Subgroups — C₃×#10611624 #14458102

Order 1920.

920 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	C₃×#66104	C₂	1	2	yes	maximal, complemented
2	C₃×#66085	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#443	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65430	C₂	1	2	yes	maximal, complemented
5	C₃×#65187	C₂	1	2	yes	maximal, complemented
6	C₃×#65115	C₂	1	2	yes	maximal, complemented
7	C₃×#65111	C₂	1	2	yes	maximal, complemented
8	C₃×#64989	C₂	1	1	yes	maximal, characteristic, complemented
9	C₃×#64982	C₂	1	1	yes	maximal, characteristic, complemented
10	#10611624	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×#4150	C₂²	1	2	yes	—
12	C₃×#4149	C₂²	1	2	yes	complemented
13	C₃×C₅×#135	C₂²	1	1	yes	characteristic
14	C₃×C₅×#131	C₂²	1	2	yes	complemented
15	C₃×#4097	C₂²	1	2	yes	complemented
16	C₃×#4095	C₂²	1	2	yes	—
17	C₃×#4064	—	2	2	no	—
18	C₃×#4062	—	2	2	no	—
19	C₃×D₅×SD₁₆	—	2	2	no	—
20	C₃×#4057	—	2	2	no	—
21	C₃×#4055	—	2	2	no	—
22	C₃×#4055	C₂²	1	2	yes	complemented
23	C₃×#4054	—	2	2	no	—
24	C₃×#4054	C₂²	1	2	yes	—
25	C₃×#4050	—	2	2	no	—
26	C₃×#4050	C₂²	1	1	yes	characteristic
27	C₂×C₃×#677	—	2	2	no	—
28	C₂×C₃×#677	C₂²	1	2	yes	complemented
29	C₂×C₃×#677	C₂²	1	2	yes	complemented
30	C₃×#4047	C₂²	1	2	yes	complemented
31	C₃×#4020	C₂²	1	1	yes	characteristic
32	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#108	C₂²	1	1	yes	characteristic, complemented
34	C₃×C₅×#104	C₂²	1	2	yes	complemented
35	C₃×C₄×C₅×C₈	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3956	C₂²	1	2	yes	complemented
37	C₃×#3955	C₂²	1	2	yes	complemented
38	C₃×#3951	C₂²	1	1	yes	characteristic, complemented
39	C₃×#3937	C₂²	1	2	yes	complemented
40	C₃×#3291	—	5	1	no	maximal, Hall
41	#66104	C₂×C₃	1	2	yes	complemented
42	#66085	C₂×C₃	1	2	yes	complemented
43	C₅×#443	C₂×C₃	1	1	yes	characteristic, complemented
44	#65430	C₂×C₃	1	2	yes	complemented
45	#65187	C₂×C₃	1	2	yes	complemented
46	#65115	C₂×C₃	1	2	yes	complemented
47	#65111	C₂×C₃	1	2	yes	complemented
48	#64989	C₂×C₃	1	1	yes	characteristic, complemented
49	#64982	C₂×C₃	1	1	yes	characteristic, complemented
50	C₃×C₅×#41	C₂³	1	2	yes	—
51	C₃×#713	—	2	2	no	—
52	C₃×Q₈×D₅	—	2	2	no	—
53	C₃×#711	—	2	2	no	—
54	C₃×#711	—	4	2	no	—
55	C₃×D₄×D₅	—	2	2	no	—
56	C₃×D₄×D₅	—	4	2	no	—
57	C₃×#709	—	2	2	no	—
58	C₃×#709	—	2	2	no	—
59	C₃×#709	C₂³	1	2	yes	—
60	C₂×C₃×D₂₀	—	2	2	no	—
61	C₂×C₃×D₂₀	—	4	1	no	—
62	C₂×C₃×D₂₀	C₂³	1	2	yes	—
