Subgroups — C₃×#10612753 #14459113

Order 1920.

840 conjugacy classes of subgroups.

The subgroup lattice has 516 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66060	C₂	1	1	yes	maximal, characteristic
2	C₃×Q₈×D₂₀	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×C₅×#475	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65382	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×#688	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65153	C₂	1	2	yes	maximal, complemented
7	C₃×#65151	C₂	1	2	yes	maximal, complemented
8	C₃×#65130	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#65123	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×#65095	C₂	1	2	yes	maximal, complemented
11	C₃×D₅×#103	C₂	1	2	yes	maximal, complemented
12	#10612753	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	—	2	1	no	—
14	C₂×C₃×Q₈×D₅	C₂²	1	2	yes	—
15	C₃×C₅×C₄⋊Q₈	C₂²	1	1	yes	characteristic
16	C₃×C₄×C₅×Q₈	C₂²	1	1	yes	characteristic
17	C₃×#4092	—	2	1	no	—
18	C₂×C₃×#688	C₂²	1	1	yes	characteristic
19	C₂×C₃×#677	C₂²	1	2	yes	—
20	C₂×C₃×C₈×D₅	C₂²	1	2	yes	—
21	C₃×#4043	—	2	2	no	—
22	C₃×#4043	C₂²	1	2	yes	—
23	C₃×#4041	C₂²	1	2	yes	—
24	C₃×#4040	—	2	2	no	—
25	C₃×D₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₃×C₄×D₂₀	—	2	1	no	—
27	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
28	C₃×C₄×D₂₀	C₂²	1	1	yes	characteristic
29	C₃×#4015	—	2	1	no	—
30	C₃×#4015	C₂²	1	1	yes	characteristic
31	C₃×C₅×#106	C₂²	1	2	yes	—
32	C₃×C₅×C₄⋊C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×#103	C₂²	1	2	yes	—
34	C₃×#3967	C₂²	1	1	yes	characteristic
35	C₃×#3952	C₂²	1	2	yes	—
36	C₃×#3948	C₂²	1	2	yes	—
37	C₃×#3942	C₂²	1	2	yes	—
38	C₃×#3942	C₂²	1	2	yes	—
39	C₃×#3941	C₂²	1	1	yes	characteristic
40	C₃×#3940	C₂²	1	1	yes	characteristic
41	C₃×C₄×#168	C₂²	1	1	yes	characteristic
42	C₃×#3298	—	5	1	no	maximal, Hall
43	#66060	C₂×C₃	1	1	yes	characteristic
44	Q₈×D₂₀	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#475	C₂×C₃	1	1	yes	characteristic, complemented
46	#65382	C₂×C₃	1	1	yes	characteristic, complemented
47	C₄×#688	C₂×C₃	1	1	yes	characteristic, complemented
48	#65153	C₂×C₃	1	2	yes	complemented
49	#65151	C₂×C₃	1	2	yes	complemented
50	#65130	C₂×C₃	1	1	yes	characteristic, complemented
51	#65123	C₂×C₃	1	1	yes	characteristic, complemented
52	#65095	C₂×C₃	1	2	yes	complemented
53	D₅×#103	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	C₃×#713	—	4	4	no	—
57	C₃×Q₈×D₅	—	2	4	no	—
58	C₃×Q₈×D₅	—	4	2	no	—
