Subgroups — C₃×#10613601 #14439205

Order 1920.

1104 conjugacy classes of subgroups.

The subgroup lattice has 524 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4064	C₂	1	2	yes	maximal, complemented
2	C₂×C₃×#4061	C₂	1	2	yes	maximal, complemented
3	C₃×D₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#66002	C₂	1	1	yes	maximal, characteristic
5	C₃×C₅×#497	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65470	C₂	1	2	yes	maximal, complemented
7	C₃×#65464	C₂	1	2	yes	maximal, complemented
8	C₃×#65375	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65349	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65004	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×#64996	C₂	1	1	yes	maximal, characteristic, complemented
12	#10613601	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	1	yes	characteristic
14	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
15	C₂×C₃×#711	C₂²	1	1	yes	characteristic
16	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	—
17	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
18	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
19	C₃×C₅×#124	C₂²	1	1	yes	characteristic
20	C₃×#4090	C₂²	1	1	yes	characteristic
21	C₃×#4090	C₂²	1	2	yes	—
22	C₂×C₃×#689	C₂²	1	2	yes	—
23	C₂×C₃×#689	C₂²	1	2	yes	—
24	C₂×C₃×#688	C₂²	1	2	yes	—
25	C₃×#4086	C₂²	1	1	yes	characteristic
26	C₂×C₃×#687	C₂²	1	2	yes	—
27	C₃×#4064	—	2	8	no	—
28	C₃×#4061	—	2	8	no	—
29	C₂×C₃×Dic₂₀	C₂²	1	2	yes	—
30	C₂×C₃×#677	C₂²	1	2	yes	—
31	C₂×C₃×#676	C₂²	1	2	yes	—
32	C₃×D₅×C₄⋊C₄	—	2	2	no	—
33	C₃×#4034	—	2	2	no	—
34	C₃×#4030	—	2	2	no	—
35	C₃×#4027	—	2	2	no	—
36	C₃×#4021	C₂²	1	1	yes	characteristic
37	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
38	C₃×#4015	C₂²	1	1	yes	characteristic
39	C₃×C₅×#97	C₂²	1	1	yes	characteristic
40	C₃×C₈×Dic₅	C₂²	1	2	yes	—
41	C₃×#3935	C₂²	1	1	yes	characteristic
42	C₃×#3152	—	5	1	no	maximal, Hall
43	C₂×#4064	C₂×C₃	1	2	yes	complemented
44	C₂×#4061	C₂×C₃	1	2	yes	complemented
45	D₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
46	#66002	C₂×C₃	1	1	yes	characteristic
47	C₅×#497	C₂×C₃	1	1	yes	characteristic, complemented
48	#65470	C₂×C₃	1	2	yes	complemented
49	#65464	C₂×C₃	1	2	yes	complemented
50	#65375	C₂×C₃	1	1	yes	characteristic, complemented
51	#65349	C₂×C₃	1	1	yes	characteristic, complemented
52	#65004	C₂×C₃	1	1	yes	characteristic, complemented
53	#64996	C₂×C₃	1	1	yes	characteristic, complemented
54	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
58	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
59	C₂²×C₃×Dic₅	—	2	1	no	—
60	C₃×#713	—	2	4	no	—
61	C₃×Q₈×D₅	—	2	4	no	—
62	C₃×Q₈×D₅	—	2	4	no	—
63	C₃×#711	—	2	4	no	—
64	C₂×C₃×D₂₀	—	2	1	no	—
65	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₄×D₅	—	2	2	no	—
67	C₂×C₃×C₄×D₅	—	2	1	no	—
68	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