63	C₂×C₃×Dic₁₀	—	2	2	no	—
64	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
65	C₃×C₅×Q₁₆	D₄	1	1	yes	characteristic, complemented
66	C₃×C₅×SD₁₆	D₄	1	2	yes	complemented
67	C₃×C₅×D₈	D₄	1	1	yes	characteristic, complemented
68	C₃×C₅×M₁₆	—	2	2	no	—
69	C₃×C₅×M₁₆	C₂³	1	2	yes	—
70	C₂×C₃×C₅×C₈	—	2	2	no	—
71	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
72	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
73	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
74	C₃×#689	—	2	2	no	—
75	C₃×#688	—	2	2	no	—
76	C₃×#687	—	2	2	no	—
77	C₃×#686	—	2	2	no	—
78	C₃×C₄⋊Dic₅	—	4	1	no	—
79	C₃×#681	C₂³	1	2	yes	—
80	C₃×Dic₂₀	—	2	2	no	—
81	C₃×Dic₂₀	D₄	1	1	yes	characteristic, complemented
82	C₃×D₄₀	—	2	2	no	—
83	C₃×D₄₀	D₄	1	1	yes	characteristic, complemented
84	C₃×#677	—	2	2	no	—
85	C₃×#677	—	2	2	no	—
86	C₃×#677	—	2	2	no	—
87	C₃×#677	—	2	2	no	—
88	C₃×#677	—	2	2	no	—
89	C₃×#677	—	2	2	no	—
90	C₃×#677	D₄	1	2	yes	complemented
91	C₃×#676	—	2	2	no	—
92	C₃×C₈×D₅	—	2	2	no	—
93	C₃×#577	—	5	2	no	—
94	C₃×#577	—	5	2	no	—
95	C₃×#492	—	5	1	no	—
96	C₃×#471	—	5	2	no	—
97	C₃×#471	—	5	2	no	—
98	C₃×#456	—	5	2	no	—
99	C₃×#453	—	5	2	no	—
100	C₃×#443	—	5	1	no	—
101	C₃×#443	D₅	1	1	yes	characteristic, complemented
102	#4150	C₂²×C₃	1	2	yes	—
103	#4149	C₂²×C₃	1	2	yes	complemented
104	C₅×#135	C₂²×C₃	1	1	yes	characteristic
105	C₅×#131	C₂²×C₃	1	2	yes	complemented
106	#4097	C₂²×C₃	1	2	yes	complemented
107	#4095	C₂²×C₃	1	2	yes	—
108	#4064	—	2	2	no	—
109	#4062	—	2	2	no	—
110	D₅×SD₁₆	—	2	2	no	—
111	#4057	—	2	2	no	—
112	#4055	—	2	2	no	—
113	#4055	C₂²×C₃	1	2	yes	complemented
114	#4054	—	2	2	no	—
115	#4054	C₂²×C₃	1	2	yes	—
116	#4050	—	2	2	no	—
117	#4050	C₂²×C₃	1	1	yes	characteristic
118	C₂×#677	—	2	2	no	—
119	C₂×#677	C₂²×C₃	1	2	yes	complemented
120	C₂×#677	C₂²×C₃	1	2	yes	complemented
121	#4047	C₂²×C₃	1	2	yes	complemented
122	#4020	C₂²×C₃	1	1	yes	characteristic
123	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
124	C₅×#108	C₂²×C₃	1	1	yes	characteristic, complemented
125	C₅×#104	C₂²×C₃	1	2	yes	complemented
126	C₄×C₅×C₈	C₂²×C₃	1	1	yes	characteristic, complemented
127	#3956	C₂²×C₃	1	2	yes	complemented
128	#3955	C₂²×C₃	1	2	yes	complemented
129	#3951	C₂²×C₃	1	1	yes	characteristic, complemented
130	#3937	C₂²×C₃	1	2	yes	complemented
131	#3291	—	5	1	no	Sylow
132	C₂²×C₃×D₅	—	2	2	no	—
133	C₂²×C₃×D₅	—	4	2	no	—
134	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