59	C₂×C₃×D₂₀	—	2	2	no	—
60	C₂×C₃×D₂₀	D₄	1	1	yes	characteristic
61	C₂×C₃×D₂₀	C₂³	1	1	yes	characteristic
62	C₂×C₃×C₄×D₅	—	2	2	no	—
63	C₂×C₃×C₄×D₅	—	2	2	no	—
64	C₂×C₃×C₄×D₅	—	2	1	no	—
65	C₂×C₃×C₄×D₅	C₂³	1	2	yes	—
66	C₂×C₃×Dic₁₀	—	2	2	no	—
67	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
68	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
69	C₃×C₅×C₄⋊C₄	—	2	1	no	—
70	C₃×C₅×C₄⋊C₄	—	2	1	no	—
71	C₃×C₅×C₄⋊C₄	C₂³	1	1	yes	characteristic
72	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
73	C₃×C₄²×C₅	—	2	1	no	—
74	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
75	C₃×#688	—	2	2	no	—
76	C₃×#685	—	2	2	no	—
77	C₃×#685	—	2	1	no	—
78	C₃×#685	—	2	2	no	—
79	C₃×#685	D₄	1	2	yes	—
80	C₃×C₄⋊Dic₅	—	2	1	no	—
81	C₃×C₄⋊Dic₅	—	2	1	no	—
82	C₃×C₄⋊Dic₅	—	2	2	no	—
83	C₃×C₄⋊Dic₅	D₄	1	1	yes	characteristic
84	C₃×C₄⋊Dic₅	C₂³	1	1	yes	characteristic
85	C₃×#683	—	2	2	no	—
86	C₂×C₃×#168	C₂³	1	1	yes	characteristic
87	C₂×C₃×#168	C₂³	1	1	yes	characteristic
88	C₃×#677	—	4	2	no	—
89	C₃×C₈×D₅	—	4	2	no	—
90	C₃×D₄×Q₈	—	5	1	no	—
91	C₃×#547	—	5	1	no	—
92	C₃×#487	—	5	1	no	—
93	C₃×#483	—	5	2	no	—
94	C₃×#475	D₅	1	1	yes	characteristic, complemented
95	C₃×#465	—	5	2	no	—
96	C₃×#461	—	5	1	no	—
97	C₃×#448	—	5	2	no	—
98	C₃×C₄×SD₁₆	—	5	1	no	—
99	C₃×C₈×D₄	—	5	1	no	—
100	C₂×C₃×#103	—	5	2	no	—
101	C₂×#713	—	2	1	no	—
102	C₂×Q₈×D₅	C₂²×C₃	1	2	yes	—
103	C₅×C₄⋊Q₈	C₂²×C₃	1	1	yes	characteristic
104	C₄×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
105	#4092	—	2	1	no	—
106	C₂×#688	C₂²×C₃	1	1	yes	characteristic
107	C₂×#677	C₂²×C₃	1	2	yes	—
108	C₂×C₈×D₅	C₂²×C₃	1	2	yes	—
109	#4043	—	2	2	no	—
110	#4043	C₂²×C₃	1	2	yes	—
111	#4041	C₂²×C₃	1	2	yes	—
112	#4040	—	2	2	no	—
113	D₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
114	C₄×D₂₀	—	2	1	no	—
115	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
116	C₄×D₂₀	C₂²×C₃	1	1	yes	characteristic
117	#4015	—	2	1	no	—
118	#4015	C₂²×C₃	1	1	yes	characteristic
119	C₅×#106	C₂²×C₃	1	2	yes	—
120	C₅×C₄⋊C₈	C₂²×C₃	1	1	yes	characteristic
121	C₅×#103	C₂²×C₃	1	2	yes	—
122	#3967	C₂²×C₃	1	1	yes	characteristic
123	#3952	C₂²×C₃	1	2	yes	—
124	#3948	C₂²×C₃	1	2	yes	—
125	#3942	C₂²×C₃	1	2	yes	—
126	#3942	C₂²×C₃	1	2	yes	—
127	#3941	C₂²×C₃	1	1	yes	characteristic
128	#3940	C₂²×C₃	1	1	yes	characteristic
129	C₄×#168	C₂²×C₃	1	1	yes	characteristic
130	#3298	—	5	1	no	Sylow
131	C₂²×C₃×D₅	—	2	1	no	—
132	C₂²×C₃×D₅	C₂×D₄	1	2	yes	—
133	C₃×C₅×Q₈	—	2	1	no	—
134	C₃×C₅×Q₈	—	4	2	no	—
