Subgroups — C₃×#10615134 #14439640

Order 1920.

1064 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4097	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4096	C₂	1	1	yes	maximal, characteristic
4	C₂²×C₃×#689	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#4088	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65860	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65381	C₂	1	2	yes	maximal, complemented
8	C₃×#65375	C₂	1	2	yes	maximal, complemented
9	C₃×#65349	C₂	1	2	yes	maximal, complemented
10	C₃×#65348	C₂	1	2	yes	maximal, complemented
11	C₃×#65286	C₂	1	1	yes	maximal, characteristic, complemented
12	#10615134	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₂×C₃×#709	C₂²	1	1	yes	characteristic
16	C₂²×C₃×Dic₁₀	C₂²	1	1	yes	characteristic
17	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	—
18	C₃×C₅×#124	C₂²	1	2	yes	—
19	C₃×C₅×#123	—	2	2	no	—
20	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
21	C₃×C₅×#117	C₂²	1	1	yes	characteristic
22	C₃×#4097	—	2	4	no	—
23	C₃×#4096	—	2	4	no	—
24	C₂×C₃×#689	—	2	4	no	—
25	C₂×C₃×#689	C₂²	1	2	yes	—
26	C₂×C₃×#689	C₂²	1	2	yes	—
27	C₂×C₃×#689	C₂²	1	2	yes	—
28	C₂×C₃×#689	C₂²	1	1	yes	characteristic
29	C₂×C₃×#689	C₂²	1	2	yes	—
30	C₃×#4088	—	2	4	no	—
31	C₂×C₃×#688	C₂²	1	2	yes	—
32	C₂×C₃×#688	C₂²	1	1	yes	characteristic
33	C₂×C₃×#687	C₂²	1	1	yes	characteristic
34	C₂×C₃×#687	C₂²	1	2	yes	—
35	C₂×C₃×#686	C₂²	1	1	yes	characteristic
36	C₂×C₃×#681	C₂²	1	1	yes	characteristic
37	C₂²×C₃×#168	C₂²	1	1	yes	characteristic
38	C₃×#4043	—	2	2	no	—
39	C₃×#4032	—	2	2	no	—
40	C₃×#4021	C₂²	1	2	yes	—
41	C₃×#4015	C₂²	1	2	yes	—
42	C₃×#3935	C₂²	1	2	yes	—
43	C₃×C₄×#168	C₂²	1	2	yes	—
44	C₃×#3156	—	5	1	no	maximal, Hall
45	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×#4097	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×#4096	C₂×C₃	1	1	yes	characteristic
48	C₂²×#689	C₂×C₃	1	1	yes	characteristic, complemented
49	C₂×#4088	C₂×C₃	1	1	yes	characteristic, complemented
50	#65860	C₂×C₃	1	1	yes	characteristic, complemented
51	#65381	C₂×C₃	1	2	yes	complemented
52	#65375	C₂×C₃	1	2	yes	complemented
53	#65349	C₂×C₃	1	2	yes	complemented
54	#65348	C₂×C₃	1	2	yes	complemented
55	#65286	C₂×C₃	1	1	yes	characteristic, complemented
56	C₃×C₅×#41	—	2	2	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₂×C₃×C₅×Q₈	—	2	1	no	—
59	C₂×C₃×C₅×Q₈	—	2	2	no	—
60	C₂×C₃×C₅×Q₈	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
62	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
63	C₂×C₃×C₅×D₄	—	2	1	no	—
64	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	—	2	1	no	—
66	C₂²×C₃×C₄×C₅	—	2	1	no	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