135	C₃×C₅×D₄	—	2	2	no	—
136	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
140	C₃×C₂²⋊D₅	—	2	2	no	—
141	C₃×C₂²⋊D₅	—	4	2	no	—
142	C₃×C₂²⋊D₅	—	4	2	no	—
143	C₂×C₃×Dic₅	—	2	2	no	—
144	C₂×C₃×Dic₅	—	4	2	no	—
145	C₃×D₂₀	—	2	2	no	—
146	C₃×D₂₀	—	2	2	no	—
147	C₃×D₂₀	—	4	2	no	—
148	C₃×D₂₀	—	8	2	no	—
149	C₃×D₂₀	C₂×D₄	1	2	yes	—
150	C₃×C₄×D₅	—	2	2	no	—
151	C₃×C₄×D₅	—	4	2	no	—
152	C₃×C₄×D₅	—	4	2	no	—
153	C₃×Dic₁₀	—	2	2	no	—
154	C₃×Dic₁₀	—	2	2	no	—
155	C₃×Dic₁₀	—	4	2	no	—
156	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
157	C₃×C₅×C₈	—	2	2	no	—
158	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
159	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
160	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
161	C₃×C₅×C₈	C₂×D₄	1	1	yes	characteristic
162	C₃×#168	—	2	2	no	—
163	C₃×2₋¹⁺⁴	—	5	2	no	—
164	C₃×H(5,𝔽₂)	—	5	2	no	—
165	C₃×#137	—	5	2	no	—
166	C₃×#137	—	5	2	no	—
167	C₃×#137	—	10	2	no	—
168	C₃×#137	—	10	2	no	—
169	C₃×AGL(1,ℤ/8)	—	5	2	no	—
170	C₃×AGL(1,ℤ/8)	—	5	2	no	—
171	C₃×AGL(1,ℤ/8)	—	10	2	no	—
172	C₃×AGL(1,ℤ/8)	—	10	2	no	—
173	C₃×#135	—	5	1	no	—
174	C₃×#135	—	10	2	no	—
175	C₃×#135	—	10	2	no	—
176	C₃×#135	C₂×D₅	1	1	yes	characteristic
177	C₂×C₃×SD₁₆	—	5	2	no	—
178	C₂×C₃×SD₁₆	—	5	2	no	—
179	C₂×C₃×SD₁₆	—	10	2	no	—
180	C₂×C₃×SD₁₆	—	10	2	no	—
181	C₃×#131	—	5	2	no	—
182	C₃×#131	C₂×D₅	1	2	yes	complemented
183	C₃×C₄⋊Q₈	—	5	1	no	—
184	C₃×#127	—	5	1	no	—
185	C₃×#108	—	5	1	no	—
186	C₃×#108	C₂×D₅	1	1	yes	characteristic, complemented
187	C₃×#104	—	5	2	no	—
188	C₃×#104	C₂×D₅	1	2	yes	complemented
189	C₃×#101	—	5	2	no	—
190	C₃×#100	—	5	2	no	—
191	C₃×C₄×C₈	C₂×D₅	1	1	yes	characteristic, complemented
192	C₅×#41	C₂³×C₃	1	2	yes	—
193	#713	—	2	2	no	—
194	Q₈×D₅	—	2	2	no	—
195	#711	—	2	2	no	—
196	#711	—	4	2	no	—
197	D₄×D₅	—	2	2	no	—
198	D₄×D₅	—	4	2	no	—
199	#709	—	2	2	no	—
200	#709	—	2	2	no	—
201	#709	C₂³×C₃	1	2	yes	—
202	C₂×D₂₀	—	2	2	no	—
203	C₂×D₂₀	—	4	1	no	—
204	C₂×D₂₀	C₂³×C₃	1	2	yes	—
205	C₂×Dic₁₀	—	2	2	no	—
206	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
207	C₅×Q₁₆	C₃×D₄	1	1	yes	characteristic, complemented
208	C₅×SD₁₆	C₃×D₄	1	2	yes	complemented
209	C₅×D₈	C₃×D₄	1	1	yes	characteristic, complemented
210	C₅×M₁₆	—	2	2	no	—
211	C₅×M₁₆	C₂³×C₃	1	2	yes	—
212	C₂×C₅×C₈	—	2	2	no	—
213	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
214	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
