Subgroups — C₃×#10615404 #14460250

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 512 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#556	C₂	1	1	yes	maximal, characteristic, complemented
2	C₃×#65887	C₂	1	1	yes	maximal, characteristic
3	C₃×#65383	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65377	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65337	C₂	1	2	yes	maximal, complemented
6	C₃×#65336	C₂	1	2	yes	maximal, complemented
7	C₃×C₄×#689	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65316	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×D₄×#168	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65292	C₂	1	2	yes	maximal, complemented
11	C₃×#65291	C₂	1	2	yes	maximal, complemented
12	#10615404	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#709	C₂²	1	2	yes	—
14	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×#126	—	2	2	no	—
16	C₃×C₅×#124	—	2	1	no	—
17	C₃×C₅×C₂²⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₄×C₅×Q₈	—	2	1	no	—
19	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
20	C₃×C₄×C₅×D₄	C₂²	1	1	yes	characteristic
21	C₃×C₅×#117	C₂²	1	2	yes	—
22	C₂×C₃×#689	C₂²	1	1	yes	characteristic
23	C₂×C₃×#688	C₂²	1	2	yes	—
24	C₃×#4086	—	2	1	no	—
25	C₃×#4076	C₂²	1	2	yes	—
26	C₂²×C₃×#168	C₂²	1	2	yes	—
27	C₃×#4039	—	2	1	no	—
28	C₃×#4030	—	2	2	no	—
29	C₃×#4020	C₂²	1	1	yes	characteristic
30	C₃×C₄×Dic₁₀	C₂²	1	1	yes	characteristic
31	C₃×#3967	C₂²	1	1	yes	characteristic
32	C₃×C₂²⋊#168	C₂²	1	2	yes	—
33	C₃×#3942	C₂²	1	1	yes	characteristic
34	C₃×#3942	C₂²	1	2	yes	—
35	C₃×#3941	C₂²	1	2	yes	—
36	C₃×#3941	C₂²	1	2	yes	—
37	C₃×#3941	C₂²	1	2	yes	—
38	C₃×#3940	C₂²	1	2	yes	—
39	C₃×#3939	C₂²	1	1	yes	characteristic
40	C₃×C₄⋊#168	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3304	—	5	1	no	maximal, Hall
43	C₅×#556	C₂×C₃	1	1	yes	characteristic, complemented
44	#65887	C₂×C₃	1	1	yes	characteristic
45	#65383	C₂×C₃	1	1	yes	characteristic, complemented
46	#65377	C₂×C₃	1	1	yes	characteristic, complemented
47	#65337	C₂×C₃	1	2	yes	complemented
48	#65336	C₂×C₃	1	2	yes	complemented
49	C₄×#689	C₂×C₃	1	1	yes	characteristic, complemented
50	#65316	C₂×C₃	1	1	yes	characteristic, complemented
51	D₄×#168	C₂×C₃	1	1	yes	characteristic, complemented
52	#65292	C₂×C₃	1	2	yes	complemented
53	#65291	C₂×C₃	1	2	yes	complemented
54	C₂×C₃×C₅×Q₈	—	2	1	no	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
60	C₃×#709	—	2	4	no	—
61	C₃×#709	—	4	2	no	—
62	C₂×C₃×D₂₀	—	2	1	no	—
63	C₂×C₃×D₂₀	—	2	1	no	—
64	C₂×C₃×D₂₀	C₂³	1	2	yes	—
65	C₂×C₃×C₄×D₅	—	2	2	no	—
66	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	2	no	—
68	C₃×C₅×C₄⋊C₄	—	2	1	no	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	D₄	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