135	C₃×C₅×Q₈	#41	1	2	yes	complemented
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
140	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
141	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
142	C₂×C₃×Dic₅	—	2	1	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
145	C₃×D₂₀	—	2	1	no	—
146	C₃×D₂₀	—	2	1	no	—
147	C₃×D₂₀	—	4	4	no	—
148	C₃×D₂₀	SD₁₆	1	4	yes	complemented
149	C₃×C₄×D₅	—	2	2	no	—
150	C₃×C₄×D₅	—	2	2	no	—
151	C₃×C₄×D₅	—	4	4	no	—
152	C₃×C₄×D₅	—	4	4	no	—
153	C₃×C₄×D₅	—	4	2	no	—
154	C₃×Dic₁₀	—	2	2	no	—
155	C₃×Dic₁₀	—	2	2	no	—
156	C₃×Dic₁₀	—	4	4	no	—
157	C₃×C₅×C₈	—	2	2	no	—
158	C₃×#168	—	2	1	no	—
159	C₃×#168	—	2	1	no	—
160	C₂×C₃×#41	—	10	1	no	—
161	C₂²×C₃×Q₈	—	5	2	no	—
162	C₂×C₃×SD₁₆	—	5	1	no	—
163	C₂×C₃×SD₁₆	—	5	2	no	—
164	C₂²×C₃×C₈	—	5	2	no	—
165	C₃×C₄⋊Q₈	—	5	1	no	—
166	C₃×C₄⋊Q₈	—	10	1	no	—
167	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic
168	C₃×#123	—	10	2	no	—
169	C₃×C₂²⋊Q₈	—	5	2	no	—
170	C₃×C₂²⋊Q₈	—	10	2	no	—
171	C₃×C₂²⋊Q₈	—	10	1	no	—
172	C₃×#121	—	5	2	no	—
173	C₃×C₄×Q₈	C₂×D₅	1	1	yes	characteristic
174	C₃×C₄×D₄	—	5	1	no	—
175	C₃×C₄×D₄	—	5	1	no	—
176	C₃×C₄×D₄	—	10	1	no	—
177	C₂×C₃×C₄⋊C₄	—	5	2	no	—
178	C₃×#106	—	5	1	no	—
179	C₃×#106	C₂×D₅	1	2	yes	—
180	C₃×C₄⋊C₈	C₂×D₅	1	1	yes	characteristic
181	C₃×#103	—	5	1	no	—
182	C₃×#103	—	5	2	no	—
183	C₃×#103	—	5	2	no	—
184	C₃×#103	—	5	2	no	—
185	C₃×#103	C₂×D₅	1	2	yes	—
186	C₃×#102	—	5	1	no	—
187	C₃×C₂²⋊C₈	—	5	2	no	—
188	C₃×C₄×C₈	—	5	1	no	—
189	C₂×C₅×Q₈	—	2	1	no	—
190	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
191	#713	—	4	4	no	—
192	Q₈×D₅	—	2	4	no	—
193	Q₈×D₅	—	4	2	no	—
194	C₂×D₂₀	—	2	2	no	—
195	C₂×D₂₀	C₃×D₄	1	1	yes	characteristic
196	C₂×D₂₀	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₄×D₅	—	2	2	no	—
198	C₂×C₄×D₅	—	2	2	no	—
199	C₂×C₄×D₅	—	2	1	no	—
200	C₂×C₄×D₅	C₂³×C₃	1	2	yes	—
201	C₂×Dic₁₀	—	2	2	no	—
202	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
203	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
204	C₅×C₄⋊C₄	—	2	1	no	—
205	C₅×C₄⋊C₄	—	2	1	no	—
206	C₅×C₄⋊C₄	C₂³×C₃	1	1	yes	characteristic
207	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
208	C₄²×C₅	—	2	1	no	—
209	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
210	#688	—	2	2	no	—
211	#685	—	2	2	no	—
212	#685	—	2	1	no	—
213	#685	—	2	2	no	—
214	#685	C₃×D₄	1	2	yes	—
215	C₄⋊Dic₅	—	2	1	no	—
216	C₄⋊Dic₅	—	2	1	no	—
217	C₄⋊Dic₅	—	2	2	no	—
218	C₄⋊Dic₅	C₃×D₄	1	1	yes	characteristic
219	C₄⋊Dic₅	C₂³×C₃	1	1	yes	characteristic
