Subgroups — C₃×#10610600 #14417723

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 560 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66161	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic
3	C₃×#65838	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#417	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65422	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65411	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₃×#3940	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65078	C₂	1	2	yes	maximal, complemented
9	C₃×#65077	C₂	1	2	yes	maximal, complemented
10	C₃×#65074	C₂	1	2	yes	maximal, complemented
11	C₃×#65047	C₂	1	2	yes	maximal, complemented
12	#10610600	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×#709	C₂²	1	1	yes	characteristic
15	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
17	C₃×#4096	C₄	1	8	yes	complemented
18	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
19	C₂×C₃×#689	C₂²	1	1	yes	characteristic
20	C₂×C₃×#688	C₂²	1	1	yes	characteristic
21	C₃×D₄×Dic₅	—	2	2	no	—
22	C₃×D₄×Dic₅	C₂²	1	2	yes	—
23	C₂×C₃×#687	C₂²	1	1	yes	characteristic
24	C₂×C₃×#686	C₂²	1	1	yes	characteristic
25	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
26	C₃×#4072	—	2	1	no	—
27	C₃×#4072	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄⋊Dic₅	—	2	1	no	—
29	C₂×C₃×C₄⋊Dic₅	C₂²	1	1	yes	characteristic
30	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
31	C₃×#4039	C₂²	1	2	yes	—
32	C₃×#4038	—	2	1	no	—
33	C₃×D₅×C₄⋊C₄	—	2	1	no	—
34	C₃×#4033	C₂²	1	2	yes	—
35	C₃×C₅×#103	C₂²	1	2	yes	—
36	C₃×C₅×#102	C₂²	1	2	yes	—
37	C₃×#3953	C₂²	1	2	yes	—
38	C₃×#3948	C₂²	1	2	yes	—
39	C₃×#3947	C₂²	1	2	yes	—
40	C₃×C₈×Dic₅	C₂²	1	2	yes	—
41	C₃×#3940	C₂²	1	2	yes	—
42	C₃×#3940	C₂²	1	2	yes	—
43	C₃×#2952	—	5	1	no	maximal, Hall
44	#66161	C₂×C₃	1	1	yes	characteristic, complemented
45	C₂×#4096	C₂×C₃	1	1	yes	characteristic
46	#65838	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#417	C₂×C₃	1	1	yes	characteristic, complemented
48	#65422	C₂×C₃	1	1	yes	characteristic, complemented
49	#65411	C₂×C₃	1	1	yes	characteristic, complemented
50	C₂×#3940	C₂×C₃	1	1	yes	characteristic, complemented
51	#65078	C₂×C₃	1	2	yes	complemented
52	#65077	C₂×C₃	1	2	yes	complemented
53	#65074	C₂×C₃	1	2	yes	complemented
54	#65047	C₂×C₃	1	2	yes	complemented
55	C₃×C₅×#41	—	2	2	no	—
56	C₃×C₅×#41	C₂×C₄	1	4	yes	complemented
57	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
58	C₂×C₃×C₅×D₄	—	2	1	no	—
59	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
60	C₂²×C₃×C₄×C₅	—	2	1	no	—
61	C₂²×C₃×C₄×C₅	—	2	1	no	—
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
64	C₂²×C₃×Dic₅	—	2	1	no	—
65	C₂²×C₃×Dic₅	—	2	2	no	—
66	C₃×#709	—	2	2	no	—
67	C₃×#709	C₂×C₄	1	4	yes	complemented
68	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
