41	C₃×#2951	—	5	1	no	maximal, Hall
42	C₂×#4065	C₂×C₃	1	1	yes	characteristic
43	#65908	C₂×C₃	1	2	yes	complemented
44	C₄×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
45	Q₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
46	#65315	C₂×C₃	1	2	yes	complemented
47	D₅×#107	C₂×C₃	1	1	yes	characteristic, complemented
48	#65161	C₂×C₃	1	1	yes	characteristic, complemented
49	#65106	C₂×C₃	1	2	yes	complemented
50	#65092	C₂×C₃	1	2	yes	complemented
51	C₄×D₄₀	C₂×C₃	1	1	yes	characteristic, complemented
52	#64978	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₃×#713	—	2	4	no	—
55	C₃×#713	C₂×C₄	1	8	yes	complemented
56	C₂×C₃×D₂₀	—	2	2	no	—
57	C₂×C₃×D₂₀	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	—	2	2	no	—
59	C₂×C₃×C₄×D₅	—	2	2	no	—
60	C₂×C₃×C₄×D₅	—	2	2	no	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×#688	C₂×C₄	1	8	yes	complemented
71	C₃×#685	—	2	2	no	—
72	C₃×#685	—	2	2	no	—
73	C₃×#685	D₄	1	1	yes	characteristic
74	C₃×#685	D₄	1	1	yes	characteristic
75	C₃×C₄⋊Dic₅	—	2	2	no	—
76	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
77	C₃×#683	—	2	2	no	—
78	C₃×#683	D₄	1	1	yes	characteristic
79	C₃×#683	D₄	1	1	yes	characteristic
80	C₃×C₄×Dic₅	—	2	2	no	—
81	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
82	C₂×C₃×#168	C₂³	1	1	yes	characteristic
83	C₂×C₃×#168	C₂³	1	1	yes	characteristic
84	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
85	C₃×#676	—	2	2	no	—
86	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
87	C₂×C₃×#135	—	5	1	no	—
88	C₃×#520	—	5	2	no	—
89	C₃×#440	—	5	2	no	—
90	C₃×#440	—	5	2	no	—
91	C₃×C₄×Q₁₆	—	5	1	no	—
92	C₃×C₄×Q₁₆	D₅	1	1	yes	characteristic, complemented
93	C₃×C₄×D₈	—	5	1	no	—
94	C₃×C₄×D₈	—	5	1	no	—
95	C₂×C₃×#107	—	5	1	no	—
96	C₃×#417	—	5	2	no	—
97	C₃×#405	—	5	1	no	—
98	C₂×#713	C₂²×C₃	1	2	yes	—
99	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
100	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
101	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
102	C₂×#688	C₂²×C₃	1	2	yes	—
103	#4065	C₃×C₄	1	8	yes	complemented
104	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
105	C₂×#676	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
107	#4039	—	2	2	no	—
108	#4039	C₂²×C₃	1	2	yes	—
109	D₅×C₄⋊C₄	—	2	2	no	—
110	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
111	C₄×D₂₀	—	2	2	no	—
112	C₄×D₂₀	C₂²×C₃	1	2	yes	—
113	#4018	—	2	2	no	—
114	#4018	C₂²×C₃	1	1	yes	characteristic
115	C₅×#107	C₂²×C₃	1	1	yes	characteristic
116	C₅×#103	C₂²×C₃	1	2	yes	—
117	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
118	#3967	C₂²×C₃	1	2	yes	—
119	#3953	C₂²×C₃	1	2	yes	—
120	#3950	C₂²×C₃	1	1	yes	characteristic
121	#3947	C₂²×C₃	1	1	yes	characteristic
