Subgroups — C₃×#10610556 #14437777

Order 1920.

800 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66166	C₂	1	1	yes	maximal, characteristic
2	C₃×#65851	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#416	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65522	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65402	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₈×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65291	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65089	C₂	1	2	yes	maximal, complemented
9	C₃×#65081	C₂	1	2	yes	maximal, complemented
10	C₃×#65057	C₂	1	2	yes	maximal, complemented
11	C₃×#65049	C₂	1	2	yes	maximal, complemented
12	#10610556	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	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
16	C₃×C₅×#117	C₂²	1	1	yes	characteristic
17	C₃×#4093	C₂²	1	1	yes	characteristic
18	C₃×#4090	C₂²	1	1	yes	characteristic
19	C₃×#4086	C₂²	1	1	yes	characteristic
20	C₃×#4085	—	2	2	no	—
21	C₃×#4082	C₂²	1	1	yes	characteristic
22	C₃×C₄×C₂²⋊D₅	—	2	2	no	—
23	C₃×#4072	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
25	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
26	C₃×#4036	C₂²	1	2	yes	—
27	C₃×#4034	C₂²	1	2	yes	—
28	C₃×#4024	—	2	2	no	—
29	C₃×C₄×Dic₁₀	—	2	2	no	—
30	C₃×C₅×#103	C₂²	1	2	yes	—
31	C₃×C₅×#102	C₂²	1	2	yes	—
32	C₃×#3967	C₂²	1	2	yes	—
33	C₃×#3964	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3948	C₂²	1	2	yes	—
36	C₃×C₈×Dic₅	C₂²	1	2	yes	—
37	C₃×C₈×Dic₅	C₂²	1	2	yes	—
38	C₃×#3942	C₂²	1	2	yes	—
39	C₃×#3941	C₂²	1	2	yes	—
40	C₃×#3131	—	5	1	no	maximal, Hall
41	#66166	C₂×C₃	1	1	yes	characteristic
42	#65851	C₂×C₃	1	1	yes	characteristic, complemented
43	C₅×#416	C₂×C₃	1	1	yes	characteristic, complemented
44	#65522	C₂×C₃	1	1	yes	characteristic, complemented
45	#65402	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₈×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
47	#65291	C₂×C₃	1	1	yes	characteristic, complemented
48	#65089	C₂×C₃	1	2	yes	complemented
49	#65081	C₂×C₃	1	2	yes	complemented
50	#65057	C₂×C₃	1	2	yes	complemented
51	#65049	C₂×C₃	1	2	yes	complemented
52	C₃×C₅×#41	—	2	2	no	—
53	C₃×C₅×#41	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×D₄	—	2	1	no	—
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	—	2	1	no	—
58	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
59	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
60	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
61	C₂²×C₃×Dic₅	D₄	1	2	yes	—
62	C₃×#709	—	2	2	no	—
63	C₃×#709	—	2	2	no	—
64	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₄×D₅	—	2	1	no	—
66	C₂×C₃×Dic₁₀	—	2	2	no	—
67	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₅×C₈	—	2	2	no	—
69	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