220	#683	—	2	2	no	—
221	C₂×#168	C₂³×C₃	1	1	yes	characteristic
222	C₂×#168	C₂³×C₃	1	1	yes	characteristic
223	#677	—	4	2	no	—
224	C₈×D₅	—	4	2	no	—
225	D₄×Q₈	—	5	1	no	—
226	#547	—	5	1	no	—
227	#487	—	5	1	no	—
228	#483	—	5	2	no	—
229	#475	C₃×D₅	1	1	yes	characteristic, complemented
230	#465	—	5	2	no	—
231	#461	—	5	1	no	—
232	#448	—	5	2	no	—
233	C₄×SD₁₆	—	5	1	no	—
234	C₈×D₄	—	5	1	no	—
235	C₂×#103	—	5	2	no	—
236	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
237	C₂×C₃×D₅	—	2	2	no	—
238	C₂×C₃×D₅	—	2	2	no	—
239	C₂×C₃×D₅	—	4	1	no	—
240	C₂×C₃×D₅	—	4	1	no	—
241	C₂×C₃×D₅	—	4	1	no	—
242	C₂×C₃×D₅	C₂×SD₁₆	1	4	yes	—
243	C₃×C₄×C₅	—	2	2	no	—
244	C₃×C₄×C₅	—	2	1	no	—
245	C₃×C₄×C₅	—	4	2	no	—
246	C₃×C₄×C₅	—	4	1	no	—
247	C₃×C₄×C₅	C₂×SD₁₆	1	2	yes	—
248	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
249	C₃×C₄×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₃×Dic₅	—	2	2	no	—
251	C₃×Dic₅	—	4	2	no	—
252	C₃×Dic₅	—	4	1	no	—
253	C₃×#41	—	20	4	no	—
254	C₂×C₃×Q₈	—	2	1	no	—
255	C₂×C₃×Q₈	—	5	2	no	—
256	C₂×C₃×Q₈	—	10	2	no	—
257	C₂×C₃×Q₈	—	10	4	no	—
258	C₂×C₃×Q₈	—	20	2	no	—
259	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
260	C₂×C₃×D₄	—	5	1	no	—
261	C₂×C₃×D₄	—	5	1	no	—
262	C₂×C₃×D₄	—	10	2	no	—
263	C₂²×C₃×C₄	—	5	2	no	—
264	C₂²×C₃×C₄	—	10	2	no	—
265	C₂²×C₃×C₄	—	10	2	no	—
266	C₂²×C₃×C₄	—	10	1	no	—
267	C₃×SD₁₆	—	10	2	no	—
268	C₃×SD₁₆	—	20	2	no	—
269	C₂×C₃×C₈	—	5	1	no	—
270	C₂×C₃×C₈	—	5	1	no	—
271	C₂×C₃×C₈	—	20	2	no	—
272	C₂×C₃×C₈	C₂²×D₅	1	2	yes	—
273	C₃×C₄⋊C₄	—	2	1	no	—
274	C₃×C₄⋊C₄	—	2	1	no	—
275	C₃×C₄⋊C₄	—	5	1	no	—
276	C₃×C₄⋊C₄	—	5	1	no	—
277	C₃×C₄⋊C₄	—	10	2	no	—
278	C₃×C₄⋊C₄	—	10	2	no	—
279	C₃×C₄⋊C₄	—	10	1	no	—
280	C₃×C₄⋊C₄	—	10	1	no	—
281	C₃×C₄⋊C₄	C₂²×D₅	1	1	yes	characteristic
282	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
283	C₃×C₂²⋊C₄	—	5	2	no	—
284	C₃×C₂²⋊C₄	—	10	2	no	—
285	C₃×C₂²⋊C₄	—	10	2	no	—
286	C₃×C₂²⋊C₄	—	10	1	no	—
287	C₃×C₄²	—	2	1	no	—
288	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
289	C₂²×D₅	—	2	1	no	—
290	C₂²×D₅	C₂×C₃×D₄	1	2	yes	—
291	C₅×Q₈	—	2	1	no	—
292	C₅×Q₈	—	4	2	no	—
293	C₅×Q₈	C₃×#41	1	2	yes	complemented
294	C₂×C₄×C₅	—	2	1	no	—
295	C₂×C₄×C₅	—	2	2	no	—
296	C₂×C₄×C₅	—	2	1	no	—
297	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
298	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
299	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
300	C₂×Dic₅	—	2	1	no	—
301	C₂×Dic₅	—	2	2	no	—