122	C₈×Dic₅	C₂²×C₃	1	1	yes	characteristic
123	#3941	C₂²×C₃	1	2	yes	—
124	#3939	C₂²×C₃	1	2	yes	—
125	#3935	C₂²×C₃	1	1	yes	characteristic
126	#2951	—	5	1	no	Sylow
127	C₂²×C₃×D₅	—	2	2	no	—
128	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
129	C₃×C₅×Q₈	—	2	2	no	—
130	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
131	C₂×C₃×C₄×C₅	—	2	2	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
134	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
135	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
136	C₂×C₃×Dic₅	—	2	2	no	—
137	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
139	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
140	C₃×D₂₀	—	2	8	no	—
141	C₃×D₂₀	—	2	2	no	—
142	C₃×D₂₀	C₂²×C₄	1	4	yes	—
143	C₃×C₄×D₅	—	2	8	no	—
144	C₃×C₄×D₅	—	8	2	no	—
145	C₃×C₄×D₅	—	8	2	no	—
146	C₃×C₄×D₅	—	8	2	no	—
147	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
148	C₃×C₄×D₅	#41	1	2	yes	—
149	C₃×C₅×C₈	—	2	1	no	—
150	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
151	C₃×#168	—	2	1	no	—
152	C₃×#168	C₂²×C₄	1	2	yes	—
153	C₂×C₃×#41	—	5	2	no	—
154	C₃×#135	—	5	8	no	—
155	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
156	C₂×C₃×SD₁₆	—	5	2	no	—
157	C₂×C₃×D₈	—	5	1	no	—
158	C₂×C₃×M₁₆	—	5	1	no	—
159	C₂²×C₃×C₈	—	5	1	no	—
160	C₃×C₄×Q₈	—	5	2	no	—
161	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
162	C₃×C₄×D₄	—	5	2	no	—
163	C₃×C₄×D₄	—	5	2	no	—
164	C₃×C₄×D₄	—	10	2	no	—
165	C₃×C₄×D₄	—	10	2	no	—
166	C₃×#117	—	5	1	no	—
167	C₃×#117	—	10	2	no	—
168	C₂×C₃×C₄⋊C₄	—	5	2	no	—
169	C₂×C₃×C₄⋊C₄	—	10	2	no	—
170	C₃×#107	—	5	1	no	—
171	C₃×#107	—	5	2	no	—
172	C₃×#107	C₂×D₅	1	1	yes	characteristic
173	C₃×#103	—	5	2	no	—
174	C₃×#103	C₂×D₅	1	2	yes	—
175	C₃×#102	—	5	2	no	—
176	C₃×#102	—	5	2	no	—
177	C₃×#97	—	5	1	no	—
178	C₃×#97	—	5	1	no	—
179	C₃×C₄×C₈	—	5	1	no	—
180	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic
181	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
182	#713	—	2	4	no	—
183	#713	C₂×C₃×C₄	1	8	yes	complemented
184	C₂×D₂₀	—	2	2	no	—
185	C₂×D₂₀	C₂³×C₃	1	2	yes	—
186	C₂×C₄×D₅	—	2	2	no	—
187	C₂×C₄×D₅	—	2	2	no	—
188	C₂×C₄×D₅	—	2	2	no	—
189	C₂×C₄×D₅	—	2	2	no	—
190	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
191	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
192	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
193	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
194	C₅×C₄⋊C₄	—	2	2	no	—
195	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
196	C₄²×C₅	—	2	2	no	—
197	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
198	#688	C₂×C₃×C₄	1	8	yes	complemented
199	#685	—	2	2	no	—
200	#685	—	2	2	no	—
201	#685	C₃×D₄	1	1	yes	characteristic