74	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
75	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
76	C₃×C₄²×C₅	—	2	2	no	—
77	C₃×C₄²×C₅	—	2	1	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₃×#689	—	2	2	no	—
80	C₃×#688	—	4	2	no	—
81	C₃×#685	—	2	2	no	—
82	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
83	C₃×#683	—	2	1	no	—
84	C₃×C₄×Dic₅	—	2	1	no	—
85	C₂×C₃×#168	—	4	2	no	—
86	C₂×C₃×#168	C₂³	1	2	yes	—
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₂×C₃×#168	C₂³	1	1	yes	characteristic
89	C₃×#556	D₅	1	1	yes	characteristic, complemented
90	C₃×#550	—	5	1	no	—
91	C₃×#486	—	5	1	no	—
92	C₃×#482	—	5	2	no	—
93	C₃×#475	—	5	1	no	—
94	C₃×#465	—	5	2	no	—
95	C₃×#460	—	5	1	no	—
96	C₃×#452	—	5	2	no	—
97	C₃×C₄×Q₁₆	—	5	1	no	—
98	C₃×C₈×D₄	—	5	1	no	—
99	C₃×#416	—	5	2	no	—
100	C₂×#709	C₂²×C₃	1	2	yes	—
101	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
102	C₅×#126	—	2	2	no	—
103	C₅×#124	—	2	1	no	—
104	C₅×C₂²⋊Q₈	C₂²×C₃	1	2	yes	—
105	C₄×C₅×Q₈	—	2	1	no	—
106	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
107	C₄×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
108	C₅×#117	C₂²×C₃	1	2	yes	—
109	C₂×#689	C₂²×C₃	1	1	yes	characteristic
110	C₂×#688	C₂²×C₃	1	2	yes	—
111	#4086	—	2	1	no	—
112	#4076	C₂²×C₃	1	2	yes	—
113	C₂²×#168	C₂²×C₃	1	2	yes	—
114	#4039	—	2	1	no	—
115	#4030	—	2	2	no	—
116	#4020	C₂²×C₃	1	1	yes	characteristic
117	C₄×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
118	#3967	C₂²×C₃	1	1	yes	characteristic
119	C₂²⋊#168	C₂²×C₃	1	2	yes	—
120	#3942	C₂²×C₃	1	1	yes	characteristic
121	#3942	C₂²×C₃	1	2	yes	—
122	#3941	C₂²×C₃	1	2	yes	—
123	#3941	C₂²×C₃	1	2	yes	—
124	#3941	C₂²×C₃	1	2	yes	—
125	#3940	C₂²×C₃	1	2	yes	—
126	#3939	C₂²×C₃	1	1	yes	characteristic
127	C₄⋊#168	C₂²×C₃	1	1	yes	characteristic
128	C₄×#168	C₂²×C₃	1	1	yes	characteristic
129	#3304	—	5	1	no	Sylow
130	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
131	C₂²×C₃×D₅	—	2	2	no	—
132	C₃×C₅×Q₈	—	2	1	no	—
133	C₃×C₅×Q₈	—	2	1	no	—
134	C₃×C₅×Q₈	—	4	2	no	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
142	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₃×C₂²⋊D₅	—	4	4	no	—
146	C₃×C₂²⋊D₅	—	8	2	no	—
147	C₂×C₃×Dic₅	—	2	1	no	—
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₃×D₂₀	—	2	2	no	—
150	C₃×D₂₀	—	2	2	no	—
151	C₃×D₂₀	—	4	2	no	—
152	C₃×D₂₀	—	8	1	no	—
153	C₃×C₄×D₅	—	4	4	no	—
154	C₃×Dic₁₀	—	2	1	no	—
155	C₃×Dic₁₀	#41	1	2	yes	—
156	C₃×#168	—	2	1	no	—
157	C₃×#168	—	2	1	no	—
158	C₃×#168	—	2	2	no	—
159	C₂×C₃×#41	—	5	2	no	—
160	C₂×C₃×Q₁₆	—	5	1	no	—
161	C₂×C₃×SD₁₆	—	5	2	no	—
162	C₂²×C₃×C₈	—	5	2	no	—
163	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
164	C₃×#127	—	5	1	no	—
165	C₃×#127	—	10	1	no	—
166	C₃×#126	—	2	2	no	—
167	C₃×#124	—	2	1	no	—