215	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
216	#689	—	2	2	no	—
217	#688	—	2	2	no	—
218	#687	—	2	2	no	—
219	#686	—	2	2	no	—
220	C₄⋊Dic₅	—	4	1	no	—
221	#681	C₂³×C₃	1	2	yes	—
222	Dic₂₀	—	2	2	no	—
223	Dic₂₀	C₃×D₄	1	1	yes	characteristic, complemented
224	D₄₀	—	2	2	no	—
225	D₄₀	C₃×D₄	1	1	yes	characteristic, complemented
226	#677	—	2	2	no	—
227	#677	—	2	2	no	—
228	#677	—	2	2	no	—
229	#677	—	2	2	no	—
230	#677	—	2	2	no	—
231	#677	—	2	2	no	—
232	#677	C₃×D₄	1	2	yes	complemented
233	#676	—	2	2	no	—
234	C₈×D₅	—	2	2	no	—
235	#577	—	5	2	no	—
236	#577	—	5	2	no	—
237	#492	—	5	1	no	—
238	#471	—	5	2	no	—
239	#471	—	5	2	no	—
240	#456	—	5	2	no	—
241	#453	—	5	2	no	—
242	#443	—	5	1	no	—
243	#443	C₃×D₅	1	1	yes	characteristic, complemented
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₃×D₅	—	2	2	no	—
247	C₂×C₃×D₅	—	4	2	no	—
248	C₂×C₃×D₅	—	8	2	no	—
249	C₂×C₃×D₅	—	16	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
253	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
254	C₃×Dic₅	—	2	2	no	—
255	C₃×Dic₅	—	4	2	no	—
256	C₃×#41	—	5	2	no	—
257	C₃×#41	—	10	2	no	—
258	C₃×#41	—	10	2	no	—
259	C₃×#41	—	10	2	no	—
260	C₃×#41	—	10	2	no	—
261	C₃×#41	—	20	2	no	—
262	C₃×#41	C₂²×D₅	1	2	yes	—
263	C₂×C₃×Q₈	—	5	2	no	—
264	C₂×C₃×Q₈	—	10	2	no	—
265	C₂×C₃×Q₈	—	10	2	no	—
266	C₂×C₃×D₄	—	5	2	no	—
267	C₂×C₃×D₄	—	10	2	no	—
268	C₂×C₃×D₄	—	10	2	no	—
269	C₂×C₃×D₄	—	20	1	no	—
270	C₂×C₃×D₄	—	20	2	no	—
271	C₃×Q₁₆	—	5	1	no	—
272	C₃×Q₁₆	—	10	2	no	—
273	C₃×Q₁₆	—	10	2	no	—
274	C₃×Q₁₆	D₂₀	1	1	yes	characteristic, complemented
275	C₃×SD₁₆	—	5	2	no	—
276	C₃×SD₁₆	—	10	2	no	—
277	C₃×SD₁₆	—	10	2	no	—
278	C₃×SD₁₆	—	10	2	no	—
279	C₃×SD₁₆	—	10	2	no	—
280	C₃×SD₁₆	—	10	2	no	—
281	C₃×SD₁₆	—	10	2	no	—
282	C₃×SD₁₆	—	10	2	no	—
283	C₃×SD₁₆	—	10	2	no	—
284	C₃×SD₁₆	D₂₀	1	2	yes	complemented
285	C₃×D₈	—	5	1	no	—
286	C₃×D₈	—	10	2	no	—
287	C₃×D₈	—	10	2	no	—
288	C₃×D₈	D₂₀	1	1	yes	characteristic, complemented
289	C₃×M₁₆	—	2	2	no	—
290	C₃×M₁₆	—	5	2	no	—
291	C₃×M₁₆	—	10	2	no	—
292	C₃×M₁₆	C₂²×D₅	1	2	yes	—
293	C₂×C₃×C₈	—	2	2	no	—
294	C₂×C₃×C₈	—	10	2	no	—
295	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
296	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
297	C₃×C₄⋊C₄	—	20	1	no	—
298	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
299	C₂²×D₅	—	2	2	no	—
300	C₂²×D₅	—	4	2	no	—
301	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
302	C₅×D₄	—	2	2	no	—