71	C₃×C₅×C₂²⋊C₄	—	2	1	no	—
72	C₃×C₄²×C₅	—	2	1	no	—
73	C₃×C₂²⋊Dic₅	—	2	1	no	—
74	C₃×C₂²⋊Dic₅	—	2	2	no	—
75	C₃×#685	—	2	2	no	—
76	C₃×C₄⋊Dic₅	—	2	2	no	—
77	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
78	C₃×#683	—	2	2	no	—
79	C₃×#683	—	2	2	no	—
80	C₃×#683	—	2	2	no	—
81	C₃×C₄×Dic₅	—	2	1	no	—
82	C₃×C₄×Dic₅	D₄	1	2	yes	—
83	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
84	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
85	C₂×C₃×#168	—	2	2	no	—
86	C₂×C₃×#168	C₂³	1	2	yes	—
87	C₃×#533	—	5	1	no	—
88	C₃×#532	—	5	1	no	—
89	C₃×#488	—	5	2	no	—
90	C₃×#488	—	5	2	no	—
91	C₃×#487	—	5	2	no	—
92	C₃×#486	—	5	2	no	—
93	C₃×#416	—	5	1	no	—
94	C₃×#416	—	5	1	no	—
95	C₃×#416	—	5	1	no	—
96	C₃×#416	D₅	1	1	yes	characteristic, complemented
97	C₂×C₃×C₄×C₈	—	5	1	no	—
98	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
99	C₂×#709	C₂²×C₃	1	1	yes	characteristic
100	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
101	C₅×#117	C₂²×C₃	1	1	yes	characteristic
102	#4093	C₂²×C₃	1	1	yes	characteristic
103	#4090	C₂²×C₃	1	1	yes	characteristic
104	#4086	C₂²×C₃	1	1	yes	characteristic
105	#4085	—	2	2	no	—
106	#4082	C₂²×C₃	1	1	yes	characteristic
107	C₄×C₂²⋊D₅	—	2	2	no	—
108	#4072	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
110	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
111	#4036	C₂²×C₃	1	2	yes	—
112	#4034	C₂²×C₃	1	2	yes	—
113	#4024	—	2	2	no	—
114	C₄×Dic₁₀	—	2	2	no	—
115	C₅×#103	C₂²×C₃	1	2	yes	—
116	C₅×#102	C₂²×C₃	1	2	yes	—
117	#3967	C₂²×C₃	1	2	yes	—
118	#3964	C₂²×C₃	1	2	yes	—
119	#3953	C₂²×C₃	1	2	yes	—
120	#3948	C₂²×C₃	1	2	yes	—
121	C₈×Dic₅	C₂²×C₃	1	2	yes	—
122	C₈×Dic₅	C₂²×C₃	1	2	yes	—
123	#3942	C₂²×C₃	1	2	yes	—
124	#3941	C₂²×C₃	1	2	yes	—
125	#3131	—	5	1	no	Sylow
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
128	C₂²×C₃×D₅	—	2	1	no	—
129	C₃×C₅×Q₈	—	2	1	no	—
130	C₃×C₅×Q₈	—	2	1	no	—
131	C₃×C₅×D₄	—	2	1	no	—
132	C₃×C₅×D₄	—	2	1	no	—
133	C₃×C₅×D₄	—	4	2	no	—
134	C₂×C₃×C₄×C₅	—	2	2	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	4	2	no	—
137	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
138	C₂×C₃×C₄×C₅	#41	1	2	yes	—
139	C₂×C₃×C₄×C₅	#41	1	2	yes	—
140	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
141	C₃×C₂²⋊D₅	—	4	2	no	—
142	C₃×C₂²⋊D₅	—	4	4	no	—
143	C₂×C₃×Dic₅	—	2	4	no	—
144	C₂×C₃×Dic₅	—	2	2	no	—
145	C₂×C₃×Dic₅	—	2	1	no	—
146	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
147	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
148	C₃×D₂₀	—	2	1	no	—
149	C₃×D₂₀	—	2	1	no	—
150	C₃×C₄×D₅	—	4	2	no	—
151	C₃×Dic₁₀	—	2	1	no	—
152	C₃×Dic₁₀	—	2	1	no	—
153	C₃×Dic₁₀	—	4	4	no	—
154	C₃×C₅×C₈	—	2	2	no	—
155	C₃×#168	—	2	2	no	—
156	C₂×C₃×#41	—	5	1	no	—
157	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
158	C₂²×C₃×C₈	—	5	1	no	—