168	C₃×C₂²⋊Q₈	C₂×D₅	1	2	yes	—
169	C₃×#121	—	5	2	no	—
170	C₃×#121	—	10	2	no	—
171	C₃×C₄×Q₈	—	2	1	no	—
172	C₃×C₄×Q₈	—	5	1	no	—
173	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄×D₄	—	10	1	no	—
175	C₃×C₄×D₄	C₂×D₅	1	1	yes	characteristic
176	C₃×#117	C₂×D₅	1	2	yes	—
177	C₃×#107	—	5	1	no	—
178	C₃×#106	—	5	2	no	—
179	C₃×C₄⋊C₈	—	5	1	no	—
180	C₃×#103	—	5	1	no	—
181	C₃×#103	—	5	1	no	—
182	C₃×#103	—	5	2	no	—
183	C₃×#102	—	5	2	no	—
184	C₃×#102	—	5	2	no	—
185	C₃×#102	—	5	2	no	—
186	C₃×C₂²⋊C₈	—	5	2	no	—
187	C₃×C₄×C₈	—	5	1	no	—
188	C₂×C₅×Q₈	—	2	1	no	—
189	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
190	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
192	C₂×C₂²⋊D₅	—	2	2	no	—
193	C₂×C₂²⋊D₅	—	2	2	no	—
194	#709	—	2	4	no	—
195	#709	—	4	2	no	—
196	C₂×D₂₀	—	2	1	no	—
197	C₂×D₂₀	—	2	1	no	—
198	C₂×D₂₀	C₂³×C₃	1	2	yes	—
199	C₂×C₄×D₅	—	2	2	no	—
200	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
201	C₅×C₄⋊C₄	—	2	2	no	—
202	C₅×C₄⋊C₄	—	2	1	no	—
203	C₅×C₄⋊C₄	—	2	1	no	—
204	C₅×C₄⋊C₄	C₃×D₄	1	1	yes	characteristic
205	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
206	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
207	C₅×C₂²⋊C₄	—	2	2	no	—
208	C₅×C₂²⋊C₄	—	2	2	no	—
209	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
210	C₄²×C₅	—	2	2	no	—
211	C₄²×C₅	—	2	1	no	—
212	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
213	#689	—	2	2	no	—
214	#688	—	4	2	no	—
215	#685	—	2	2	no	—
216	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
217	#683	—	2	1	no	—
218	C₄×Dic₅	—	2	1	no	—
219	C₂×#168	—	4	2	no	—
220	C₂×#168	C₂³×C₃	1	1	yes	characteristic
221	C₂×#168	C₂³×C₃	1	1	yes	characteristic
222	C₂×#168	C₂³×C₃	1	2	yes	—
223	#556	C₃×D₅	1	1	yes	characteristic, complemented
224	#550	—	5	1	no	—
225	#486	—	5	1	no	—
226	#482	—	5	2	no	—
227	#475	—	5	1	no	—
228	#465	—	5	2	no	—
229	#460	—	5	1	no	—
230	#452	—	5	2	no	—
231	C₄×Q₁₆	—	5	1	no	—
232	C₈×D₄	—	5	1	no	—
233	#416	—	5	2	no	—
234	C₂²×C₃×C₅	—	2	2	no	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
238	C₂×C₃×D₅	—	4	2	no	—
239	C₂×C₃×D₅	—	4	2	no	—
240	C₂×C₃×D₅	—	4	2	no	—
241	C₃×C₄×C₅	—	2	2	no	—
242	C₃×C₄×C₅	—	2	1	no	—
243	C₃×C₄×C₅	—	4	1	no	—
244	C₃×C₄×C₅	—	4	2	no	—
245	C₃×C₄×C₅	—	4	1	no	—
246	C₃×C₄×C₅	#135	1	2	yes	—
247	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
248	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
249	C₃×Dic₅	—	2	2	no	—
250	C₃×Dic₅	—	4	1	no	—
251	C₃×#41	—	10	4	no	—
252	C₃×#41	—	20	2	no	—
253	C₂×C₃×Q₈	—	2	1	no	—
254	C₂×C₃×Q₈	—	5	1	no	—
255	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
256	C₂×C₃×D₄	—	5	2	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	1	no	—
261	C₂×C₃×D₄	C₂²⋊D₅	1	1	yes	characteristic
262	C₂²×C₃×C₄	—	10	2	no	—
263	C₂²×C₃×C₄	C₂²×D₅	1	2	yes	—