69	C₂²×C₃×Dic₅	—	2	1	no	—
70	C₃×#709	—	2	2	no	—
71	C₃×#709	—	2	2	no	—
72	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
73	C₂×C₃×C₄×D₅	—	2	1	no	—
74	C₂×C₃×Dic₁₀	—	2	2	no	—
75	C₂×C₃×Dic₁₀	—	2	2	no	—
76	C₂×C₃×Dic₁₀	—	2	1	no	—
77	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
78	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
79	C₃×C₅×C₄⋊C₄	—	2	4	no	—
80	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
81	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
82	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
83	C₃×C₄²×C₅	C₂³	1	2	yes	—
84	C₃×#689	—	2	4	no	—
85	C₃×#689	—	2	4	no	—
86	C₃×#689	—	2	4	no	—
87	C₃×#689	—	2	2	no	—
88	C₃×#689	—	2	4	no	—
89	C₃×#688	—	2	4	no	—
90	C₃×#688	—	2	2	no	—
91	C₃×#687	—	2	2	no	—
92	C₃×#687	—	2	4	no	—
93	C₃×#686	—	2	2	no	—
94	C₃×#685	—	2	4	no	—
95	C₃×C₄⋊Dic₅	—	2	4	no	—
96	C₃×#681	D₄	1	4	yes	—
97	C₂×C₃×#168	D₄	1	4	yes	—
98	C₂×C₃×#168	C₂³	1	1	yes	characteristic
99	C₂×C₃×#168	C₂³	1	2	yes	—
100	C₂×C₃×#168	C₂³	1	1	yes	characteristic
101	C₂×C₃×#137	—	5	1	no	—
102	C₂×C₃×#137	—	5	1	no	—
103	C₂×C₃×#135	—	5	1	no	—
104	C₂²×C₃×Q₁₆	—	5	1	no	—
105	C₃×#536	—	5	1	no	—
106	C₃×#536	D₅	1	1	yes	characteristic, complemented
107	C₃×#497	—	5	2	no	—
108	C₃×#497	—	5	2	no	—
109	C₃×#495	—	5	2	no	—
110	C₃×#494	—	5	2	no	—
111	C₃×#405	—	5	1	no	—
112	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
114	C₂×#709	C₂²×C₃	1	1	yes	characteristic
115	C₂²×Dic₁₀	C₂²×C₃	1	1	yes	characteristic
116	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	—
117	C₅×#124	C₂²×C₃	1	2	yes	—
118	C₅×#123	—	2	2	no	—
119	C₅×C₂²⋊Q₈	—	2	2	no	—
120	C₅×#117	C₂²×C₃	1	1	yes	characteristic
121	#4097	—	2	4	no	—
122	#4096	—	2	4	no	—
123	C₂×#689	—	2	4	no	—
124	C₂×#689	C₂²×C₃	1	2	yes	—
125	C₂×#689	C₂²×C₃	1	2	yes	—
126	C₂×#689	C₂²×C₃	1	2	yes	—
127	C₂×#689	C₂²×C₃	1	2	yes	—
128	C₂×#689	C₂²×C₃	1	1	yes	characteristic
129	#4088	—	2	4	no	—
130	C₂×#688	C₂²×C₃	1	2	yes	—
131	C₂×#688	C₂²×C₃	1	1	yes	characteristic
132	C₂×#687	C₂²×C₃	1	2	yes	—
133	C₂×#687	C₂²×C₃	1	1	yes	characteristic
134	C₂×#686	C₂²×C₃	1	1	yes	characteristic
135	C₂×#681	C₂²×C₃	1	1	yes	characteristic
136	C₂²×#168	C₂²×C₃	1	1	yes	characteristic
137	#4043	—	2	2	no	—
138	#4032	—	2	2	no	—
139	#4021	C₂²×C₃	1	2	yes	—
140	#4015	C₂²×C₃	1	2	yes	—
141	#3935	C₂²×C₃	1	2	yes	—
142	C₄×#168	C₂²×C₃	1	2	yes	—
143	#3156	—	5	1	no	Sylow
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
146	C₂²×C₃×D₅	—	2	1	no	—
147	C₃×C₅×Q₈	—	2	2	no	—
148	C₃×C₅×Q₈	—	2	1	no	—
149	C₃×C₅×Q₈	—	2	2	no	—
150	C₃×C₅×Q₈	—	2	1	no	—
151	C₃×C₅×Q₈	—	4	2	no	—
152	C₃×C₅×D₄	—	2	1	no	—
153	C₃×C₅×D₄	—	2	1	no	—
154	C₃×C₅×D₄	—	4	2	no	—