69	C₂×C₃×C₄×D₅	—	2	1	no	—
70	C₂×C₃×C₄×D₅	—	2	2	no	—
71	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
72	C₃×C₅×M₁₆	—	2	2	no	—
73	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
74	C₃×C₅×C₄⋊C₄	—	2	1	no	—
75	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
76	C₃×C₂²⋊Dic₅	—	2	2	no	—
77	C₃×C₂²⋊Dic₅	D₄	1	2	yes	—
78	C₃×#689	C₂×C₄	1	4	yes	complemented
79	C₃×#688	C₂×C₄	1	4	yes	complemented
80	C₃×#687	C₂×C₄	1	4	yes	complemented
81	C₃×#686	C₂×C₄	1	4	yes	complemented
82	C₃×#685	—	2	2	no	—
83	C₃×C₄⋊Dic₅	—	2	1	no	—
84	C₃×C₄⋊Dic₅	—	2	2	no	—
85	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
86	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
87	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
88	C₃×#683	—	2	2	no	—
89	C₃×C₄×Dic₅	—	2	2	no	—
90	C₃×C₄×Dic₅	—	2	2	no	—
91	C₃×C₄×Dic₅	C₂³	1	2	yes	—
92	C₂×C₃×#168	C₂×C₄	1	4	yes	complemented
93	C₂×C₃×#168	C₂³	1	1	yes	characteristic
94	C₂×C₃×#168	C₂³	1	1	yes	characteristic
95	C₂×C₃×#135	—	5	1	no	—
96	C₃×#520	—	5	1	no	—
97	C₃×#520	—	5	1	no	—
98	C₃×#442	—	5	2	no	—
99	C₃×#441	—	5	2	no	—
100	C₃×C₄×SD₁₆	—	5	2	no	—
101	C₃×C₄×SD₁₆	—	5	2	no	—
102	C₂×C₃×#106	—	5	1	no	—
103	C₃×#417	—	5	1	no	—
104	C₃×#417	D₅	1	1	yes	characteristic, complemented
105	C₃×#405	—	5	1	no	—
106	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
107	C₂×#709	C₂²×C₃	1	1	yes	characteristic
108	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	#4096	C₃×C₄	1	8	yes	complemented
111	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
112	C₂×#689	C₂²×C₃	1	1	yes	characteristic
113	C₂×#688	C₂²×C₃	1	1	yes	characteristic
114	D₄×Dic₅	—	2	2	no	—
115	D₄×Dic₅	C₂²×C₃	1	2	yes	—
116	C₂×#687	C₂²×C₃	1	1	yes	characteristic
117	C₂×#686	C₂²×C₃	1	1	yes	characteristic
118	C₄×C₂²⋊D₅	—	2	2	no	—
119	#4072	—	2	1	no	—
120	#4072	C₂²×C₃	1	1	yes	characteristic
121	C₂×C₄⋊Dic₅	—	2	1	no	—
122	C₂×C₄⋊Dic₅	C₂²×C₃	1	1	yes	characteristic
123	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
124	#4039	C₂²×C₃	1	2	yes	—
125	#4038	—	2	1	no	—
126	D₅×C₄⋊C₄	—	2	1	no	—
127	#4033	C₂²×C₃	1	2	yes	—
128	C₅×#103	C₂²×C₃	1	2	yes	—
129	C₅×#102	C₂²×C₃	1	2	yes	—
130	#3953	C₂²×C₃	1	2	yes	—
131	#3948	C₂²×C₃	1	2	yes	—
132	#3947	C₂²×C₃	1	2	yes	—
133	C₈×Dic₅	C₂²×C₃	1	2	yes	—
134	#3940	C₂²×C₃	1	2	yes	—
135	#3940	C₂²×C₃	1	2	yes	—
136	#2952	—	5	1	no	Sylow
137	C₂³×C₃×C₅	—	2	1	no	—
138	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
139	C₂²×C₃×D₅	—	2	1	no	—
140	C₃×C₅×Q₈	—	2	1	no	—
141	C₃×C₅×Q₈	C₂²×C₄	1	2	yes	—
142	C₃×C₅×D₄	—	2	4	no	—
143	C₃×C₅×D₄	—	2	1	no	—
144	C₃×C₅×D₄	C₂²×C₄	1	2	yes	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	4	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	8	1	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
150	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