264	C₃×Q₁₆	—	10	2	no	—
265	C₃×SD₁₆	—	20	2	no	—
266	C₂×C₃×C₈	—	5	1	no	—
267	C₂×C₃×C₈	—	5	1	no	—
268	C₂×C₃×C₈	—	5	2	no	—
269	C₂×C₃×C₈	—	20	2	no	—
270	C₃×C₄⋊C₄	—	2	2	no	—
271	C₃×C₄⋊C₄	—	2	1	no	—
272	C₃×C₄⋊C₄	—	2	1	no	—
273	C₃×C₄⋊C₄	—	5	1	no	—
274	C₃×C₄⋊C₄	—	10	1	no	—
275	C₃×C₄⋊C₄	C₂²⋊D₅	1	1	yes	characteristic
276	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
277	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
278	C₃×C₂²⋊C₄	—	2	2	no	—
279	C₃×C₂²⋊C₄	—	2	2	no	—
280	C₃×C₂²⋊C₄	—	10	2	no	—
281	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
282	C₃×C₄²	—	2	2	no	—
283	C₃×C₄²	—	2	1	no	—
284	C₃×C₄²	—	10	1	no	—
285	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
286	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
287	C₂²×D₅	—	2	2	no	—
288	C₅×Q₈	—	2	1	no	—
289	C₅×Q₈	—	2	1	no	—
290	C₅×Q₈	—	4	2	no	—
291	C₅×D₄	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	1	no	—
296	C₂×C₄×C₅	—	2	2	no	—
297	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
299	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
301	C₂²⋊D₅	—	4	4	no	—
302	C₂²⋊D₅	—	8	2	no	—
303	C₂×Dic₅	—	2	1	no	—
304	C₂×Dic₅	—	2	1	no	—
305	D₂₀	—	2	2	no	—
306	D₂₀	—	2	2	no	—
307	D₂₀	—	4	2	no	—
308	D₂₀	—	8	1	no	—
309	C₄×D₅	—	4	4	no	—
310	Dic₁₀	—	2	1	no	—
311	Dic₁₀	C₃×#41	1	2	yes	—
312	#168	—	2	1	no	—
313	#168	—	2	1	no	—
314	#168	—	2	2	no	—
315	C₂×#41	—	5	2	no	—
316	C₂×Q₁₆	—	5	1	no	—
317	C₂×SD₁₆	—	5	2	no	—
318	C₂²×C₈	—	5	2	no	—
319	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
320	#127	—	5	1	no	—
321	#127	—	10	1	no	—
322	#126	—	2	2	no	—
323	#124	—	2	1	no	—
324	C₂²⋊Q₈	C₂×C₃×D₅	1	2	yes	—
325	#121	—	5	2	no	—
326	#121	—	10	2	no	—
327	C₄×Q₈	—	2	1	no	—
328	C₄×Q₈	—	5	1	no	—
329	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
330	C₄×D₄	—	10	1	no	—
331	C₄×D₄	C₂×C₃×D₅	1	1	yes	characteristic
332	#117	C₂×C₃×D₅	1	2	yes	—
333	#107	—	5	1	no	—
334	#106	—	5	2	no	—
335	C₄⋊C₈	—	5	1	no	—
336	#103	—	5	1	no	—
337	#103	—	5	1	no	—
338	#103	—	5	2	no	—
339	#102	—	5	2	no	—
340	#102	—	5	2	no	—
341	#102	—	5	2	no	—
342	C₂²⋊C₈	—	5	2	no	—
343	C₄×C₈	—	5	1	no	—
344	C₂×C₃×C₅	—	4	2	no	—
345	C₂×C₃×C₅	#546	1	1	yes	characteristic
346	C₂×C₃×C₅	C₂×#135	1	1	yes	characteristic
347	C₂×C₃×C₅	#577	1	1	yes	characteristic
348	C₃×D₅	—	8	2	no	—
349	C₂³×C₃	—	10	2	no	—
350	C₂³×C₃	C₂×C₂²⋊D₅	1	2	yes	—
351	C₃×Q₈	—	2	1	no	—
352	C₃×Q₈	—	2	1	no	—
353	C₃×Q₈	—	4	2	no	—
354	C₃×Q₈	—	5	2	no	—
355	C₃×Q₈	—	10	1	no	—
356	C₃×D₄	—	2	2	no	—
357	C₃×D₄	—	10	2	no	—
358	C₃×D₄	—	10	2	no	—
359	C₃×D₄	—	20	4	no	—
360	C₃×D₄	—	20	2	no	—
361	C₃×D₄	—	40	1	no	—
362	C₃×D₄	—	40	2	no	—
363	C₂×C₃×C₄	—	2	2	no	—
364	C₂×C₃×C₄	—	2	2	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	1	no	—
367	C₂×C₃×C₄	—	2	2	no	—
368	C₂×C₃×C₄	—	10	1	no	—