303	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
307	C₂²⋊D₅	—	2	2	no	—
308	C₂²⋊D₅	—	4	2	no	—
309	C₂²⋊D₅	—	4	2	no	—
310	C₂×Dic₅	—	2	2	no	—
311	C₂×Dic₅	—	4	2	no	—
312	D₂₀	—	2	2	no	—
313	D₂₀	—	2	2	no	—
314	D₂₀	—	4	2	no	—
315	D₂₀	—	8	2	no	—
316	D₂₀	C₂×C₃×D₄	1	2	yes	—
317	C₄×D₅	—	2	2	no	—
318	C₄×D₅	—	4	2	no	—
319	C₄×D₅	—	4	2	no	—
320	Dic₁₀	—	2	2	no	—
321	Dic₁₀	—	2	2	no	—
322	Dic₁₀	—	4	2	no	—
323	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
324	C₅×C₈	—	2	2	no	—
325	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
326	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
327	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
328	C₅×C₈	C₂×C₃×D₄	1	1	yes	characteristic
329	#168	—	2	2	no	—
330	2₋¹⁺⁴	—	5	2	no	—
331	H(5,𝔽₂)	—	5	2	no	—
332	#137	—	5	2	no	—
333	#137	—	5	2	no	—
334	#137	—	10	2	no	—
335	#137	—	10	2	no	—
336	AGL(1,ℤ/8)	—	5	2	no	—
337	AGL(1,ℤ/8)	—	5	2	no	—
338	AGL(1,ℤ/8)	—	10	2	no	—
339	AGL(1,ℤ/8)	—	10	2	no	—
340	#135	—	5	1	no	—
341	#135	—	10	2	no	—
342	#135	—	10	2	no	—
343	#135	C₂×C₃×D₅	1	1	yes	characteristic
344	C₂×SD₁₆	—	5	2	no	—
345	C₂×SD₁₆	—	5	2	no	—
346	C₂×SD₁₆	—	10	2	no	—
347	C₂×SD₁₆	—	10	2	no	—
348	#131	—	5	2	no	—
349	#131	C₂×C₃×D₅	1	2	yes	complemented
350	C₄⋊Q₈	—	5	1	no	—
351	#127	—	5	1	no	—
352	#108	—	5	1	no	—
353	#108	C₂×C₃×D₅	1	1	yes	characteristic, complemented
354	#104	—	5	2	no	—
355	#104	C₂×C₃×D₅	1	2	yes	complemented
356	#101	—	5	2	no	—
357	#100	—	5	2	no	—
358	C₄×C₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
359	C₂×C₃×C₅	—	2	1	no	—
360	C₂×C₃×C₅	—	4	2	no	—
361	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
362	C₃×D₅	—	4	2	no	—
363	C₃×D₅	—	8	2	no	—
364	C₂³×C₃	—	10	2	no	—
365	C₂³×C₃	—	20	2	no	—
366	C₃×Q₈	—	5	2	no	—
367	C₃×Q₈	—	10	2	no	—
368	C₃×Q₈	—	10	2	no	—
369	C₃×Q₈	—	20	2	no	—
370	C₃×Q₈	C₂×D₂₀	1	2	yes	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	5	2	no	—
373	C₃×D₄	—	10	2	no	—
374	C₃×D₄	—	10	2	no	—
375	C₃×D₄	—	10	2	no	—
376	C₃×D₄	—	20	2	no	—
377	C₃×D₄	—	20	2	no	—
378	C₃×D₄	—	20	2	no	—
379	C₃×D₄	—	40	2	no	—
380	C₃×D₄	C₂×D₂₀	1	2	yes	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	10	2	no	—
384	C₂×C₃×C₄	—	10	2	no	—
385	C₂×C₃×C₄	—	20	2	no	—
386	C₂×C₃×C₄	—	20	2	no	—
387	C₂×C₃×C₄	—	20	2	no	—
388	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
389	C₃×C₈	—	2	2	no	—
390	C₃×C₈	—	10	2	no	—
391	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
392	C₃×C₈	C₂×D₂₀	1	1	yes	characteristic