69	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
70	C₂×C₃×Dic₁₀	—	2	2	no	—
71	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
72	C₂×C₃×Dic₁₀	C₂³	1	1	yes	characteristic
73	C₃×C₅×Q₁₆	—	2	4	no	—
74	C₃×C₅×SD₁₆	—	2	4	no	—
75	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
76	C₃×C₅×C₄⋊C₄	—	2	2	no	—
77	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
78	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
79	C₃×#689	—	2	4	no	—
80	C₃×#689	—	2	4	no	—
81	C₃×#688	—	2	4	no	—
82	C₃×#687	—	2	4	no	—
83	C₃×#685	—	2	2	no	—
84	C₃×C₄⋊Dic₅	—	2	2	no	—
85	C₃×#683	—	2	2	no	—
86	C₃×#683	—	2	4	no	—
87	C₃×C₄×Dic₅	D₄	1	2	yes	—
88	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
89	C₂×C₃×#168	C₂³	1	2	yes	—
90	C₃×Dic₂₀	—	2	4	no	—
91	C₃×#677	—	2	4	no	—
92	C₃×#676	D₄	1	8	yes	complemented
93	C₂×C₃×#137	—	5	2	no	—
94	C₂×C₃×#137	—	5	2	no	—
95	C₃×#532	—	5	1	no	—
96	C₂×C₃×C₄⋊Q₈	—	5	1	no	—
97	C₃×#497	—	5	1	no	—
98	C₃×#497	—	5	1	no	—
99	C₃×#497	—	5	1	no	—
100	C₃×#497	D₅	1	1	yes	characteristic, complemented
101	C₃×#494	—	5	2	no	—
102	C₃×#492	—	5	2	no	—
103	C₃×C₄×M₁₆	—	5	1	no	—
104	C₂×#713	C₂²×C₃	1	1	yes	characteristic
105	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
106	C₂×#711	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	—
108	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
109	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
110	C₅×#124	C₂²×C₃	1	1	yes	characteristic
111	#4090	C₂²×C₃	1	2	yes	—
112	#4090	C₂²×C₃	1	1	yes	characteristic
113	C₂×#689	C₂²×C₃	1	2	yes	—
114	C₂×#689	C₂²×C₃	1	2	yes	—
115	C₂×#688	C₂²×C₃	1	2	yes	—
116	#4086	C₂²×C₃	1	1	yes	characteristic
117	C₂×#687	C₂²×C₃	1	2	yes	—
118	#4064	—	2	8	no	—
119	#4061	—	2	8	no	—
120	C₂×Dic₂₀	C₂²×C₃	1	2	yes	—
121	C₂×#677	C₂²×C₃	1	2	yes	—
122	C₂×#676	C₂²×C₃	1	2	yes	—
123	D₅×C₄⋊C₄	—	2	2	no	—
124	#4034	—	2	2	no	—
125	#4030	—	2	2	no	—
126	#4027	—	2	2	no	—
127	#4021	C₂²×C₃	1	1	yes	characteristic
128	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
129	#4015	C₂²×C₃	1	1	yes	characteristic
130	C₅×#97	C₂²×C₃	1	1	yes	characteristic
131	C₈×Dic₅	C₂²×C₃	1	2	yes	—
132	#3935	C₂²×C₃	1	1	yes	characteristic
133	#3152	—	5	1	no	Sylow
134	C₂³×C₃×C₅	—	2	1	no	—
135	C₂²×C₃×D₅	—	2	1	no	—
136	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
137	C₃×C₅×Q₈	—	2	2	no	—
138	C₃×C₅×Q₈	—	2	2	no	—
139	C₃×C₅×Q₈	—	2	2	no	—
140	C₃×C₅×D₄	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₃×C₂²⋊D₅	—	4	2	no	—
146	C₃×C₂²⋊D₅	—	4	4	no	—
147	C₂×C₃×Dic₅	—	2	2	no	—
148	C₂×C₃×Dic₅	—	2	1	no	—
149	C₂×C₃×Dic₅	—	4	2	no	—
150	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
151	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
152	C₃×D₂₀	—	2	2	no	—
153	C₃×D₂₀	—	4	2	no	—
154	C₃×C₄×D₅	—	2	4	no	—
155	C₃×C₄×D₅	—	4	4	no	—
156	C₃×C₄×D₅	—	4	2	no	—
157	C₃×C₄×D₅	C₂×D₄	1	4	yes	—
158	C₃×Dic₁₀	—	2	2	no	—
159	C₃×Dic₁₀	—	2	2	no	—