302	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
303	D₂₀	—	2	1	no	—
304	D₂₀	—	2	1	no	—
305	D₂₀	—	4	4	no	—
306	D₂₀	C₃×SD₁₆	1	4	yes	complemented
307	C₄×D₅	—	2	2	no	—
308	C₄×D₅	—	2	2	no	—
309	C₄×D₅	—	4	4	no	—
310	C₄×D₅	—	4	4	no	—
311	C₄×D₅	—	4	2	no	—
312	Dic₁₀	—	2	2	no	—
313	Dic₁₀	—	2	2	no	—
314	Dic₁₀	—	4	4	no	—
315	C₅×C₈	—	2	2	no	—
316	#168	—	2	1	no	—
317	#168	—	2	1	no	—
318	C₂×#41	—	10	1	no	—
319	C₂²×Q₈	—	5	2	no	—
320	C₂×SD₁₆	—	5	1	no	—
321	C₂×SD₁₆	—	5	2	no	—
322	C₂²×C₈	—	5	2	no	—
323	C₄⋊Q₈	—	5	1	no	—
324	C₄⋊Q₈	—	10	1	no	—
325	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic
326	#123	—	10	2	no	—
327	C₂²⋊Q₈	—	5	2	no	—
328	C₂²⋊Q₈	—	10	2	no	—
329	C₂²⋊Q₈	—	10	1	no	—
330	#121	—	5	2	no	—
331	C₄×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
332	C₄×D₄	—	5	1	no	—
333	C₄×D₄	—	5	1	no	—
334	C₄×D₄	—	10	1	no	—
335	C₂×C₄⋊C₄	—	5	2	no	—
336	#106	—	5	1	no	—
337	#106	C₂×C₃×D₅	1	2	yes	—
338	C₄⋊C₈	C₂×C₃×D₅	1	1	yes	characteristic
339	#103	—	5	1	no	—
340	#103	—	5	2	no	—
341	#103	—	5	2	no	—
342	#103	—	5	2	no	—
343	#103	C₂×C₃×D₅	1	2	yes	—
344	#102	—	5	1	no	—
345	C₂²⋊C₈	—	5	2	no	—
346	C₄×C₈	—	5	1	no	—
347	C₂×C₃×C₅	#546	1	1	yes	characteristic
348	C₂×C₃×C₅	C₂²×SD₁₆	1	1	yes	characteristic
349	C₂×C₃×C₅	#578	1	1	yes	characteristic
350	C₃×D₅	—	2	4	no	—
351	C₃×D₅	—	8	1	no	—
352	C₂³×C₃	—	5	2	no	—
353	C₂³×C₃	—	10	1	no	—
354	C₃×Q₈	—	2	1	no	—
355	C₃×Q₈	—	4	2	no	—
356	C₃×Q₈	—	10	2	no	—
357	C₃×Q₈	—	10	2	no	—
358	C₃×Q₈	—	20	4	no	—
359	C₃×Q₈	#713	1	2	yes	complemented
360	C₃×D₄	—	5	4	no	—
361	C₃×D₄	—	10	1	no	—
362	C₃×D₄	—	10	1	no	—
363	C₃×D₄	—	20	4	no	—
364	C₂×C₃×C₄	—	2	1	no	—
365	C₂×C₃×C₄	—	2	1	no	—
366	C₂×C₃×C₄	—	2	2	no	—
367	C₂×C₃×C₄	—	5	2	no	—
368	C₂×C₃×C₄	—	10	2	no	—
369	C₂×C₃×C₄	—	10	2	no	—
370	C₂×C₃×C₄	—	10	1	no	—
371	C₂×C₃×C₄	—	10	2	no	—
372	C₂×C₃×C₄	—	20	4	no	—
373	C₂×C₃×C₄	—	20	4	no	—
374	C₂×C₃×C₄	—	20	2	no	—
375	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
376	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
377	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
378	C₃×C₈	—	2	2	no	—
379	C₃×C₈	—	10	1	no	—
380	C₃×C₈	—	10	1	no	—
381	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
382	C₂×D₅	—	2	2	no	—
383	C₂×D₅	—	2	2	no	—
384	C₂×D₅	—	4	1	no	—
385	C₂×D₅	—	4	1	no	—
386	C₂×D₅	—	4	1	no	—
387	C₂×D₅	C₂×C₃×SD₁₆	1	4	yes	—
388	C₄×C₅	—	2	1	no	—
389	C₄×C₅	—	2	2	no	—
390	C₄×C₅	—	4	2	no	—
391	C₄×C₅	—	4	1	no	—
392	C₄×C₅	C₂×C₃×SD₁₆	1	2	yes	—
393	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