155	C₂×C₃×C₄×C₅	—	2	2	no	—
156	C₂×C₃×C₄×C₅	—	2	1	no	—
157	C₂×C₃×C₄×C₅	—	4	2	no	—
158	C₂×C₃×C₄×C₅	—	4	2	no	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
161	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
164	C₃×C₂²⋊D₅	—	4	2	no	—
165	C₂×C₃×Dic₅	—	2	1	no	—
166	C₂×C₃×Dic₅	—	2	2	no	—
167	C₂×C₃×Dic₅	—	4	2	no	—
168	C₃×D₂₀	—	2	1	no	—
169	C₃×D₂₀	—	2	1	no	—
170	C₃×C₄×D₅	—	4	2	no	—
171	C₃×Dic₁₀	—	2	2	no	—
172	C₃×Dic₁₀	—	2	1	no	—
173	C₃×Dic₁₀	—	2	2	no	—
174	C₃×Dic₁₀	—	2	1	no	—
175	C₃×Dic₁₀	—	4	2	no	—
176	C₃×#168	C₂×D₄	1	2	yes	—
177	C₃×#168	C₂×D₄	1	2	yes	—
178	C₃×#168	C₂×D₄	1	4	yes	—
179	C₂×C₃×#41	—	5	1	no	—
180	C₂×C₃×#41	C₂×D₅	1	1	yes	characteristic
181	C₂²×C₃×Q₈	—	5	1	no	—
182	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
183	C₃×#137	—	10	4	no	—
184	C₃×#137	—	10	4	no	—
185	C₃×#135	—	10	4	no	—
186	C₂×C₃×Q₁₆	—	5	2	no	—
187	C₂×C₃×Q₁₆	—	5	2	no	—
188	C₂×C₃×Q₁₆	—	5	1	no	—
189	C₂×C₃×Q₁₆	—	5	2	no	—
190	C₂×C₃×Q₁₆	—	5	2	no	—
191	C₂×C₃×Q₁₆	—	10	4	no	—
192	C₂×C₃×SD₁₆	—	5	1	no	—
193	C₂×C₃×SD₁₆	—	5	2	no	—
194	C₂×C₃×SD₁₆	—	5	1	no	—
195	C₂×C₃×SD₁₆	—	5	2	no	—
196	C₂×C₃×D₈	—	5	1	no	—
197	C₂×C₃×M₁₆	—	5	1	no	—
198	C₂²×C₃×C₈	—	5	1	no	—
199	C₃×C₄⋊Q₈	—	5	2	no	—
200	C₃×C₄⋊Q₈	C₂×D₅	1	2	yes	—
201	C₃×#124	—	5	2	no	—
202	C₃×#124	C₂×D₅	1	2	yes	—
203	C₃×#123	—	2	2	no	—
204	C₃×#123	—	10	2	no	—
205	C₃×C₂²⋊Q₈	—	2	2	no	—
206	C₃×C₂²⋊Q₈	—	10	2	no	—
207	C₃×#117	C₂×D₅	1	1	yes	characteristic
208	C₃×#97	—	5	2	no	—
209	C₃×C₄×C₈	—	5	2	no	—
210	C₅×#41	—	2	2	no	—
211	C₅×#41	—	2	2	no	—
212	C₂×C₅×Q₈	—	2	1	no	—
213	C₂×C₅×Q₈	—	2	2	no	—
214	C₂×C₅×Q₈	—	2	2	no	—
215	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
216	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
217	C₂×C₅×D₄	—	2	1	no	—
218	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
219	C₂²×C₄×C₅	—	2	1	no	—
220	C₂²×C₄×C₅	—	2	1	no	—
221	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
222	C₂×C₂²⋊D₅	—	2	1	no	—
223	C₂²×Dic₅	—	2	1	no	—
224	#709	—	2	2	no	—
225	#709	—	2	2	no	—
226	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
227	C₂×C₄×D₅	—	2	1	no	—
228	C₂×Dic₁₀	—	2	2	no	—
229	C₂×Dic₁₀	—	2	2	no	—
230	C₂×Dic₁₀	—	2	1	no	—
231	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
232	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
233	C₅×C₄⋊C₄	—	2	4	no	—
234	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
235	C₅×C₂²⋊C₄	—	2	4	no	—
236	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
237	C₄²×C₅	C₂³×C₃	1	2	yes	—
238	#689	—	2	2	no	—
239	#689	—	2	4	no	—
240	#689	—	2	4	no	—
241	#689	—	2	4	no	—
242	#689	—	2	4	no	—
243	#688	—	2	2	no	—
244	#688	—	2	4	no	—
245	#687	—	2	2	no	—
246	#687	—	2	4	no	—