153	C₃×C₂²⋊D₅	—	2	4	no	—
154	C₂×C₃×Dic₅	—	2	1	no	—
155	C₂×C₃×Dic₅	—	2	2	no	—
156	C₂×C₃×Dic₅	—	8	2	no	—
157	C₂×C₃×Dic₅	—	8	1	no	—
158	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
159	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
160	C₃×D₂₀	—	2	1	no	—
161	C₃×D₂₀	C₂²×C₄	1	2	yes	—
162	C₃×C₄×D₅	—	2	4	no	—
163	C₃×C₄×D₅	—	8	2	no	—
164	C₃×Dic₁₀	—	2	1	no	—
165	C₃×Dic₁₀	C₂²×C₄	1	2	yes	—
166	C₃×C₅×C₈	—	2	2	no	—
167	C₃×#168	C₂²×C₄	1	2	yes	—
168	C₃×#168	C₂²×C₄	1	2	yes	—
169	C₂×C₃×#41	—	5	1	no	—
170	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
171	C₃×#135	—	5	8	no	—
172	C₂×C₃×Q₁₆	—	5	1	no	—
173	C₂×C₃×SD₁₆	—	5	1	no	—
174	C₂×C₃×SD₁₆	—	5	1	no	—
175	C₂×C₃×D₈	—	5	1	no	—
176	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
177	C₂²×C₃×C₈	—	5	1	no	—
178	C₃×C₄×Q₈	—	5	2	no	—
179	C₃×C₄×Q₈	—	5	2	no	—
180	C₃×C₄×D₄	—	5	2	no	—
181	C₃×C₄×D₄	—	5	2	no	—
182	C₃×C₄×D₄	—	10	2	no	—
183	C₃×C₄×D₄	—	10	2	no	—
184	C₃×#117	—	5	1	no	—
185	C₃×#117	—	10	1	no	—
186	C₃×#117	—	10	1	no	—
187	C₂×C₃×C₄⋊C₄	—	5	1	no	—
188	C₂×C₃×C₄⋊C₄	—	10	1	no	—
189	C₂×C₃×C₄⋊C₄	—	10	1	no	—
190	C₂×C₃×C₄⋊C₄	C₂×D₅	1	1	yes	characteristic
191	C₃×#106	—	5	2	no	—
192	C₃×#106	—	5	2	no	—
193	C₃×#103	—	5	2	no	—
194	C₃×#103	C₂×D₅	1	2	yes	—
195	C₃×#102	—	5	2	no	—
196	C₃×#102	C₂×D₅	1	2	yes	—
197	C₃×#97	—	5	2	no	—
198	C₃×C₄×C₈	—	5	2	no	—
199	C₅×#41	—	2	2	no	—
200	C₅×#41	C₂×C₃×C₄	1	4	yes	complemented
201	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
202	C₂×C₅×D₄	—	2	1	no	—
203	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
204	C₂²×C₄×C₅	—	2	1	no	—
205	C₂²×C₄×C₅	—	2	1	no	—
206	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
207	C₂×C₂²⋊D₅	—	2	1	no	—
208	C₂²×Dic₅	—	2	1	no	—
209	C₂²×Dic₅	—	2	2	no	—
210	#709	—	2	2	no	—
211	#709	C₂×C₃×C₄	1	4	yes	complemented
212	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
213	C₂×C₄×D₅	—	2	1	no	—
214	C₂×C₄×D₅	—	2	2	no	—
215	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
216	C₅×M₁₆	—	2	2	no	—
217	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
218	C₅×C₄⋊C₄	—	2	1	no	—
219	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
220	C₂²⋊Dic₅	—	2	2	no	—
221	C₂²⋊Dic₅	C₃×D₄	1	2	yes	—
222	#689	C₂×C₃×C₄	1	4	yes	complemented
223	#688	C₂×C₃×C₄	1	4	yes	complemented
224	#687	C₂×C₃×C₄	1	4	yes	complemented
225	#686	C₂×C₃×C₄	1	4	yes	complemented
226	#685	—	2	2	no	—
227	C₄⋊Dic₅	—	2	1	no	—
228	C₄⋊Dic₅	—	2	2	no	—
229	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
230	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
231	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
232	#683	—	2	2	no	—
233	C₄×Dic₅	—	2	2	no	—
234	C₄×Dic₅	—	2	2	no	—
235	C₄×Dic₅	C₂³×C₃	1	2	yes	—
236	C₂×#168	C₂×C₃×C₄	1	4	yes	complemented
237	C₂×#168	C₂³×C₃	1	1	yes	characteristic