394	C₄×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
395	Dic₅	—	2	2	no	—
396	Dic₅	—	4	1	no	—
397	Dic₅	—	4	2	no	—
398	#41	—	20	4	no	—
399	C₂×Q₈	—	2	1	no	—
400	C₂×Q₈	—	5	2	no	—
401	C₂×Q₈	—	10	2	no	—
402	C₂×Q₈	—	10	4	no	—
403	C₂×Q₈	—	20	2	no	—
404	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
405	C₂×D₄	—	5	1	no	—
406	C₂×D₄	—	5	1	no	—
407	C₂×D₄	—	10	2	no	—
408	C₂²×C₄	—	5	2	no	—
409	C₂²×C₄	—	10	2	no	—
410	C₂²×C₄	—	10	2	no	—
411	C₂²×C₄	—	10	1	no	—
412	SD₁₆	—	10	2	no	—
413	SD₁₆	—	20	2	no	—
414	C₂×C₈	—	5	1	no	—
415	C₂×C₈	—	5	1	no	—
416	C₂×C₈	—	20	2	no	—
417	C₂×C₈	C₂²×C₃×D₅	1	2	yes	—
418	C₄⋊C₄	—	2	1	no	—
419	C₄⋊C₄	—	2	1	no	—
420	C₄⋊C₄	—	5	1	no	—
421	C₄⋊C₄	—	5	1	no	—
422	C₄⋊C₄	—	10	2	no	—
423	C₄⋊C₄	—	10	2	no	—
424	C₄⋊C₄	—	10	1	no	—
425	C₄⋊C₄	—	10	1	no	—
426	C₄⋊C₄	C₂²×C₃×D₅	1	1	yes	characteristic
427	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
428	C₂²⋊C₄	—	5	2	no	—
429	C₂²⋊C₄	—	10	2	no	—
430	C₂²⋊C₄	—	10	2	no	—
431	C₂²⋊C₄	—	10	1	no	—
432	C₄²	—	2	1	no	—
433	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
434	C₃×C₅	#3298	1	1	yes	characteristic, complemented, Hall
435	C₂²×C₃	—	5	4	no	—
436	C₂²×C₃	—	10	2	no	—
437	C₂²×C₃	—	10	2	no	—
438	C₂²×C₃	—	20	1	no	—
439	C₂²×C₃	—	20	1	no	—
440	C₂²×C₃	—	20	1	no	—
441	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
442	C₃×C₄	—	2	1	no	—
443	C₃×C₄	—	2	2	no	—
444	C₃×C₄	—	4	2	no	—
445	C₃×C₄	—	4	1	no	—
446	C₃×C₄	—	10	2	no	—
447	C₃×C₄	—	20	1	no	—
448	C₃×C₄	—	20	2	no	—
449	C₃×C₄	D₅×SD₁₆	1	2	yes	—
450	C₃×C₄	C₂×#713	1	1	yes	characteristic
451	C₃×C₄	#4149	1	1	yes	characteristic
452	C₂×C₅	C₃×#546	1	1	yes	characteristic
453	C₂×C₅	C₂²×C₃×SD₁₆	1	1	yes	characteristic
454	C₂×C₅	C₃×#578	1	1	yes	characteristic
455	D₅	—	2	4	no	—
456	D₅	—	8	1	no	—
457	C₂³	—	5	2	no	—
458	C₂³	—	10	1	no	—
459	Q₈	—	2	1	no	—
460	Q₈	—	4	2	no	—
461	Q₈	—	10	2	no	—
462	Q₈	—	10	2	no	—
463	Q₈	—	20	4	no	—
464	Q₈	C₃×#713	1	2	yes	complemented
465	D₄	—	5	4	no	—
466	D₄	—	10	1	no	—
467	D₄	—	10	1	no	—
468	D₄	—	20	4	no	—
469	C₂×C₄	—	2	1	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	—	5	2	no	—
473	C₂×C₄	—	10	2	no	—
474	C₂×C₄	—	10	2	no	—
475	C₂×C₄	—	10	1	no	—
476	C₂×C₄	—	10	2	no	—
477	C₂×C₄	—	20	4	no	—
478	C₂×C₄	—	20	4	no	—
479	C₂×C₄	—	20	2	no	—
480	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
481	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
482	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
483	C₈	—	2	2	no	—
484	C₈	—	10	1	no	—