160	C₃×Dic₁₀	—	2	2	no	—
161	C₃×Dic₁₀	—	4	4	no	—
162	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
163	C₃×#168	C₂×D₄	1	4	yes	—
164	C₂×C₃×#41	—	5	1	no	—
165	C₂×C₃×#41	—	5	1	no	—
166	C₂²×C₃×Q₈	—	5	2	no	—
167	C₃×#137	—	10	8	no	—
168	C₃×#137	—	10	8	no	—
169	C₂×C₃×Q₁₆	—	5	2	no	—
170	C₂×C₃×Q₁₆	—	5	2	no	—
171	C₂×C₃×Q₁₆	—	5	2	no	—
172	C₂×C₃×Q₁₆	C₂×D₅	1	2	yes	—
173	C₂×C₃×SD₁₆	—	5	2	no	—
174	C₂×C₃×SD₁₆	—	5	2	no	—
175	C₂×C₃×SD₁₆	—	5	2	no	—
176	C₂×C₃×SD₁₆	C₂×D₅	1	2	yes	—
177	C₂×C₃×M₁₆	—	5	2	no	—
178	C₃×C₄⋊Q₈	—	5	2	no	—
179	C₃×C₄⋊Q₈	—	5	1	no	—
180	C₃×C₄⋊Q₈	—	5	1	no	—
181	C₃×C₄⋊Q₈	—	10	2	no	—
182	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
183	C₃×#127	—	5	1	no	—
184	C₃×#124	—	5	1	no	—
185	C₃×#124	C₂×D₅	1	1	yes	characteristic
186	C₃×#121	—	10	2	no	—
187	C₃×C₄×D₄	—	10	2	no	—
188	C₂×C₃×C₄⋊C₄	—	10	2	no	—
189	C₂×C₃×C₄²	—	5	1	no	—
190	C₃×#97	—	5	1	no	—
191	C₃×#97	C₂×D₅	1	1	yes	characteristic
192	C₃×C₄×C₈	—	5	2	no	—
193	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
194	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
195	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₂²⋊D₅	—	2	1	no	—
197	C₂×C₂²⋊D₅	—	2	2	no	—
198	C₂²×Dic₅	—	2	1	no	—
199	#713	—	2	4	no	—
200	Q₈×D₅	—	2	4	no	—
201	Q₈×D₅	—	2	4	no	—
202	#711	—	2	4	no	—
203	C₂×D₂₀	—	2	1	no	—
204	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
205	C₂×C₄×D₅	—	2	2	no	—
206	C₂×C₄×D₅	—	2	1	no	—
207	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
208	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
209	C₂×Dic₁₀	—	2	2	no	—
210	C₂×Dic₁₀	C₂³×C₃	1	1	yes	characteristic
211	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
212	C₅×Q₁₆	—	2	4	no	—
213	C₅×SD₁₆	—	2	4	no	—
214	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
215	C₅×C₄⋊C₄	—	2	2	no	—
216	C₅×C₂²⋊C₄	—	2	2	no	—
217	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
218	#689	—	2	4	no	—
219	#689	—	2	4	no	—
220	#688	—	2	4	no	—
221	#687	—	2	4	no	—
222	#685	—	2	2	no	—
223	C₄⋊Dic₅	—	2	2	no	—
224	#683	—	2	2	no	—
225	#683	—	2	4	no	—
226	C₄×Dic₅	C₃×D₄	1	2	yes	—
227	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
228	C₂×#168	C₂³×C₃	1	2	yes	—
229	Dic₂₀	—	2	4	no	—
230	#677	—	2	4	no	—
231	#676	C₃×D₄	1	8	yes	complemented
232	C₂×#137	—	5	2	no	—
233	C₂×#137	—	5	2	no	—
234	#532	—	5	1	no	—
235	C₂×C₄⋊Q₈	—	5	1	no	—
236	#497	—	5	1	no	—
237	#497	—	5	1	no	—
238	#497	—	5	1	no	—
239	#497	C₃×D₅	1	1	yes	characteristic, complemented
240	#494	—	5	2	no	—
241	#492	—	5	2	no	—
242	C₄×M₁₆	—	5	1	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	4	2	no	—
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂×C₃×D₅	—	2	2	no	—
247	C₂×C₃×D₅	—	4	1	no	—
248	C₂×C₃×D₅	—	4	2	no	—
249	C₂×C₃×D₅	#127	1	2	yes	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	4	2	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
254	C₃×Dic₅	—	4	2	no	—
255	C₃×Dic₅	—	4	1	no	—