238	C₂×#168	C₂³×C₃	1	1	yes	characteristic
239	C₂×#135	—	5	1	no	—
240	#520	—	5	1	no	—
241	#520	—	5	1	no	—
242	#442	—	5	2	no	—
243	#441	—	5	2	no	—
244	C₄×SD₁₆	—	5	2	no	—
245	C₄×SD₁₆	—	5	2	no	—
246	C₂×#106	—	5	1	no	—
247	#417	—	5	1	no	—
248	#417	C₃×D₅	1	1	yes	characteristic, complemented
249	#405	—	5	1	no	—
250	C₂²×C₃×C₅	—	2	1	no	—
251	C₂²×C₃×C₅	—	2	1	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	4	1	no	—
254	C₂²×C₃×C₅	—	4	1	no	—
255	C₂²×C₃×C₅	C₄×D₄	1	2	yes	—
256	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
257	C₂×C₃×D₅	—	2	2	no	—
258	C₂×C₃×D₅	—	4	1	no	—
259	C₂×C₃×D₅	—	4	1	no	—
260	C₃×C₄×C₅	—	2	2	no	—
261	C₃×C₄×C₅	—	4	2	no	—
262	C₃×C₄×C₅	C₄×D₄	1	2	yes	—
263	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
264	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
265	C₃×Dic₅	—	2	2	no	—
266	C₃×Dic₅	—	2	2	no	—
267	C₃×Dic₅	—	2	2	no	—
268	C₃×Dic₅	—	4	2	no	—
269	C₃×#41	—	2	2	no	—
270	C₃×#41	—	5	4	no	—
271	C₃×#41	—	10	2	no	—
272	C₃×#41	C₄×D₅	1	4	yes	complemented
273	C₂×C₃×Q₈	—	5	1	no	—
274	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
275	C₂×C₃×D₄	—	2	1	no	—
276	C₂×C₃×D₄	—	5	1	no	—
277	C₂×C₃×D₄	—	10	1	no	—
278	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
279	C₂²×C₃×C₄	—	2	1	no	—
280	C₂²×C₃×C₄	—	2	1	no	—
281	C₂²×C₃×C₄	—	10	2	no	—
282	C₂²×C₃×C₄	—	10	2	no	—
283	C₂²×C₃×C₄	—	10	1	no	—
284	C₂²×C₃×C₄	—	10	1	no	—
285	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
286	C₃×Q₁₆	—	5	4	no	—
287	C₃×SD₁₆	—	5	4	no	—
288	C₃×SD₁₆	—	5	4	no	—
289	C₃×D₈	—	5	4	no	—
290	C₃×M₁₆	—	2	2	no	—
291	C₂×C₃×C₈	—	5	4	no	—
292	C₂×C₃×C₈	—	5	1	no	—
293	C₂×C₃×C₈	—	5	1	no	—
294	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
295	C₃×C₄⋊C₄	—	2	1	no	—
296	C₃×C₄⋊C₄	—	5	1	no	—
297	C₃×C₄⋊C₄	—	5	1	no	—
298	C₃×C₄⋊C₄	—	5	2	no	—
299	C₃×C₄⋊C₄	—	10	2	no	—
300	C₃×C₄⋊C₄	—	10	2	no	—
301	C₃×C₄⋊C₄	—	10	1	no	—
302	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
303	C₃×C₂²⋊C₄	—	5	2	no	—
304	C₃×C₂²⋊C₄	—	10	2	no	—
305	C₃×C₂²⋊C₄	—	10	2	no	—
306	C₃×C₄²	—	5	2	no	—
307	C₃×C₄²	—	10	2	no	—
308	C₃×C₄²	—	10	2	no	—
309	C₂³×C₅	—	2	1	no	—
310	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
311	C₂²×D₅	—	2	1	no	—
312	C₅×Q₈	—	2	1	no	—
313	C₅×Q₈	C₂²×C₃×C₄	1	2	yes	—
314	C₅×D₄	—	2	4	no	—
315	C₅×D₄	—	2	1	no	—
316	C₅×D₄	C₂²×C₃×C₄	1	2	yes	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	4	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	8	1	no	—
321	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
322	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
323	C₂×C₄×C₅	C₃×#41	1	2	yes	—
324	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
325	C₂²⋊D₅	—	2	4	no	—
326	C₂×Dic₅	—	2	1	no	—
327	C₂×Dic₅	—	2	2	no	—
328	C₂×Dic₅	—	8	2	no	—
329	C₂×Dic₅	—	8	1	no	—
330	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