202	#685	C₃×D₄	1	1	yes	characteristic
203	C₄⋊Dic₅	—	2	2	no	—
204	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
205	#683	—	2	2	no	—
206	#683	C₃×D₄	1	1	yes	characteristic
207	#683	C₃×D₄	1	1	yes	characteristic
208	C₄×Dic₅	—	2	2	no	—
209	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
210	C₂×#168	C₂³×C₃	1	1	yes	characteristic
211	C₂×#168	C₂³×C₃	1	1	yes	characteristic
212	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
213	#676	—	2	2	no	—
214	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
215	C₂×#135	—	5	1	no	—
216	#520	—	5	2	no	—
217	#440	—	5	2	no	—
218	#440	—	5	2	no	—
219	C₄×Q₁₆	—	5	1	no	—
220	C₄×Q₁₆	C₃×D₅	1	1	yes	characteristic, complemented
221	C₄×D₈	—	5	1	no	—
222	C₄×D₈	—	5	1	no	—
223	C₂×#107	—	5	1	no	—
224	#417	—	5	2	no	—
225	#405	—	5	1	no	—
226	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
227	C₂×C₃×D₅	—	2	1	no	—
228	C₂×C₃×D₅	—	2	1	no	—
229	C₂×C₃×D₅	—	2	4	no	—
230	C₂×C₃×D₅	—	4	2	no	—
231	C₂×C₃×D₅	—	4	2	no	—
232	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
233	C₃×C₄×C₅	—	2	4	no	—
234	C₃×C₄×C₅	—	2	1	no	—
235	C₃×C₄×C₅	—	2	1	no	—
236	C₃×C₄×C₅	—	4	2	no	—
237	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
238	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
239	C₃×Dic₅	—	2	1	no	—
240	C₃×Dic₅	—	2	1	no	—
241	C₃×Dic₅	—	4	2	no	—
242	C₃×Dic₅	C₄×D₄	1	2	yes	—
243	C₃×#41	—	5	8	no	—
244	C₃×#41	—	10	4	no	—
245	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
246	C₂×C₃×D₄	—	5	2	no	—
247	C₂×C₃×D₄	—	10	2	no	—
248	C₂²×C₃×C₄	—	5	1	no	—
249	C₂²×C₃×C₄	—	10	2	no	—
250	C₂²×C₃×C₄	—	10	2	no	—
251	C₂²×C₃×C₄	—	10	2	no	—
252	C₂²×C₃×C₄	—	10	2	no	—
253	C₃×Q₁₆	C₄×D₅	1	4	yes	complemented
254	C₃×SD₁₆	—	5	8	no	—
255	C₃×D₈	—	5	4	no	—
256	C₃×M₁₆	—	10	2	no	—
257	C₂×C₃×C₈	—	5	1	no	—
258	C₂×C₃×C₈	—	5	4	no	—
259	C₂×C₃×C₈	—	5	1	no	—
260	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
261	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
262	C₃×C₄⋊C₄	—	2	2	no	—
263	C₃×C₄⋊C₄	—	5	1	no	—
264	C₃×C₄⋊C₄	—	5	1	no	—
265	C₃×C₄⋊C₄	—	5	2	no	—
266	C₃×C₄⋊C₄	—	10	2	no	—
267	C₃×C₄⋊C₄	—	10	2	no	—
268	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
269	C₃×C₂²⋊C₄	—	5	1	no	—
270	C₃×C₂²⋊C₄	—	5	1	no	—
271	C₃×C₂²⋊C₄	—	10	2	no	—
272	C₃×C₂²⋊C₄	—	10	2	no	—
273	C₃×C₄²	—	2	2	no	—
274	C₃×C₄²	—	5	1	no	—
275	C₃×C₄²	—	10	2	no	—
276	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
277	C₂²×D₅	—	2	2	no	—
278	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
279	C₅×Q₈	—	2	2	no	—
280	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
281	C₂×C₄×C₅	—	2	2	no	—
282	C₂×C₄×C₅	—	2	2	no	—
283	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