256	C₃×Dic₅	#127	1	2	yes	—
257	C₃×Dic₅	#137	1	4	yes	complemented
258	C₃×#41	—	10	4	no	—
259	C₃×#41	—	10	4	no	—
260	C₂×C₃×Q₈	—	5	1	no	—
261	C₂×C₃×Q₈	—	5	2	no	—
262	C₂×C₃×Q₈	—	10	2	no	—
263	C₂×C₃×Q₈	—	10	4	no	—
264	C₂×C₃×Q₈	—	10	4	no	—
265	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
267	C₂×C₃×D₄	—	5	1	no	—
268	C₂×C₃×D₄	—	10	1	no	—
269	C₂×C₃×D₄	—	10	2	no	—
270	C₂×C₃×D₄	—	10	1	no	—
271	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	—	5	1	no	—
273	C₂²×C₃×C₄	—	5	2	no	—
274	C₂²×C₃×C₄	—	10	1	no	—
275	C₂²×C₃×C₄	—	10	2	no	—
276	C₂²×C₃×C₄	—	10	1	no	—
277	C₃×Q₁₆	—	2	4	no	—
278	C₃×Q₁₆	—	10	4	no	—
279	C₃×Q₁₆	—	10	4	no	—
280	C₃×Q₁₆	—	10	4	no	—
281	C₃×SD₁₆	—	2	4	no	—
282	C₃×SD₁₆	—	10	4	no	—
283	C₃×SD₁₆	—	10	4	no	—
284	C₃×SD₁₆	—	10	4	no	—
285	C₃×M₁₆	—	5	8	no	—
286	C₂×C₃×C₈	—	5	2	no	—
287	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
288	C₃×C₄⋊C₄	—	2	2	no	—
289	C₃×C₄⋊C₄	—	10	4	no	—
290	C₃×C₄⋊C₄	—	10	2	no	—
291	C₃×C₄⋊C₄	—	10	2	no	—
292	C₃×C₂²⋊C₄	—	2	2	no	—
293	C₃×C₂²⋊C₄	—	10	2	no	—
294	C₃×C₄²	—	5	2	no	—
295	C₃×C₄²	—	5	1	no	—
296	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
297	C₂³×C₅	—	2	1	no	—
298	C₂²×D₅	—	2	1	no	—
299	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	2	2	no	—
302	C₅×Q₈	—	2	2	no	—
303	C₅×D₄	—	2	2	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
307	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
308	C₂²⋊D₅	—	4	2	no	—
309	C₂²⋊D₅	—	4	4	no	—
310	C₂×Dic₅	—	2	2	no	—
311	C₂×Dic₅	—	2	1	no	—
312	C₂×Dic₅	—	4	2	no	—
313	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
314	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
315	D₂₀	—	2	2	no	—
316	D₂₀	—	4	2	no	—
317	C₄×D₅	—	2	4	no	—
318	C₄×D₅	—	4	4	no	—
319	C₄×D₅	—	4	2	no	—
320	C₄×D₅	C₂×C₃×D₄	1	4	yes	—
321	Dic₁₀	—	2	2	no	—
322	Dic₁₀	—	2	2	no	—
323	Dic₁₀	—	2	2	no	—
324	Dic₁₀	—	4	4	no	—
325	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
326	#168	C₂×C₃×D₄	1	4	yes	—
327	C₂×#41	—	5	1	no	—
328	C₂×#41	—	5	1	no	—
329	C₂²×Q₈	—	5	2	no	—
330	#137	—	10	8	no	—
331	#137	—	10	8	no	—
332	C₂×Q₁₆	—	5	2	no	—
333	C₂×Q₁₆	—	5	2	no	—
334	C₂×Q₁₆	—	5	2	no	—
335	C₂×Q₁₆	C₂×C₃×D₅	1	2	yes	—
336	C₂×SD₁₆	—	5	2	no	—
337	C₂×SD₁₆	—	5	2	no	—
338	C₂×SD₁₆	—	5	2	no	—
339	C₂×SD₁₆	C₂×C₃×D₅	1	2	yes	—
340	C₂×M₁₆	—	5	2	no	—
341	C₄⋊Q₈	—	5	2	no	—
342	C₄⋊Q₈	—	5	1	no	—
343	C₄⋊Q₈	—	5	1	no	—
344	C₄⋊Q₈	—	10	2	no	—
345	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
346	#127	—	5	1	no	—
347	#124	—	5	1	no	—
348	#124	C₂×C₃×D₅	1	1	yes	characteristic
349	#121	—	10	2	no	—
350	C₄×D₄	—	10	2	no	—
351	C₂×C₄⋊C₄	—	10	2	no	—
352	C₂×C₄²	—	5	1	no	—
353	#97	—	5	1	no	—
354	#97	C₂×C₃×D₅	1	1	yes	characteristic
355	C₄×C₈	—	5	2	no	—
356	C₂×C₃×C₅	—	8	1	no	—
357	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
358	C₂×C₃×C₅	C₂×#137	1	2	yes	—
359	C₃×D₅	—	2	2	no	—
360	C₃×D₅	—	8	1	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	5	1	no	—