247	#686	—	2	2	no	—
248	#685	—	2	4	no	—
249	C₄⋊Dic₅	—	2	4	no	—
250	#681	C₃×D₄	1	4	yes	—
251	C₂×#168	C₃×D₄	1	4	yes	—
252	C₂×#168	C₂³×C₃	1	1	yes	characteristic
253	C₂×#168	C₂³×C₃	1	2	yes	—
254	C₂×#168	C₂³×C₃	1	1	yes	characteristic
255	C₂×#137	—	5	1	no	—
256	C₂×#137	—	5	1	no	—
257	C₂×#135	—	5	1	no	—
258	C₂²×Q₁₆	—	5	1	no	—
259	#536	—	5	1	no	—
260	#536	C₃×D₅	1	1	yes	characteristic, complemented
261	#497	—	5	2	no	—
262	#497	—	5	2	no	—
263	#495	—	5	2	no	—
264	#494	—	5	2	no	—
265	#405	—	5	1	no	—
266	C₂²×C₃×C₅	—	2	2	no	—
267	C₂²×C₃×C₅	—	4	1	no	—
268	C₂²×C₃×C₅	—	4	2	no	—
269	C₂²×C₃×C₅	#127	1	2	yes	—
270	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
271	C₂×C₃×D₅	—	4	1	no	—
272	C₂×C₃×D₅	—	4	2	no	—
273	C₃×C₄×C₅	—	2	4	no	—
274	C₃×C₄×C₅	—	4	1	no	—
275	C₃×C₄×C₅	—	4	2	no	—
276	C₃×C₄×C₅	#127	1	2	yes	—
277	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
279	C₃×Dic₅	—	4	2	no	—
280	C₃×Dic₅	—	4	1	no	—
281	C₃×#41	—	2	2	no	—
282	C₃×#41	—	2	2	no	—
283	C₃×#41	—	10	2	no	—
284	C₃×#41	—	10	2	no	—
285	C₂×C₃×Q₈	—	2	1	no	—
286	C₂×C₃×Q₈	—	2	2	no	—
287	C₂×C₃×Q₈	—	2	2	no	—
288	C₂×C₃×Q₈	—	5	2	no	—
289	C₂×C₃×Q₈	—	5	1	no	—
290	C₂×C₃×Q₈	—	10	1	no	—
291	C₂×C₃×Q₈	—	10	2	no	—
292	C₂×C₃×Q₈	—	10	2	no	—
293	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
294	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
295	C₂×C₃×D₄	—	2	1	no	—
296	C₂×C₃×D₄	—	5	1	no	—
297	C₂×C₃×D₄	—	10	1	no	—
298	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
299	C₂²×C₃×C₄	—	2	1	no	—
300	C₂²×C₃×C₄	—	2	1	no	—
301	C₂²×C₃×C₄	—	10	1	no	—
302	C₂²×C₃×C₄	—	10	1	no	—
303	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
304	C₃×Q₁₆	—	10	4	no	—
305	C₃×Q₁₆	—	10	4	no	—
306	C₃×Q₁₆	—	10	2	no	—
307	C₃×Q₁₆	—	10	4	no	—
308	C₃×Q₁₆	—	10	4	no	—
309	C₃×SD₁₆	—	10	2	no	—
310	C₃×SD₁₆	—	10	4	no	—
311	C₃×SD₁₆	—	10	2	no	—
312	C₃×SD₁₆	—	10	4	no	—
313	C₃×D₈	—	10	2	no	—
314	C₃×M₁₆	—	5	4	no	—
315	C₂×C₃×C₈	—	5	4	no	—
316	C₂×C₃×C₈	—	5	1	no	—
317	C₂×C₃×C₈	—	5	2	no	—
318	C₂×C₃×C₈	—	5	1	no	—
319	C₃×C₄⋊C₄	—	2	4	no	—
320	C₃×C₄⋊C₄	—	10	4	no	—
321	C₃×C₄⋊C₄	C₂²⋊D₅	1	2	yes	—
322	C₃×C₂²⋊C₄	—	2	4	no	—
323	C₃×C₂²⋊C₄	—	10	4	no	—
324	C₃×C₂²⋊C₄	C₂²⋊D₅	1	2	yes	—
325	C₃×C₄²	C₂²×D₅	1	2	yes	—
326	C₂³×C₅	—	2	1	no	—
327	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
328	C₂²×D₅	—	2	1	no	—
329	C₅×Q₈	—	2	2	no	—
330	C₅×Q₈	—	2	1	no	—
331	C₅×Q₈	—	2	2	no	—
332	C₅×Q₈	—	2	1	no	—
333	C₅×Q₈	—	4	2	no	—
334	C₅×D₄	—	2	1	no	—
335	C₅×D₄	—	2	1	no	—
336	C₅×D₄	—	4	2	no	—
337	C₂×C₄×C₅	—	2	2	no	—
338	C₂×C₄×C₅	—	2	1	no	—
339	C₂×C₄×C₅	—	4	2	no	—
340	C₂×C₄×C₅	—	4	2	no	—
341	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
342	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