159	C₂²×C₃×C₈	C₂×D₅	1	1	yes	characteristic
160	C₃×C₄⋊Q₈	—	5	2	no	—
161	C₃×C₄⋊Q₈	—	5	1	no	—
162	C₃×#127	—	5	1	no	—
163	C₃×#125	—	5	2	no	—
164	C₃×#124	—	5	1	no	—
165	C₃×#124	—	5	1	no	—
166	C₃×C₂²⋊Q₈	—	10	2	no	—
167	C₃×#121	—	10	2	no	—
168	C₃×C₄×Q₈	—	10	2	no	—
169	C₃×C₄×D₄	—	10	2	no	—
170	C₃×#117	—	5	1	no	—
171	C₃×#117	C₂×D₅	1	1	yes	characteristic
172	C₂×C₃×C₄²	—	5	1	no	—
173	C₃×#103	—	5	2	no	—
174	C₃×#103	—	5	2	no	—
175	C₃×#103	—	5	2	no	—
176	C₃×#103	C₂×D₅	1	2	yes	—
177	C₃×#102	—	5	2	no	—
178	C₃×#102	—	5	2	no	—
179	C₃×#102	—	5	2	no	—
180	C₃×#102	C₂×D₅	1	2	yes	—
181	C₃×C₄×C₈	—	5	2	no	—
182	C₃×C₄×C₈	—	5	2	no	—
183	C₅×#41	—	2	2	no	—
184	C₅×#41	—	2	2	no	—
185	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
186	C₂×C₅×D₄	—	2	1	no	—
187	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
188	C₂²×C₄×C₅	—	2	1	no	—
189	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₂²⋊D₅	—	2	1	no	—
191	C₂×C₂²⋊D₅	—	2	2	no	—
192	C₂²×Dic₅	C₃×D₄	1	2	yes	—
193	#709	—	2	2	no	—
194	#709	—	2	2	no	—
195	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₄×D₅	—	2	1	no	—
197	C₂×Dic₁₀	—	2	2	no	—
198	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₅×C₈	—	2	2	no	—
200	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
201	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
202	C₅×C₂²⋊C₄	—	2	1	no	—
203	C₄²×C₅	—	2	1	no	—
204	C₂²⋊Dic₅	—	2	1	no	—
205	C₂²⋊Dic₅	—	2	2	no	—
206	#685	—	2	2	no	—
207	C₄⋊Dic₅	—	2	2	no	—
208	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
209	#683	—	2	2	no	—
210	#683	—	2	2	no	—
211	#683	—	2	2	no	—
212	C₄×Dic₅	—	2	1	no	—
213	C₄×Dic₅	C₃×D₄	1	2	yes	—
214	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
215	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
216	C₂×#168	—	2	2	no	—
217	C₂×#168	C₂³×C₃	1	2	yes	—
218	#533	—	5	1	no	—
219	#532	—	5	1	no	—
220	#488	—	5	2	no	—
221	#488	—	5	2	no	—
222	#487	—	5	2	no	—
223	#486	—	5	2	no	—
224	#416	—	5	1	no	—
225	#416	—	5	1	no	—
226	#416	—	5	1	no	—
227	#416	C₃×D₅	1	1	yes	characteristic, complemented
228	C₂×C₄×C₈	—	5	1	no	—
229	C₂²×C₃×C₅	—	2	2	no	—
230	C₂²×C₃×C₅	—	4	1	no	—
231	C₂²×C₃×C₅	—	4	2	no	—
232	C₂²×C₃×C₅	#124	1	2	yes	—
233	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
234	C₂×C₃×D₅	—	4	1	no	—
235	C₂×C₃×D₅	—	4	2	no	—
236	C₃×C₄×C₅	—	4	1	no	—
237	C₃×C₄×C₅	—	4	2	no	—
238	C₃×C₄×C₅	#124	1	2	yes	—
239	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
240	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
241	C₃×Dic₅	—	2	2	no	—
242	C₃×Dic₅	—	4	1	no	—
243	C₃×Dic₅	—	4	2	no	—
244	C₃×Dic₅	#135	1	4	yes	—
245	C₃×#41	—	2	2	no	—
246	C₃×#41	—	2	2	no	—
247	C₃×#41	—	10	2	no	—
248	C₃×#41	—	10	2	no	—
249	C₂×C₃×Q₈	—	5	1	no	—
250	C₂×C₃×Q₈	—	10	2	no	—
251	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