363	C₂³×C₃	—	10	1	no	—
364	C₃×Q₈	—	2	2	no	—
365	C₃×Q₈	—	2	2	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	10	2	no	—
368	C₃×Q₈	—	10	2	no	—
369	C₃×Q₈	—	10	2	no	—
370	C₃×Q₈	—	20	4	no	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	10	2	no	—
373	C₃×D₄	—	20	2	no	—
374	C₃×D₄	—	20	4	no	—
375	C₃×D₄	—	20	2	no	—
376	C₂×C₃×C₄	—	2	1	no	—
377	C₂×C₃×C₄	—	2	2	no	—
378	C₂×C₃×C₄	—	5	2	no	—
379	C₂×C₃×C₄	—	5	1	no	—
380	C₂×C₃×C₄	—	5	4	no	—
381	C₂×C₃×C₄	—	10	4	no	—
382	C₂×C₃×C₄	—	10	1	no	—
383	C₂×C₃×C₄	—	10	2	no	—
384	C₂×C₃×C₄	—	20	2	no	—
385	C₂×C₃×C₄	—	20	4	no	—
386	C₂×C₃×C₄	—	20	2	no	—
387	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
388	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
389	C₃×C₈	—	5	4	no	—
390	C₃×C₈	D₄×D₅	1	4	yes	—
391	C₂²×C₅	—	4	2	no	—
392	C₂²×C₅	—	4	1	no	—
393	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
394	C₂×D₅	—	2	2	no	—
395	C₂×D₅	—	4	2	no	—
396	C₂×D₅	—	4	1	no	—
397	C₂×D₅	C₃×#127	1	2	yes	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	4	2	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
402	Dic₅	—	4	2	no	—
403	Dic₅	—	4	1	no	—
404	Dic₅	C₃×#127	1	2	yes	—
405	Dic₅	C₃×#137	1	4	yes	complemented
406	#41	—	10	4	no	—
407	#41	—	10	4	no	—
408	C₂×Q₈	—	5	1	no	—
409	C₂×Q₈	—	5	2	no	—
410	C₂×Q₈	—	10	2	no	—
411	C₂×Q₈	—	10	4	no	—
412	C₂×Q₈	—	10	4	no	—
413	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
414	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
415	C₂×D₄	—	5	1	no	—
416	C₂×D₄	—	10	1	no	—
417	C₂×D₄	—	10	2	no	—
418	C₂×D₄	—	10	1	no	—
419	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
420	C₂²×C₄	—	5	1	no	—
421	C₂²×C₄	—	5	2	no	—
422	C₂²×C₄	—	10	1	no	—
423	C₂²×C₄	—	10	2	no	—
424	C₂²×C₄	—	10	1	no	—
425	Q₁₆	—	2	4	no	—
426	Q₁₆	—	10	4	no	—
427	Q₁₆	—	10	4	no	—
428	Q₁₆	—	10	4	no	—
429	SD₁₆	—	2	4	no	—
430	SD₁₆	—	10	4	no	—
431	SD₁₆	—	10	4	no	—
432	SD₁₆	—	10	4	no	—
433	M₁₆	—	5	8	no	—
434	C₂×C₈	—	5	2	no	—
435	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
436	C₄⋊C₄	—	2	2	no	—
437	C₄⋊C₄	—	10	4	no	—
438	C₄⋊C₄	—	10	2	no	—
439	C₄⋊C₄	—	10	2	no	—
440	C₂²⋊C₄	—	2	2	no	—
441	C₂²⋊C₄	—	10	2	no	—
442	C₄²	—	5	2	no	—
443	C₄²	—	5	1	no	—
444	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
445	C₃×C₅	#3152	1	1	yes	characteristic, complemented, Hall
446	C₂²×C₃	—	4	1	no	—
447	C₂²×C₃	—	4	2	no	—
448	C₂²×C₃	—	5	2	no	—
449	C₂²×C₃	—	10	2	no	—
450	C₂²×C₃	—	20	1	no	—
451	C₂²×C₃	—	20	2	no	—
452	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	2	no	—
456	C₃×C₄	—	5	2	no	—
457	C₃×C₄	—	5	4	no	—
458	C₃×C₄	—	20	1	no	—
459	C₃×C₄	—	20	2	no	—
460	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
461	C₂×C₅	—	8	1	no	—
462	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
463	C₂×C₅	C₂×C₃×#137	1	2	yes	—
464	D₅	—	2	2	no	—
465	D₅	—	8	1	no	—
466	C₂³	—	2	1	no	—
467	C₂³	—	5	1	no	—