284	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
285	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
286	C₂×Dic₅	—	2	2	no	—
287	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
288	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
289	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
290	D₂₀	—	2	8	no	—
291	D₂₀	—	2	2	no	—
292	D₂₀	C₂²×C₃×C₄	1	4	yes	—
293	C₄×D₅	—	2	8	no	—
294	C₄×D₅	—	8	2	no	—
295	C₄×D₅	—	8	2	no	—
296	C₄×D₅	—	8	2	no	—
297	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
298	C₄×D₅	C₃×#41	1	2	yes	—
299	C₅×C₈	—	2	1	no	—
300	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
301	#168	—	2	1	no	—
302	#168	C₂²×C₃×C₄	1	2	yes	—
303	C₂×#41	—	5	2	no	—
304	#135	—	5	8	no	—
305	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
306	C₂×SD₁₆	—	5	2	no	—
307	C₂×D₈	—	5	1	no	—
308	C₂×M₁₆	—	5	1	no	—
309	C₂²×C₈	—	5	1	no	—
310	C₄×Q₈	—	5	2	no	—
311	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
312	C₄×D₄	—	5	2	no	—
313	C₄×D₄	—	5	2	no	—
314	C₄×D₄	—	10	2	no	—
315	C₄×D₄	—	10	2	no	—
316	#117	—	5	1	no	—
317	#117	—	10	2	no	—
318	C₂×C₄⋊C₄	—	5	2	no	—
319	C₂×C₄⋊C₄	—	10	2	no	—
320	#107	—	5	1	no	—
321	#107	—	5	2	no	—
322	#107	C₂×C₃×D₅	1	1	yes	characteristic
323	#103	—	5	2	no	—
324	#103	C₂×C₃×D₅	1	2	yes	—
325	#102	—	5	2	no	—
326	#102	—	5	2	no	—
327	#97	—	5	1	no	—
328	#97	—	5	1	no	—
329	C₄×C₈	—	5	1	no	—
330	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
332	C₂×C₃×C₅	#576	1	1	yes	characteristic
333	C₂×C₃×C₅	#578	1	1	yes	characteristic
334	C₃×D₅	—	2	2	no	—
335	C₃×D₅	—	4	4	no	—
336	C₂³×C₃	—	5	1	no	—
337	C₂³×C₃	—	10	2	no	—
338	C₃×Q₈	—	2	2	no	—
339	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
340	C₃×D₄	—	5	4	no	—
341	C₃×D₄	—	10	8	no	—
342	C₃×D₄	—	10	2	no	—
343	C₂×C₃×C₄	—	2	2	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	5	1	no	—
346	C₂×C₃×C₄	—	5	2	no	—
347	C₂×C₃×C₄	—	5	2	no	—
348	C₂×C₃×C₄	—	5	1	no	—
349	C₂×C₃×C₄	—	5	1	no	—
350	C₂×C₃×C₄	—	10	8	no	—
351	C₂×C₃×C₄	—	10	2	no	—
352	C₂×C₃×C₄	—	40	2	no	—
353	C₂×C₃×C₄	—	40	2	no	—
354	C₂×C₃×C₄	—	40	2	no	—
355	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
356	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
357	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
358	C₃×C₈	—	2	1	no	—
359	C₃×C₈	—	5	2	no	—
360	C₃×C₈	—	10	1	no	—
361	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
362	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
363	C₂×D₅	—	2	1	no	—
364	C₂×D₅	—	2	1	no	—
365	C₂×D₅	—	2	4	no	—
366	C₂×D₅	—	4	2	no	—
367	C₂×D₅	—	4	2	no	—
368	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
369	C₄×C₅	—	2	1	no	—
370	C₄×C₅	—	2	1	no	—
371	C₄×C₅	—	2	4	no	—
372	C₄×C₅	—	4	2	no	—