485	C₈	—	10	1	no	—
486	C₂×C₃	—	10	4	no	—
487	C₂×C₃	—	40	1	no	—
488	C₂×C₃	#65964	1	1	yes	characteristic
489	C₂×C₃	C₂×D₅×SD₁₆	1	1	yes	characteristic
490	C₂×C₃	#66113	1	1	yes	characteristic
491	C₅	C₃×#3298	1	1	yes	characteristic, complemented, Sylow
492	C₂²	—	5	4	no	—
493	C₂²	—	10	2	no	—
494	C₂²	—	10	2	no	—
495	C₂²	—	20	1	no	—
496	C₂²	—	20	1	no	—
497	C₂²	—	20	1	no	—
498	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
499	C₄	—	2	1	no	—
500	C₄	—	2	2	no	—
501	C₄	—	4	1	no	—
502	C₄	—	4	2	no	—
503	C₄	—	10	2	no	—
504	C₄	—	20	2	no	—
505	C₄	—	20	1	no	—
506	C₄	C₃×D₅×SD₁₆	1	2	yes	—
507	C₄	C₂×C₃×#713	1	1	yes	characteristic
508	C₄	C₃×#4149	1	1	yes	characteristic
509	C₃	#10612753	1	1	yes	characteristic, direct product factor, Sylow
510	C₂	—	10	4	no	—
511	C₂	—	40	1	no	—
512	C₂	C₃×#65964	1	1	yes	characteristic
513	C₂	C₂×C₃×D₅×SD₁₆	1	1	yes	characteristic
514	C₂	C₃×#66113	1	1	yes	characteristic

	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×#475	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₃×#66060	C₂
hypercenter	C₃×#475	D₅
hypocenter	C₅	C₃×#3298
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#475

Complements

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

N	H ≅ G/N	type
2. C₃×Q₈×D₂₀	C₂	semidirect
3. C₃×C₅×#475	C₂	semidirect
4. C₃×#65382	C₂	semidirect
5. C₃×C₄×#688	C₂	semidirect
6. C₃×#65153	C₂	semidirect
7. C₃×#65151	C₂	semidirect
8. C₃×#65130	C₂	semidirect
9. C₃×#65123	C₂	semidirect
10. C₃×#65095	C₂	semidirect
11. C₃×D₅×#103	C₂	semidirect
12. #10612753	C₃	direct (N × H)
44. Q₈×D₂₀	C₂×C₃	semidirect
45. C₅×#475	C₂×C₃	semidirect
46. #65382	C₂×C₃	semidirect
47. C₄×#688	C₂×C₃	semidirect
48. #65153	C₂×C₃	semidirect
49. #65151	C₂×C₃	semidirect
50. #65130	C₂×C₃	semidirect
51. #65123	C₂×C₃	semidirect
52. #65095	C₂×C₃	semidirect
53. D₅×#103	C₂×C₃	semidirect
94. C₃×#475	D₅	semidirect
135. C₃×C₅×Q₈	#41	semidirect
148. C₃×D₂₀	SD₁₆	semidirect
229. #475	C₃×D₅	semidirect
293. C₅×Q₈	C₃×#41	semidirect
306. D₂₀	C₃×SD₁₆	semidirect
359. C₃×Q₈	#713	semidirect
434. C₃×C₅	#3298	semidirect
464. Q₈	C₃×#713	semidirect
491. C₅	C₃×#3298	semidirect
509. C₃	#10612753	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×#66060	2
C₃×Q₈×D₂₀	2
C₃×C₅×#475	2
C₃×#65382	2
C₃×C₄×#688	2
C₃×#65153	2
C₃×#65151	2
C₃×#65130	2
C₃×#65123	2
C₃×#65095	2
C₃×D₅×#103	2
#10612753	3
C₃×#3298	5

Subgroups — C3×#10612753 #14459113

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612753 #14459113