331	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
332	D₂₀	—	2	1	no	—
333	D₂₀	C₂²×C₃×C₄	1	2	yes	—
334	C₄×D₅	—	2	4	no	—
335	C₄×D₅	—	8	2	no	—
336	Dic₁₀	—	2	1	no	—
337	Dic₁₀	C₂²×C₃×C₄	1	2	yes	—
338	C₅×C₈	—	2	2	no	—
339	#168	C₂²×C₃×C₄	1	2	yes	—
340	#168	C₂²×C₃×C₄	1	2	yes	—
341	C₂×#41	—	5	1	no	—
342	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
343	#135	—	5	8	no	—
344	C₂×Q₁₆	—	5	1	no	—
345	C₂×SD₁₆	—	5	1	no	—
346	C₂×SD₁₆	—	5	1	no	—
347	C₂×D₈	—	5	1	no	—
348	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
349	C₂²×C₈	—	5	1	no	—
350	C₄×Q₈	—	5	2	no	—
351	C₄×Q₈	—	5	2	no	—
352	C₄×D₄	—	5	2	no	—
353	C₄×D₄	—	5	2	no	—
354	C₄×D₄	—	10	2	no	—
355	C₄×D₄	—	10	2	no	—
356	#117	—	5	1	no	—
357	#117	—	10	1	no	—
358	#117	—	10	1	no	—
359	C₂×C₄⋊C₄	—	5	1	no	—
360	C₂×C₄⋊C₄	—	10	1	no	—
361	C₂×C₄⋊C₄	—	10	1	no	—
362	C₂×C₄⋊C₄	C₂×C₃×D₅	1	1	yes	characteristic
363	#106	—	5	2	no	—
364	#106	—	5	2	no	—
365	#103	—	5	2	no	—
366	#103	C₂×C₃×D₅	1	2	yes	—
367	#102	—	5	2	no	—
368	#102	C₂×C₃×D₅	1	2	yes	—
369	#97	—	5	2	no	—
370	C₄×C₈	—	5	2	no	—
371	C₂×C₃×C₅	—	2	2	no	—
372	C₂×C₃×C₅	—	4	2	no	—
373	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
374	C₂×C₃×C₅	#577	1	1	yes	characteristic
375	C₂×C₃×C₅	#577	1	1	yes	characteristic
376	C₃×D₅	—	4	2	no	—
377	C₂³×C₃	—	2	1	no	—
378	C₂³×C₃	—	10	1	no	—
379	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
380	C₃×Q₈	—	2	1	no	—
381	C₃×Q₈	—	5	2	no	—
382	C₃×Q₈	—	10	1	no	—
383	C₃×Q₈	C₂×C₄×D₅	1	2	yes	—
384	C₃×D₄	—	2	4	no	—
385	C₃×D₄	—	2	1	no	—
386	C₃×D₄	—	5	2	no	—
387	C₃×D₄	—	10	4	no	—
388	C₃×D₄	—	10	1	no	—
389	C₃×D₄	C₂×C₄×D₅	1	2	yes	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	4	no	—
392	C₂×C₃×C₄	—	2	2	no	—
393	C₂×C₃×C₄	—	5	2	no	—
394	C₂×C₃×C₄	—	5	2	no	—
395	C₂×C₃×C₄	—	8	1	no	—
396	C₂×C₃×C₄	—	10	1	no	—
397	C₂×C₃×C₄	—	10	4	no	—
398	C₂×C₃×C₄	—	10	2	no	—
399	C₂×C₃×C₄	—	40	2	no	—
400	C₂×C₃×C₄	—	40	2	no	—
401	C₂×C₃×C₄	—	40	1	no	—
402	C₂×C₃×C₄	C₂×C₄×D₅	1	2	yes	—
403	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
404	C₂×C₃×C₄	#711	1	2	yes	—
405	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
406	C₃×C₈	—	2	2	no	—
407	C₃×C₈	—	5	2	no	—
408	C₃×C₈	—	5	2	no	—
409	C₂²×C₅	—	2	1	no	—
410	C₂²×C₅	—	2	1	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	4	1	no	—
413	C₂²×C₅	—	4	1	no	—
414	C₂²×C₅	C₃×C₄×D₄	1	2	yes	—
415	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
416	C₂×D₅	—	2	2	no	—
417	C₂×D₅	—	4	1	no	—
418	C₂×D₅	—	4	1	no	—
419	C₄×C₅	—	2	2	no	—
420	C₄×C₅	—	4	2	no	—
421	C₄×C₅	C₃×C₄×D₄	1	2	yes	—
422	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
423	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
424	Dic₅	—	2	2	no	—
425	Dic₅	—	2	2	no	—
426	Dic₅	—	2	2	no	—
427	Dic₅	—	4	2	no	—
428	#41	—	2	2	no	—
429	#41	—	5	4	no	—
430	#41	—	10	2	no	—
431	#41	C₃×C₄×D₅	1	4	yes	complemented