343	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
344	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
345	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
346	C₂²⋊D₅	—	4	2	no	—
347	C₂×Dic₅	—	2	1	no	—
348	C₂×Dic₅	—	2	2	no	—
349	C₂×Dic₅	—	4	2	no	—
350	D₂₀	—	2	1	no	—
351	D₂₀	—	2	1	no	—
352	C₄×D₅	—	4	2	no	—
353	Dic₁₀	—	2	2	no	—
354	Dic₁₀	—	2	1	no	—
355	Dic₁₀	—	2	2	no	—
356	Dic₁₀	—	2	1	no	—
357	Dic₁₀	—	4	2	no	—
358	#168	C₂×C₃×D₄	1	2	yes	—
359	#168	C₂×C₃×D₄	1	2	yes	—
360	#168	C₂×C₃×D₄	1	4	yes	—
361	C₂×#41	—	5	1	no	—
362	C₂×#41	C₂×C₃×D₅	1	1	yes	characteristic
363	C₂²×Q₈	—	5	1	no	—
364	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
365	#137	—	10	4	no	—
366	#137	—	10	4	no	—
367	#135	—	10	4	no	—
368	C₂×Q₁₆	—	5	2	no	—
369	C₂×Q₁₆	—	5	2	no	—
370	C₂×Q₁₆	—	5	1	no	—
371	C₂×Q₁₆	—	5	2	no	—
372	C₂×Q₁₆	—	5	2	no	—
373	C₂×Q₁₆	—	10	4	no	—
374	C₂×SD₁₆	—	5	1	no	—
375	C₂×SD₁₆	—	5	2	no	—
376	C₂×SD₁₆	—	5	1	no	—
377	C₂×SD₁₆	—	5	2	no	—
378	C₂×D₈	—	5	1	no	—
379	C₂×M₁₆	—	5	1	no	—
380	C₂²×C₈	—	5	1	no	—
381	C₄⋊Q₈	—	5	2	no	—
382	C₄⋊Q₈	C₂×C₃×D₅	1	2	yes	—
383	#124	—	5	2	no	—
384	#124	C₂×C₃×D₅	1	2	yes	—
385	#123	—	2	2	no	—
386	#123	—	10	2	no	—
387	C₂²⋊Q₈	—	2	2	no	—
388	C₂²⋊Q₈	—	10	2	no	—
389	#117	C₂×C₃×D₅	1	1	yes	characteristic
390	#97	—	5	2	no	—
391	C₄×C₈	—	5	2	no	—
392	C₂×C₃×C₅	—	2	2	no	—
393	C₂×C₃×C₅	—	8	1	no	—
394	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
395	C₂×C₃×C₅	#578	1	2	yes	—
396	C₃×D₅	—	8	1	no	—
397	C₂³×C₃	—	2	1	no	—
398	C₂³×C₃	—	10	1	no	—
399	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
400	C₃×Q₈	—	2	2	no	—
401	C₃×Q₈	—	2	1	no	—
402	C₃×Q₈	—	2	2	no	—
403	C₃×Q₈	—	2	1	no	—
404	C₃×Q₈	—	4	2	no	—
405	C₃×Q₈	—	10	2	no	—
406	C₃×Q₈	—	10	1	no	—
407	C₃×Q₈	—	10	2	no	—
408	C₃×Q₈	—	10	1	no	—
409	C₃×Q₈	—	20	2	no	—
410	C₃×D₄	—	2	1	no	—
411	C₃×D₄	—	2	1	no	—
412	C₃×D₄	—	4	2	no	—
413	C₃×D₄	—	10	1	no	—
414	C₃×D₄	—	10	1	no	—
415	C₃×D₄	—	20	2	no	—
416	C₂×C₃×C₄	—	2	2	no	—
417	C₂×C₃×C₄	—	2	1	no	—
418	C₂×C₃×C₄	—	4	2	no	—
419	C₂×C₃×C₄	—	4	2	no	—
420	C₂×C₃×C₄	—	10	2	no	—
421	C₂×C₃×C₄	—	10	1	no	—
422	C₂×C₃×C₄	—	20	2	no	—
423	C₂×C₃×C₄	—	20	2	no	—
424	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
425	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
426	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
427	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
428	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
429	C₃×C₈	—	5	2	no	—
430	C₃×C₈	—	5	2	no	—
431	C₃×C₈	—	5	4	no	—
432	C₂²×C₅	—	2	2	no	—
433	C₂²×C₅	—	4	2	no	—
434	C₂²×C₅	—	4	1	no	—
435	C₂²×C₅	C₃×#127	1	2	yes	—
436	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