373	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
374	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
375	Dic₅	—	2	1	no	—
376	Dic₅	—	2	1	no	—
377	Dic₅	—	4	2	no	—
378	Dic₅	C₃×C₄×D₄	1	2	yes	—
379	#41	—	5	8	no	—
380	#41	—	10	4	no	—
381	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
382	C₂×D₄	—	5	2	no	—
383	C₂×D₄	—	10	2	no	—
384	C₂²×C₄	—	5	1	no	—
385	C₂²×C₄	—	10	2	no	—
386	C₂²×C₄	—	10	2	no	—
387	C₂²×C₄	—	10	2	no	—
388	C₂²×C₄	—	10	2	no	—
389	Q₁₆	C₃×C₄×D₅	1	4	yes	complemented
390	SD₁₆	—	5	8	no	—
391	D₈	—	5	4	no	—
392	M₁₆	—	10	2	no	—
393	C₂×C₈	—	5	1	no	—
394	C₂×C₈	—	5	4	no	—
395	C₂×C₈	—	5	1	no	—
396	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
397	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
398	C₄⋊C₄	—	2	2	no	—
399	C₄⋊C₄	—	5	1	no	—
400	C₄⋊C₄	—	5	1	no	—
401	C₄⋊C₄	—	5	2	no	—
402	C₄⋊C₄	—	10	2	no	—
403	C₄⋊C₄	—	10	2	no	—
404	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
405	C₂²⋊C₄	—	5	1	no	—
406	C₂²⋊C₄	—	5	1	no	—
407	C₂²⋊C₄	—	10	2	no	—
408	C₂²⋊C₄	—	10	2	no	—
409	C₄²	—	2	2	no	—
410	C₄²	—	5	1	no	—
411	C₄²	—	10	2	no	—
412	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
413	C₃×C₅	#2951	1	1	yes	characteristic, complemented, Hall
414	C₂²×C₃	—	5	2	no	—
415	C₂²×C₃	—	10	1	no	—
416	C₂²×C₃	—	10	1	no	—
417	C₂²×C₃	—	10	4	no	—
418	C₂²×C₃	—	20	2	no	—
419	C₂²×C₃	—	20	2	no	—
420	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
421	C₃×C₄	—	2	1	no	—
422	C₃×C₄	—	2	1	no	—
423	C₃×C₄	—	2	4	no	—
424	C₃×C₄	—	4	2	no	—
425	C₃×C₄	—	5	2	no	—
426	C₃×C₄	—	10	1	no	—
427	C₃×C₄	—	10	1	no	—
428	C₃×C₄	—	20	2	no	—
429	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
430	C₃×C₄	D₅×#41	1	1	yes	characteristic
431	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
432	C₂×C₅	C₃×#576	1	1	yes	characteristic
433	C₂×C₅	C₃×#578	1	1	yes	characteristic
434	D₅	—	2	2	no	—
435	D₅	—	4	4	no	—
436	C₂³	—	5	1	no	—
437	C₂³	—	10	2	no	—
438	Q₈	—	2	2	no	—
439	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
440	D₄	—	5	4	no	—
441	D₄	—	10	8	no	—
442	D₄	—	10	2	no	—
443	C₂×C₄	—	2	2	no	—
444	C₂×C₄	—	2	2	no	—
445	C₂×C₄	—	5	1	no	—
446	C₂×C₄	—	5	2	no	—
447	C₂×C₄	—	5	2	no	—
448	C₂×C₄	—	5	1	no	—
449	C₂×C₄	—	5	1	no	—
450	C₂×C₄	—	10	8	no	—
451	C₂×C₄	—	10	2	no	—
452	C₂×C₄	—	40	2	no	—
453	C₂×C₄	—	40	2	no	—
454	C₂×C₄	—	40	2	no	—
455	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
456	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
457	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
458	C₈	—	2	1	no	—
459	C₈	—	5	2	no	—
460	C₈	—	10	1	no	—
461	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
462	C₂×C₃	—	10	2	no	—
463	C₂×C₃	—	20	4	no	—
464	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