432	C₂×Q₈	—	5	1	no	—
433	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₂×D₄	—	2	1	no	—
435	C₂×D₄	—	5	1	no	—
436	C₂×D₄	—	10	1	no	—
437	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
438	C₂²×C₄	—	2	1	no	—
439	C₂²×C₄	—	2	1	no	—
440	C₂²×C₄	—	10	2	no	—
441	C₂²×C₄	—	10	2	no	—
442	C₂²×C₄	—	10	1	no	—
443	C₂²×C₄	—	10	1	no	—
444	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
445	Q₁₆	—	5	4	no	—
446	SD₁₆	—	5	4	no	—
447	SD₁₆	—	5	4	no	—
448	D₈	—	5	4	no	—
449	M₁₆	—	2	2	no	—
450	C₂×C₈	—	5	4	no	—
451	C₂×C₈	—	5	1	no	—
452	C₂×C₈	—	5	1	no	—
453	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
454	C₄⋊C₄	—	2	1	no	—
455	C₄⋊C₄	—	5	1	no	—
456	C₄⋊C₄	—	5	1	no	—
457	C₄⋊C₄	—	5	2	no	—
458	C₄⋊C₄	—	10	2	no	—
459	C₄⋊C₄	—	10	2	no	—
460	C₄⋊C₄	—	10	1	no	—
461	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
462	C₂²⋊C₄	—	5	2	no	—
463	C₂²⋊C₄	—	10	2	no	—
464	C₂²⋊C₄	—	10	2	no	—
465	C₄²	—	5	2	no	—
466	C₄²	—	10	2	no	—
467	C₄²	—	10	2	no	—
468	C₃×C₅	#2952	1	1	yes	characteristic, complemented, Hall
469	C₂²×C₃	—	2	1	no	—
470	C₂²×C₃	—	2	1	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	4	1	no	—
473	C₂²×C₃	—	4	1	no	—
474	C₂²×C₃	—	10	2	no	—
475	C₂²×C₃	—	20	1	no	—
476	C₂²×C₃	—	20	1	no	—
477	C₂²×C₃	#4027	1	2	yes	—
478	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
479	C₃×C₄	—	2	2	no	—
480	C₃×C₄	—	4	2	no	—
481	C₃×C₄	—	10	2	no	—
482	C₃×C₄	—	10	2	no	—
483	C₃×C₄	—	10	2	no	—
484	C₃×C₄	—	20	2	no	—
485	C₃×C₄	#4027	1	2	yes	—
486	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
487	C₃×C₄	C₂×#711	1	1	yes	characteristic
488	C₂×C₅	—	2	2	no	—
489	C₂×C₅	—	4	2	no	—
490	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
491	C₂×C₅	C₃×#577	1	1	yes	characteristic
492	C₂×C₅	C₃×#577	1	1	yes	characteristic
493	D₅	—	4	2	no	—
494	C₂³	—	2	1	no	—
495	C₂³	—	10	1	no	—
496	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
497	Q₈	—	2	1	no	—
498	Q₈	—	5	2	no	—
499	Q₈	—	10	1	no	—
500	Q₈	C₂×C₃×C₄×D₅	1	2	yes	—
501	D₄	—	2	4	no	—
502	D₄	—	2	1	no	—
503	D₄	—	5	2	no	—
504	D₄	—	10	4	no	—
505	D₄	—	10	1	no	—
506	D₄	C₂×C₃×C₄×D₅	1	2	yes	—
507	C₂×C₄	—	2	1	no	—
508	C₂×C₄	—	2	4	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	5	2	no	—
511	C₂×C₄	—	5	2	no	—
512	C₂×C₄	—	8	1	no	—
513	C₂×C₄	—	10	1	no	—
514	C₂×C₄	—	10	4	no	—
515	C₂×C₄	—	10	2	no	—
516	C₂×C₄	—	40	2	no	—
517	C₂×C₄	—	40	2	no	—
518	C₂×C₄	—	40	1	no	—
519	C₂×C₄	C₂×C₃×C₄×D₅	1	2	yes	—
520	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
521	C₂×C₄	C₃×#711	1	2	yes	—
522	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
523	C₈	—	2	2	no	—
524	C₈	—	5	2	no	—
525	C₈	—	5	2	no	—
526	C₂×C₃	—	2	2	no	—
527	C₂×C₃	—	4	2	no	—
528	C₂×C₃	—	20	2	no	—
529	C₂×C₃	C₂×#4027	1	1	yes	characteristic
530	C₂×C₃	#66109	1	1	yes	characteristic
531	C₂×C₃	#66112	1	1	yes	characteristic