252	C₂×C₃×D₄	—	2	1	no	—
253	C₂×C₃×D₄	—	5	1	no	—
254	C₂×C₃×D₄	—	10	2	no	—
255	C₂×C₃×D₄	—	10	1	no	—
256	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
257	C₂²×C₃×C₄	—	2	1	no	—
258	C₂²×C₃×C₄	—	5	2	no	—
259	C₂²×C₃×C₄	—	10	1	no	—
260	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
261	C₂×C₃×C₈	—	2	2	no	—
262	C₂×C₃×C₈	—	5	2	no	—
263	C₂×C₃×C₈	—	10	2	no	—
264	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
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	—	10	2	no	—
269	C₃×C₄⋊C₄	—	10	2	no	—
270	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
271	C₃×C₂²⋊C₄	—	2	1	no	—
272	C₃×C₂²⋊C₄	—	10	2	no	—
273	C₃×C₂²⋊C₄	—	10	2	no	—
274	C₃×C₂²⋊C₄	—	10	1	no	—
275	C₃×C₄²	—	2	1	no	—
276	C₃×C₄²	—	5	2	no	—
277	C₃×C₄²	—	5	1	no	—
278	C₃×C₄²	—	5	1	no	—
279	C₃×C₄²	—	10	1	no	—
280	C₂³×C₅	—	2	1	no	—
281	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
282	C₂²×D₅	—	2	1	no	—
283	C₅×Q₈	—	2	1	no	—
284	C₅×Q₈	—	2	1	no	—
285	C₅×D₄	—	2	1	no	—
286	C₅×D₄	—	2	1	no	—
287	C₅×D₄	—	4	2	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	1	no	—
290	C₂×C₄×C₅	—	4	2	no	—
291	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
292	C₂×C₄×C₅	C₃×#41	1	2	yes	—
293	C₂×C₄×C₅	C₃×#41	1	2	yes	—
294	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
295	C₂²⋊D₅	—	4	2	no	—
296	C₂²⋊D₅	—	4	4	no	—
297	C₂×Dic₅	—	2	4	no	—
298	C₂×Dic₅	—	2	2	no	—
299	C₂×Dic₅	—	2	1	no	—
300	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
301	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
302	D₂₀	—	2	1	no	—
303	D₂₀	—	2	1	no	—
304	C₄×D₅	—	4	2	no	—
305	Dic₁₀	—	2	1	no	—
306	Dic₁₀	—	2	1	no	—
307	Dic₁₀	—	4	4	no	—
308	C₅×C₈	—	2	2	no	—
309	#168	—	2	2	no	—
310	C₂×#41	—	5	1	no	—
311	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
312	C₂²×C₈	—	5	1	no	—
313	C₂²×C₈	C₂×C₃×D₅	1	1	yes	characteristic
314	C₄⋊Q₈	—	5	2	no	—
315	C₄⋊Q₈	—	5	1	no	—
316	#127	—	5	1	no	—
317	#125	—	5	2	no	—
318	#124	—	5	1	no	—
319	#124	—	5	1	no	—
320	C₂²⋊Q₈	—	10	2	no	—
321	#121	—	10	2	no	—
322	C₄×Q₈	—	10	2	no	—
323	C₄×D₄	—	10	2	no	—
324	#117	—	5	1	no	—
325	#117	C₂×C₃×D₅	1	1	yes	characteristic
326	C₂×C₄²	—	5	1	no	—
327	#103	—	5	2	no	—
328	#103	—	5	2	no	—
329	#103	—	5	2	no	—
330	#103	C₂×C₃×D₅	1	2	yes	—
331	#102	—	5	2	no	—
332	#102	—	5	2	no	—
333	#102	—	5	2	no	—
334	#102	C₂×C₃×D₅	1	2	yes	—
335	C₄×C₈	—	5	2	no	—
336	C₄×C₈	—	5	2	no	—
337	C₂×C₃×C₅	—	2	2	no	—
338	C₂×C₃×C₅	—	8	1	no	—
339	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
340	C₂×C₃×C₅	C₂×#135	1	2	yes	—
341	C₃×D₅	—	8	1	no	—
342	C₂³×C₃	—	2	1	no	—
343	C₂³×C₃	—	10	1	no	—
344	C₂³×C₃	D₄×D₅	1	1	yes	characteristic
345	C₃×Q₈	—	2	1	no	—
346	C₃×Q₈	—	2	1	no	—
347	C₃×Q₈	—	10	1	no	—
348	C₃×Q₈	—	10	1	no	—
349	C₃×Q₈	—	20	4	no	—
350	C₃×D₄	—	2	1	no	—
351	C₃×D₄	—	2	1	no	—
352	C₃×D₄	—	4	2	no	—
353	C₃×D₄	—	10	1	no	—