465	C₂×C₃	#66100	1	1	yes	characteristic
466	C₂×C₃	#66103	1	1	yes	characteristic
467	C₅	C₃×#2951	1	1	yes	characteristic, complemented, Sylow
468	C₂²	—	5	2	no	—
469	C₂²	—	10	1	no	—
470	C₂²	—	10	1	no	—
471	C₂²	—	10	4	no	—
472	C₂²	—	20	2	no	—
473	C₂²	—	20	2	no	—
474	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
475	C₄	—	2	1	no	—
476	C₄	—	2	1	no	—
477	C₄	—	2	4	no	—
478	C₄	—	4	2	no	—
479	C₄	—	5	2	no	—
480	C₄	—	10	1	no	—
481	C₄	—	10	1	no	—
482	C₄	—	20	2	no	—
483	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
484	C₄	C₃×D₅×#41	1	1	yes	characteristic
485	C₃	#10611452	1	1	yes	characteristic, direct product factor, Sylow
486	C₂	—	10	2	no	—
487	C₂	—	20	4	no	—
488	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
489	C₂	C₃×#66100	1	1	yes	characteristic
490	C₂	C₃×#66103	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₄×C₅×Q₁₆	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4065	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×C₄×Q₁₆	D₅
hypocenter	C₅	C₃×#2951
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×C₄×Q₁₆

Complements

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

N	H ≅ G/N	type
2. C₃×#65908	C₂	semidirect
3. C₃×C₄×C₅×Q₁₆	C₂	semidirect
4. C₃×Q₁₆×Dic₅	C₂	semidirect
5. C₃×#65315	C₂	semidirect
6. C₃×D₅×#107	C₂	semidirect
7. C₃×#65161	C₂	semidirect
8. C₃×#65106	C₂	semidirect
9. C₃×#65092	C₂	semidirect
10. C₃×C₄×D₄₀	C₂	semidirect
11. C₃×#64978	C₂	semidirect
12. #10611452	C₃	direct (N × H)
18. C₃×#4065	C₄	semidirect
43. #65908	C₂×C₃	semidirect
44. C₄×C₅×Q₁₆	C₂×C₃	semidirect
45. Q₁₆×Dic₅	C₂×C₃	semidirect
46. #65315	C₂×C₃	semidirect
47. D₅×#107	C₂×C₃	semidirect
48. #65161	C₂×C₃	semidirect
49. #65106	C₂×C₃	semidirect
50. #65092	C₂×C₃	semidirect
51. C₄×D₄₀	C₂×C₃	semidirect
52. #64978	C₂×C₃	semidirect
55. C₃×#713	C₂×C₄	semidirect
63. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₃×#688	C₂×C₄	semidirect
84. C₃×D₄₀	C₂×C₄	semidirect
86. C₃×C₈×D₅	C₂×C₄	semidirect
92. C₃×C₄×Q₁₆	D₅	semidirect
103. #4065	C₃×C₄	semidirect
183. #713	C₂×C₃×C₄	semidirect
191. C₅×Q₁₆	C₂×C₃×C₄	semidirect
198. #688	C₂×C₃×C₄	semidirect
212. D₄₀	C₂×C₃×C₄	semidirect
214. C₈×D₅	C₂×C₃×C₄	semidirect
220. C₄×Q₁₆	C₃×D₅	semidirect
253. C₃×Q₁₆	C₄×D₅	semidirect
389. Q₁₆	C₃×C₄×D₅	semidirect
413. C₃×C₅	#2951	semidirect
467. C₅	C₃×#2951	semidirect
485. C₃	#10611452	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×C₃×#4065	2
C₃×#65908	2
C₃×C₄×C₅×Q₁₆	2
C₃×Q₁₆×Dic₅	2
C₃×#65315	2
C₃×D₅×#107	2
C₃×#65161	2
C₃×#65106	2
C₃×#65092	2
C₃×C₄×D₄₀	2
C₃×#64978	2
#10611452	3
C₃×#2951	5

Subgroups — C3×#10611452 #14417627

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611452 #14417627