468	C₂³	—	10	1	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	2	2	no	—
472	Q₈	—	10	2	no	—
473	Q₈	—	10	2	no	—
474	Q₈	—	10	2	no	—
475	Q₈	—	20	4	no	—
476	D₄	—	2	2	no	—
477	D₄	—	10	2	no	—
478	D₄	—	20	2	no	—
479	D₄	—	20	4	no	—
480	D₄	—	20	2	no	—
481	C₂×C₄	—	2	1	no	—
482	C₂×C₄	—	2	2	no	—
483	C₂×C₄	—	5	2	no	—
484	C₂×C₄	—	5	1	no	—
485	C₂×C₄	—	5	4	no	—
486	C₂×C₄	—	10	4	no	—
487	C₂×C₄	—	10	1	no	—
488	C₂×C₄	—	10	2	no	—
489	C₂×C₄	—	20	2	no	—
490	C₂×C₄	—	20	4	no	—
491	C₂×C₄	—	20	2	no	—
492	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
493	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
494	C₈	—	5	4	no	—
495	C₈	C₃×D₄×D₅	1	4	yes	—
496	C₂×C₃	—	8	1	no	—
497	C₂×C₃	—	10	2	no	—
498	C₂×C₃	—	40	1	no	—
499	C₂×C₃	D₅×#127	1	1	yes	characteristic
500	C₂×C₃	D₅×#137	1	2	yes	—
501	C₅	C₃×#3152	1	1	yes	characteristic, complemented, Sylow
502	C₂²	—	4	2	no	—
503	C₂²	—	4	1	no	—
504	C₂²	—	5	2	no	—
505	C₂²	—	10	2	no	—
506	C₂²	—	20	2	no	—
507	C₂²	—	20	1	no	—
508	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
509	C₄	—	2	2	no	—
510	C₄	—	4	1	no	—
511	C₄	—	4	2	no	—
512	C₄	—	5	4	no	—
513	C₄	—	5	2	no	—
514	C₄	—	20	1	no	—
515	C₄	—	20	2	no	—
516	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
517	C₃	#10613601	1	1	yes	characteristic, direct product factor, Sylow
518	C₂	—	8	1	no	—
519	C₂	—	10	2	no	—
520	C₂	—	40	1	no	—
521	C₂	C₃×D₅×#127	1	1	yes	characteristic
522	C₂	C₃×D₅×#137	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#497	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66002	C₂
hypercenter	C₃×#497	D₅
hypocenter	C₅	C₃×#3152
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#497

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4064	C₂	semidirect
2. C₂×C₃×#4061	C₂	semidirect
3. C₃×D₅×C₄⋊Q₈	C₂	semidirect
5. C₃×C₅×#497	C₂	semidirect
6. C₃×#65470	C₂	semidirect
7. C₃×#65464	C₂	semidirect
8. C₃×#65375	C₂	semidirect
9. C₃×#65349	C₂	semidirect
10. C₃×#65004	C₂	semidirect
11. C₃×#64996	C₂	semidirect
12. #10613601	C₃	direct (N × H)
43. C₂×#4064	C₂×C₃	semidirect
44. C₂×#4061	C₂×C₃	semidirect
45. D₅×C₄⋊Q₈	C₂×C₃	semidirect
47. C₅×#497	C₂×C₃	semidirect
48. #65470	C₂×C₃	semidirect
49. #65464	C₂×C₃	semidirect
50. #65375	C₂×C₃	semidirect
51. #65349	C₂×C₃	semidirect
52. #65004	C₂×C₃	semidirect
53. #64996	C₂×C₃	semidirect
92. C₃×#676	D₄	semidirect
100. C₃×#497	D₅	semidirect
231. #676	C₃×D₄	semidirect
239. #497	C₃×D₅	semidirect
257. C₃×Dic₅	#137	semidirect
405. Dic₅	C₃×#137	semidirect
445. C₃×C₅	#3152	semidirect
501. C₅	C₃×#3152	semidirect
517. C₃	#10613601	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×#4064	2
C₂×C₃×#4061	2
C₃×D₅×C₄⋊Q₈	2
C₃×#66002	2
C₃×C₅×#497	2
C₃×#65470	2
C₃×#65464	2
C₃×#65375	2
C₃×#65349	2
C₃×#65004	2
C₃×#64996	2
#10613601	3
C₃×#3152	5

Subgroups — C3×#10613601 #14439205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10613601 #14439205