437	C₂×D₅	—	4	2	no	—
438	C₂×D₅	—	4	1	no	—
439	C₄×C₅	—	2	4	no	—
440	C₄×C₅	—	4	1	no	—
441	C₄×C₅	—	4	2	no	—
442	C₄×C₅	C₃×#127	1	2	yes	—
443	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
444	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
445	Dic₅	—	4	2	no	—
446	Dic₅	—	4	1	no	—
447	#41	—	2	2	no	—
448	#41	—	2	2	no	—
449	#41	—	10	2	no	—
450	#41	—	10	2	no	—
451	C₂×Q₈	—	2	1	no	—
452	C₂×Q₈	—	2	2	no	—
453	C₂×Q₈	—	2	2	no	—
454	C₂×Q₈	—	5	2	no	—
455	C₂×Q₈	—	5	1	no	—
456	C₂×Q₈	—	10	1	no	—
457	C₂×Q₈	—	10	2	no	—
458	C₂×Q₈	—	10	2	no	—
459	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
460	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
461	C₂×D₄	—	2	1	no	—
462	C₂×D₄	—	5	1	no	—
463	C₂×D₄	—	10	1	no	—
464	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
465	C₂²×C₄	—	2	1	no	—
466	C₂²×C₄	—	2	1	no	—
467	C₂²×C₄	—	10	1	no	—
468	C₂²×C₄	—	10	1	no	—
469	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
470	Q₁₆	—	10	4	no	—
471	Q₁₆	—	10	4	no	—
472	Q₁₆	—	10	2	no	—
473	Q₁₆	—	10	4	no	—
474	Q₁₆	—	10	4	no	—
475	SD₁₆	—	10	2	no	—
476	SD₁₆	—	10	4	no	—
477	SD₁₆	—	10	2	no	—
478	SD₁₆	—	10	4	no	—
479	D₈	—	10	2	no	—
480	M₁₆	—	5	4	no	—
481	C₂×C₈	—	5	4	no	—
482	C₂×C₈	—	5	1	no	—
483	C₂×C₈	—	5	2	no	—
484	C₂×C₈	—	5	1	no	—
485	C₄⋊C₄	—	2	4	no	—
486	C₄⋊C₄	—	10	4	no	—
487	C₄⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
488	C₂²⋊C₄	—	2	4	no	—
489	C₂²⋊C₄	—	10	4	no	—
490	C₂²⋊C₄	C₃×C₂²⋊D₅	1	2	yes	—
491	C₄²	C₂²×C₃×D₅	1	2	yes	—
492	C₃×C₅	#3156	1	1	yes	characteristic, complemented, Hall
493	C₂²×C₃	—	2	2	no	—
494	C₂²×C₃	—	4	1	no	—
495	C₂²×C₃	—	4	2	no	—
496	C₂²×C₃	—	20	1	no	—
497	C₂²×C₃	—	20	2	no	—
498	C₂²×C₃	#4086	1	2	yes	—
499	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
500	C₃×C₄	—	2	4	no	—
501	C₃×C₄	—	4	1	no	—
502	C₃×C₄	—	4	2	no	—
503	C₃×C₄	—	20	1	no	—
504	C₃×C₄	—	20	2	no	—
505	C₃×C₄	#4086	1	2	yes	—
506	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
507	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
508	C₂×C₅	—	2	2	no	—
509	C₂×C₅	—	8	1	no	—
510	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
511	C₂×C₅	C₃×#578	1	2	yes	—
512	D₅	—	8	1	no	—
513	C₂³	—	2	1	no	—
514	C₂³	—	10	1	no	—
515	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
516	Q₈	—	2	2	no	—
517	Q₈	—	2	1	no	—
518	Q₈	—	2	2	no	—
519	Q₈	—	2	1	no	—
520	Q₈	—	4	2	no	—
521	Q₈	—	10	2	no	—
522	Q₈	—	10	1	no	—
523	Q₈	—	10	2	no	—
524	Q₈	—	10	1	no	—
525	Q₈	—	20	2	no	—
526	D₄	—	2	1	no	—
527	D₄	—	2	1	no	—
528	D₄	—	4	2	no	—
529	D₄	—	10	1	no	—
530	D₄	—	10	1	no	—
531	D₄	—	20	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	1	no	—
534	C₂×C₄	—	4	2	no	—
535	C₂×C₄	—	4	2	no	—