354	C₃×D₄	—	10	1	no	—
355	C₃×D₄	—	20	4	no	—
356	C₃×D₄	—	20	2	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	4	2	no	—
360	C₂×C₃×C₄	—	5	2	no	—
361	C₂×C₃×C₄	—	5	2	no	—
362	C₂×C₃×C₄	—	10	4	no	—
363	C₂×C₃×C₄	—	10	2	no	—
364	C₂×C₃×C₄	—	10	1	no	—
365	C₂×C₃×C₄	—	20	2	no	—
366	C₂×C₃×C₄	#709	1	2	yes	—
367	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
368	C₂×C₃×C₄	#711	1	2	yes	—
369	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
370	C₃×C₈	—	2	2	no	—
371	C₃×C₈	—	10	2	no	—
372	C₂²×C₅	—	2	2	no	—
373	C₂²×C₅	—	4	2	no	—
374	C₂²×C₅	—	4	1	no	—
375	C₂²×C₅	C₃×#124	1	2	yes	—
376	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
377	C₂×D₅	—	4	2	no	—
378	C₂×D₅	—	4	1	no	—
379	C₄×C₅	—	4	2	no	—
380	C₄×C₅	—	4	1	no	—
381	C₄×C₅	C₃×#124	1	2	yes	—
382	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
383	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
384	Dic₅	—	2	2	no	—
385	Dic₅	—	4	2	no	—
386	Dic₅	—	4	1	no	—
387	Dic₅	C₃×#135	1	4	yes	—
388	#41	—	2	2	no	—
389	#41	—	2	2	no	—
390	#41	—	10	2	no	—
391	#41	—	10	2	no	—
392	C₂×Q₈	—	5	1	no	—
393	C₂×Q₈	—	10	2	no	—
394	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
395	C₂×D₄	—	2	1	no	—
396	C₂×D₄	—	5	1	no	—
397	C₂×D₄	—	10	2	no	—
398	C₂×D₄	—	10	1	no	—
399	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
400	C₂²×C₄	—	2	1	no	—
401	C₂²×C₄	—	5	2	no	—
402	C₂²×C₄	—	10	1	no	—
403	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
404	C₂×C₈	—	2	2	no	—
405	C₂×C₈	—	5	2	no	—
406	C₂×C₈	—	10	2	no	—
407	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
408	C₄⋊C₄	—	5	2	no	—
409	C₄⋊C₄	—	10	2	no	—
410	C₄⋊C₄	—	10	2	no	—
411	C₄⋊C₄	—	10	2	no	—
412	C₄⋊C₄	—	10	2	no	—
413	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
414	C₂²⋊C₄	—	2	1	no	—
415	C₂²⋊C₄	—	10	2	no	—
416	C₂²⋊C₄	—	10	2	no	—
417	C₂²⋊C₄	—	10	1	no	—
418	C₄²	—	2	1	no	—
419	C₄²	—	5	2	no	—
420	C₄²	—	5	1	no	—
421	C₄²	—	5	1	no	—
422	C₄²	—	10	1	no	—
423	C₃×C₅	#3131	1	1	yes	characteristic, complemented, Hall
424	C₂²×C₃	—	2	2	no	—
425	C₂²×C₃	—	4	1	no	—
426	C₂²×C₃	—	4	2	no	—
427	C₂²×C₃	—	20	1	no	—
428	C₂²×C₃	—	20	2	no	—
429	C₂²×C₃	#4031	1	2	yes	—
430	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
431	C₃×C₄	—	4	1	no	—
432	C₃×C₄	—	4	2	no	—
433	C₃×C₄	—	5	4	no	—
434	C₃×C₄	—	10	2	no	—
435	C₃×C₄	—	20	1	no	—
436	C₃×C₄	—	20	2	no	—
437	C₃×C₄	#4031	1	2	yes	—
438	C₃×C₄	C₂×#709	1	1	yes	characteristic
439	C₃×C₄	C₂×#711	1	1	yes	characteristic
440	C₂×C₅	—	2	2	no	—
441	C₂×C₅	—	8	1	no	—
442	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
443	C₂×C₅	C₂×C₃×#135	1	2	yes	—
444	D₅	—	8	1	no	—
445	C₂³	—	2	1	no	—
446	C₂³	—	10	1	no	—
447	C₂³	C₃×D₄×D₅	1	1	yes	characteristic
448	Q₈	—	2	1	no	—
449	Q₈	—	2	1	no	—
450	Q₈	—	10	1	no	—
451	Q₈	—	10	1	no	—
452	Q₈	—	20	4	no	—
453	D₄	—	2	1	no	—