369	C₂×C₃×C₄	—	10	1	no	—
370	C₂×C₃×C₄	—	20	4	no	—
371	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
372	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
373	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
374	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
375	C₃×C₈	—	10	1	no	—
376	C₃×C₈	—	10	1	no	—
377	C₃×C₈	—	10	2	no	—
378	C₂²×C₅	—	2	2	no	—
379	C₂²×C₅	—	2	2	no	—
380	C₂²×C₅	—	2	2	no	—
381	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
382	C₂×D₅	—	4	2	no	—
383	C₂×D₅	—	4	2	no	—
384	C₂×D₅	—	4	2	no	—
385	C₄×C₅	—	2	1	no	—
386	C₄×C₅	—	2	2	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	—	4	1	no	—
389	C₄×C₅	—	4	1	no	—
390	C₄×C₅	C₃×#135	1	2	yes	—
391	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
392	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
393	Dic₅	—	2	2	no	—
394	Dic₅	—	4	1	no	—
395	#41	—	10	4	no	—
396	#41	—	20	2	no	—
397	C₂×Q₈	—	2	1	no	—
398	C₂×Q₈	—	5	1	no	—
399	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
400	C₂×D₄	—	5	2	no	—
401	C₂×D₄	—	10	2	no	—
402	C₂×D₄	—	10	2	no	—
403	C₂×D₄	—	10	1	no	—
404	C₂×D₄	—	10	1	no	—
405	C₂×D₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
406	C₂²×C₄	—	10	2	no	—
407	C₂²×C₄	C₂²×C₃×D₅	1	2	yes	—
408	Q₁₆	—	10	2	no	—
409	SD₁₆	—	20	2	no	—
410	C₂×C₈	—	5	1	no	—
411	C₂×C₈	—	5	1	no	—
412	C₂×C₈	—	5	2	no	—
413	C₂×C₈	—	20	2	no	—
414	C₄⋊C₄	—	2	2	no	—
415	C₄⋊C₄	—	2	1	no	—
416	C₄⋊C₄	—	2	1	no	—
417	C₄⋊C₄	—	5	1	no	—
418	C₄⋊C₄	—	10	1	no	—
419	C₄⋊C₄	C₃×C₂²⋊D₅	1	1	yes	characteristic
420	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
421	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
422	C₂²⋊C₄	—	2	2	no	—
423	C₂²⋊C₄	—	2	2	no	—
424	C₂²⋊C₄	—	10	2	no	—
425	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
426	C₄²	—	2	2	no	—
427	C₄²	—	2	1	no	—
428	C₄²	—	10	1	no	—
429	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
430	C₃×C₅	#3304	1	1	yes	characteristic, complemented, Hall
431	C₂²×C₃	—	2	2	no	—
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	20	2	no	—
435	C₂²×C₃	—	20	2	no	—
436	C₂²×C₃	—	20	2	no	—
437	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
438	C₃×C₄	—	2	2	no	—
439	C₃×C₄	—	2	1	no	—
440	C₃×C₄	—	4	2	no	—
441	C₃×C₄	—	4	1	no	—
442	C₃×C₄	—	4	1	no	—
443	C₃×C₄	—	10	2	no	—
444	C₃×C₄	—	20	1	no	—
445	C₃×C₄	#4096	1	2	yes	—
446	C₃×C₄	D₅×#41	1	1	yes	characteristic
447	C₃×C₄	#4149	1	1	yes	characteristic
448	C₂×C₅	—	4	2	no	—
449	C₂×C₅	C₃×#546	1	1	yes	characteristic
450	C₂×C₅	C₂×C₃×#135	1	1	yes	characteristic
451	C₂×C₅	C₃×#577	1	1	yes	characteristic
452	D₅	—	8	2	no	—
453	C₂³	—	10	2	no	—
454	C₂³	C₂×C₃×C₂²⋊D₅	1	2	yes	—
455	Q₈	—	2	1	no	—
456	Q₈	—	2	1	no	—
457	Q₈	—	4	2	no	—
458	Q₈	—	5	2	no	—
459	Q₈	—	10	1	no	—
460	D₄	—	2	2	no	—
461	D₄	—	10	2	no	—