536	C₂×C₄	—	10	2	no	—
537	C₂×C₄	—	10	1	no	—
538	C₂×C₄	—	20	2	no	—
539	C₂×C₄	—	20	2	no	—
540	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
541	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
542	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
543	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
544	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
545	C₈	—	5	2	no	—
546	C₈	—	5	2	no	—
547	C₈	—	5	4	no	—
548	C₂×C₃	—	2	2	no	—
549	C₂×C₃	—	8	1	no	—
550	C₂×C₃	—	40	1	no	—
551	C₂×C₃	C₂×#4086	1	1	yes	characteristic
552	C₂×C₃	#66172	1	2	yes	—
553	C₅	C₃×#3156	1	1	yes	characteristic, complemented, Sylow
554	C₂²	—	2	2	no	—
555	C₂²	—	4	1	no	—
556	C₂²	—	4	2	no	—
557	C₂²	—	20	1	no	—
558	C₂²	—	20	2	no	—
559	C₂²	C₃×#4086	1	2	yes	—
560	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
561	C₄	—	2	4	no	—
562	C₄	—	4	1	no	—
563	C₄	—	4	2	no	—
564	C₄	—	20	1	no	—
565	C₄	—	20	2	no	—
566	C₄	C₃×#4086	1	2	yes	—
567	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
568	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
569	C₃	#10615134	1	1	yes	characteristic, direct product factor, Sylow
570	C₂	—	2	2	no	—
571	C₂	—	8	1	no	—
572	C₂	—	40	1	no	—
573	C₂	C₂×C₃×#4086	1	1	yes	characteristic
574	C₂	C₃×#66172	1	2	yes	—

	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×#536	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4096	C₂
hypercenter	C₃×#536	D₅
hypocenter	C₅	C₃×#3156
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×#117 ◁ C₃×#536

Complements

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

N	H ≅ G/N	type
1. C₃×C₅×#536	C₂	semidirect
2. C₂×C₃×#4097	C₂	semidirect
4. C₂²×C₃×#689	C₂	semidirect
5. C₂×C₃×#4088	C₂	semidirect
6. C₃×#65860	C₂	semidirect
7. C₃×#65381	C₂	semidirect
8. C₃×#65375	C₂	semidirect
9. C₃×#65349	C₂	semidirect
10. C₃×#65348	C₂	semidirect
11. C₃×#65286	C₂	semidirect
12. #10615134	C₃	direct (N × H)
45. C₅×#536	C₂×C₃	semidirect
46. C₂×#4097	C₂×C₃	semidirect
48. C₂²×#689	C₂×C₃	semidirect
49. C₂×#4088	C₂×C₃	semidirect
50. #65860	C₂×C₃	semidirect
51. #65381	C₂×C₃	semidirect
52. #65375	C₂×C₃	semidirect
53. #65349	C₂×C₃	semidirect
54. #65348	C₂×C₃	semidirect
55. #65286	C₂×C₃	semidirect
106. C₃×#536	D₅	semidirect
260. #536	C₃×D₅	semidirect
492. C₃×C₅	#3156	semidirect
553. C₅	C₃×#3156	semidirect
569. C₃	#10615134	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×#536	2
C₂×C₃×#4097	2
C₂×C₃×#4096	2
C₂²×C₃×#689	2
C₂×C₃×#4088	2
C₃×#65860	2
C₃×#65381	2
C₃×#65375	2
C₃×#65349	2
C₃×#65348	2
C₃×#65286	2
#10615134	3
C₃×#3156	5

Subgroups — C3×#10615134 #14439640

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10615134 #14439640