532	C₅	C₃×#2952	1	1	yes	characteristic, complemented, Sylow
533	C₂²	—	2	1	no	—
534	C₂²	—	2	1	no	—
535	C₂²	—	2	2	no	—
536	C₂²	—	4	1	no	—
537	C₂²	—	4	1	no	—
538	C₂²	—	10	2	no	—
539	C₂²	—	20	1	no	—
540	C₂²	—	20	1	no	—
541	C₂²	C₃×#4027	1	2	yes	—
542	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
543	C₄	—	2	2	no	—
544	C₄	—	4	2	no	—
545	C₄	—	10	2	no	—
546	C₄	—	10	2	no	—
547	C₄	—	10	2	no	—
548	C₄	—	20	2	no	—
549	C₄	C₃×#4027	1	2	yes	—
550	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
551	C₄	C₂×C₃×#711	1	1	yes	characteristic
552	C₃	#10610600	1	1	yes	characteristic, direct product factor, Sylow
553	C₂	—	2	2	no	—
554	C₂	—	4	2	no	—
555	C₂	—	20	2	no	—
556	C₂	C₂×C₃×#4027	1	1	yes	characteristic
557	C₂	C₃×#66109	1	1	yes	characteristic
558	C₂	C₃×#66112	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×C₅×#417	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4096	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#417	D₅
hypocenter	C₅	C₃×#2952
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#417

Complements

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

N	H ≅ G/N	type
1. C₃×#66161	C₂	semidirect
3. C₃×#65838	C₂	semidirect
4. C₃×C₅×#417	C₂	semidirect
5. C₃×#65422	C₂	semidirect
6. C₃×#65411	C₂	semidirect
7. C₂×C₃×#3940	C₂	semidirect
8. C₃×#65078	C₂	semidirect
9. C₃×#65077	C₂	semidirect
10. C₃×#65074	C₂	semidirect
11. C₃×#65047	C₂	semidirect
12. #10610600	C₃	direct (N × H)
17. C₃×#4096	C₄	semidirect
44. #66161	C₂×C₃	semidirect
46. #65838	C₂×C₃	semidirect
47. C₅×#417	C₂×C₃	semidirect
48. #65422	C₂×C₃	semidirect
49. #65411	C₂×C₃	semidirect
50. C₂×#3940	C₂×C₃	semidirect
51. #65078	C₂×C₃	semidirect
52. #65077	C₂×C₃	semidirect
53. #65074	C₂×C₃	semidirect
54. #65047	C₂×C₃	semidirect
56. C₃×C₅×#41	C₂×C₄	semidirect
67. C₃×#709	C₂×C₄	semidirect
78. C₃×#689	C₂×C₄	semidirect
79. C₃×#688	C₂×C₄	semidirect
80. C₃×#687	C₂×C₄	semidirect
81. C₃×#686	C₂×C₄	semidirect
92. C₂×C₃×#168	C₂×C₄	semidirect
104. C₃×#417	D₅	semidirect
110. #4096	C₃×C₄	semidirect
200. C₅×#41	C₂×C₃×C₄	semidirect
211. #709	C₂×C₃×C₄	semidirect
222. #689	C₂×C₃×C₄	semidirect
223. #688	C₂×C₃×C₄	semidirect
224. #687	C₂×C₃×C₄	semidirect
225. #686	C₂×C₃×C₄	semidirect
236. C₂×#168	C₂×C₃×C₄	semidirect
248. #417	C₃×D₅	semidirect
272. C₃×#41	C₄×D₅	semidirect
431. #41	C₃×C₄×D₅	semidirect
468. C₃×C₅	#2952	semidirect
532. C₅	C₃×#2952	semidirect
552. C₃	#10610600	direct (N × H)

Maximal subgroups

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

subgroup	index
C₃×#66161	2
C₂×C₃×#4096	2
C₃×#65838	2
C₃×C₅×#417	2
C₃×#65422	2
C₃×#65411	2
C₂×C₃×#3940	2
C₃×#65078	2
C₃×#65077	2
C₃×#65074	2
C₃×#65047	2
#10610600	3
C₃×#2952	5

Subgroups — C3×#10610600 #14417723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610600 #14417723