462	D₄	—	10	2	no	—
463	D₄	—	20	4	no	—
464	D₄	—	20	2	no	—
465	D₄	—	40	1	no	—
466	D₄	—	40	2	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	2	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	10	1	no	—
473	C₂×C₄	—	10	1	no	—
474	C₂×C₄	—	20	4	no	—
475	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
476	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
477	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
478	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
479	C₈	—	10	1	no	—
480	C₈	—	10	1	no	—
481	C₈	—	10	2	no	—
482	C₂×C₃	—	4	2	no	—
483	C₂×C₃	—	40	2	no	—
484	C₂×C₃	C₂×#4096	1	1	yes	characteristic
485	C₂×C₃	#66163	1	1	yes	characteristic
486	C₂×C₃	#66171	1	1	yes	characteristic
487	C₅	C₃×#3304	1	1	yes	characteristic, complemented, Sylow
488	C₂²	—	2	2	no	—
489	C₂²	—	2	2	no	—
490	C₂²	—	2	2	no	—
491	C₂²	—	20	2	no	—
492	C₂²	—	20	2	no	—
493	C₂²	—	20	2	no	—
494	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
495	C₄	—	2	2	no	—
496	C₄	—	2	1	no	—
497	C₄	—	4	2	no	—
498	C₄	—	4	1	no	—
499	C₄	—	4	1	no	—
500	C₄	—	10	2	no	—
501	C₄	—	20	1	no	—
502	C₄	C₃×#4096	1	2	yes	—
503	C₄	C₃×D₅×#41	1	1	yes	characteristic
504	C₄	C₃×#4149	1	1	yes	characteristic
505	C₃	#10615404	1	1	yes	characteristic, direct product factor, Sylow
506	C₂	—	4	2	no	—
507	C₂	—	40	2	no	—
508	C₂	C₂×C₃×#4096	1	1	yes	characteristic
509	C₂	C₃×#66163	1	1	yes	characteristic
510	C₂	C₃×#66171	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#556	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#65887	C₂
hypercenter	C₃×#556	D₅
hypocenter	C₅	C₃×#3304
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄×D₄ ◁ C₃×#556

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#556	C₂	semidirect
3. C₃×#65383	C₂	semidirect
4. C₃×#65377	C₂	semidirect
5. C₃×#65337	C₂	semidirect
6. C₃×#65336	C₂	semidirect
7. C₃×C₄×#689	C₂	semidirect
8. C₃×#65316	C₂	semidirect
9. C₃×D₄×#168	C₂	semidirect
10. C₃×#65292	C₂	semidirect
11. C₃×#65291	C₂	semidirect
12. #10615404	C₃	direct (N × H)
43. C₅×#556	C₂×C₃	semidirect
45. #65383	C₂×C₃	semidirect
46. #65377	C₂×C₃	semidirect
47. #65337	C₂×C₃	semidirect
48. #65336	C₂×C₃	semidirect
49. C₄×#689	C₂×C₃	semidirect
50. #65316	C₂×C₃	semidirect
51. D₄×#168	C₂×C₃	semidirect
52. #65292	C₂×C₃	semidirect
53. #65291	C₂×C₃	semidirect
89. C₃×#556	D₅	semidirect
223. #556	C₃×D₅	semidirect
430. C₃×C₅	#3304	semidirect
487. C₅	C₃×#3304	semidirect
505. C₃	#10615404	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×C₅×#556	2
C₃×#65887	2
C₃×#65383	2
C₃×#65377	2
C₃×#65337	2
C₃×#65336	2
C₃×C₄×#689	2
C₃×#65316	2
C₃×D₄×#168	2
C₃×#65292	2
C₃×#65291	2
#10615404	3
C₃×#3304	5

Subgroups — C3×#10615404 #14460250

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615404 #14460250