454	D₄	—	2	1	no	—
455	D₄	—	4	2	no	—
456	D₄	—	10	1	no	—
457	D₄	—	10	1	no	—
458	D₄	—	20	4	no	—
459	D₄	—	20	2	no	—
460	C₂×C₄	—	2	2	no	—
461	C₂×C₄	—	2	1	no	—
462	C₂×C₄	—	4	2	no	—
463	C₂×C₄	—	5	2	no	—
464	C₂×C₄	—	5	2	no	—
465	C₂×C₄	—	10	4	no	—
466	C₂×C₄	—	10	2	no	—
467	C₂×C₄	—	10	1	no	—
468	C₂×C₄	—	20	2	no	—
469	C₂×C₄	C₃×#709	1	2	yes	—
470	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
471	C₂×C₄	C₃×#711	1	2	yes	—
472	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
473	C₈	—	2	2	no	—
474	C₈	—	10	2	no	—
475	C₂×C₃	—	2	2	no	—
476	C₂×C₃	—	8	1	no	—
477	C₂×C₃	—	40	1	no	—
478	C₂×C₃	C₂×#4031	1	1	yes	characteristic
479	C₂×C₃	D₅×#135	1	2	yes	—
480	C₅	C₃×#3131	1	1	yes	characteristic, complemented, Sylow
481	C₂²	—	2	2	no	—
482	C₂²	—	4	2	no	—
483	C₂²	—	4	1	no	—
484	C₂²	—	20	2	no	—
485	C₂²	—	20	1	no	—
486	C₂²	C₃×#4031	1	2	yes	—
487	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
488	C₄	—	4	2	no	—
489	C₄	—	4	1	no	—
490	C₄	—	5	4	no	—
491	C₄	—	10	2	no	—
492	C₄	—	20	2	no	—
493	C₄	—	20	1	no	—
494	C₄	C₃×#4031	1	2	yes	—
495	C₄	C₂×C₃×#709	1	1	yes	characteristic
496	C₄	C₂×C₃×#711	1	1	yes	characteristic
497	C₃	#10610556	1	1	yes	characteristic, direct product factor, Sylow
498	C₂	—	2	2	no	—
499	C₂	—	8	1	no	—
500	C₂	—	40	1	no	—
501	C₂	C₂×C₃×#4031	1	1	yes	characteristic
502	C₂	C₃×D₅×#135	1	2	yes	—

	subgroup	G/H
center	C₂×C₃×C₄	D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#416	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66166	C₂
hypercenter	C₃×#416	D₅
hypocenter	C₅	C₃×#3131
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃×C₄ ◁ C₂²×C₃×C₄ ◁ C₃×#416

Complements

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

N	H ≅ G/N	type
2. C₃×#65851	C₂	semidirect
3. C₃×C₅×#416	C₂	semidirect
4. C₃×#65522	C₂	semidirect
5. C₃×#65402	C₂	semidirect
6. C₂×C₃×C₈×Dic₅	C₂	semidirect
7. C₃×#65291	C₂	semidirect
8. C₃×#65089	C₂	semidirect
9. C₃×#65081	C₂	semidirect
10. C₃×#65057	C₂	semidirect
11. C₃×#65049	C₂	semidirect
12. #10610556	C₃	direct (N × H)
42. #65851	C₂×C₃	semidirect
43. C₅×#416	C₂×C₃	semidirect
44. #65522	C₂×C₃	semidirect
45. #65402	C₂×C₃	semidirect
46. C₂×C₈×Dic₅	C₂×C₃	semidirect
47. #65291	C₂×C₃	semidirect
48. #65089	C₂×C₃	semidirect
49. #65081	C₂×C₃	semidirect
50. #65057	C₂×C₃	semidirect
51. #65049	C₂×C₃	semidirect
96. C₃×#416	D₅	semidirect
227. #416	C₃×D₅	semidirect
423. C₃×C₅	#3131	semidirect
480. C₅	C₃×#3131	semidirect
497. C₃	#10610556	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×#66166	2
C₃×#65851	2
C₃×C₅×#416	2
C₃×#65522	2
C₃×#65402	2
C₂×C₃×C₈×Dic₅	2
C₃×#65291	2
C₃×#65089	2
C₃×#65081	2
C₃×#65057	2
C₃×#65049	2
#10610556	3
C₃×#3131	5

Subgroups — C3×#10610556 #14437777

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10610556 #14437777