393	C₃×C₈	D₄×D₅	1	1	yes	characteristic
394	C₃×C₈	D₄×D₅	1	1	yes	characteristic
395	C₂²×C₅	—	2	2	no	—
396	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
397	C₂×D₅	—	2	2	no	—
398	C₂×D₅	—	4	2	no	—
399	C₂×D₅	—	8	2	no	—
400	C₂×D₅	—	16	2	no	—
401	C₄×C₅	—	2	2	no	—
402	C₄×C₅	—	2	2	no	—
403	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
404	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
405	Dic₅	—	2	2	no	—
406	Dic₅	—	4	2	no	—
407	#41	—	5	2	no	—
408	#41	—	10	2	no	—
409	#41	—	10	2	no	—
410	#41	—	10	2	no	—
411	#41	—	10	2	no	—
412	#41	—	20	2	no	—
413	#41	C₂²×C₃×D₅	1	2	yes	—
414	C₂×Q₈	—	5	2	no	—
415	C₂×Q₈	—	10	2	no	—
416	C₂×Q₈	—	10	2	no	—
417	C₂×D₄	—	5	2	no	—
418	C₂×D₄	—	10	2	no	—
419	C₂×D₄	—	10	2	no	—
420	C₂×D₄	—	20	1	no	—
421	C₂×D₄	—	20	2	no	—
422	Q₁₆	—	5	1	no	—
423	Q₁₆	—	10	2	no	—
424	Q₁₆	—	10	2	no	—
425	Q₁₆	C₃×D₂₀	1	1	yes	characteristic, complemented
426	SD₁₆	—	5	2	no	—
427	SD₁₆	—	10	2	no	—
428	SD₁₆	—	10	2	no	—
429	SD₁₆	—	10	2	no	—
430	SD₁₆	—	10	2	no	—
431	SD₁₆	—	10	2	no	—
432	SD₁₆	—	10	2	no	—
433	SD₁₆	—	10	2	no	—
434	SD₁₆	—	10	2	no	—
435	SD₁₆	C₃×D₂₀	1	2	yes	complemented
436	D₈	—	5	1	no	—
437	D₈	—	10	2	no	—
438	D₈	—	10	2	no	—
439	D₈	C₃×D₂₀	1	1	yes	characteristic, complemented
440	M₁₆	—	2	2	no	—
441	M₁₆	—	5	2	no	—
442	M₁₆	—	10	2	no	—
443	M₁₆	C₂²×C₃×D₅	1	2	yes	—
444	C₂×C₈	—	2	2	no	—
445	C₂×C₈	—	10	2	no	—
446	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
447	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
448	C₄⋊C₄	—	20	1	no	—
449	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
450	C₃×C₅	#3291	1	1	yes	characteristic, complemented, Hall
451	C₂²×C₃	—	2	2	no	—
452	C₂²×C₃	—	10	2	no	—
453	C₂²×C₃	—	20	2	no	—
454	C₂²×C₃	—	40	2	no	—
455	C₂²×C₃	—	80	2	no	—
456	C₂²×C₃	#4149	1	1	yes	characteristic
457	C₃×C₄	—	2	2	no	—
458	C₃×C₄	—	2	2	no	—
459	C₃×C₄	—	10	2	no	—
460	C₃×C₄	—	20	2	no	—
461	C₃×C₄	C₂²×D₂₀	1	1	yes	characteristic
462	C₃×C₄	C₂×D₄×D₅	1	1	yes	characteristic
463	C₂×C₅	—	2	1	no	—
464	C₂×C₅	—	4	2	no	—
465	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
466	D₅	—	4	2	no	—
467	D₅	—	8	2	no	—
468	C₂³	—	10	2	no	—
469	C₂³	—	20	2	no	—
470	Q₈	—	5	2	no	—
471	Q₈	—	10	2	no	—
472	Q₈	—	10	2	no	—
473	Q₈	—	20	2	no	—
474	Q₈	C₂×C₃×D₂₀	1	2	yes	—
475	D₄	—	2	2	no	—
476	D₄	—	5	2	no	—
477	D₄	—	10	2	no	—
478	D₄	—	10	2	no	—
479	D₄	—	10	2	no	—
480	D₄	—	20	2	no	—
481	D₄	—	20	2	no	—
482	D₄	—	20	2	no	—
483	D₄	—	40	2	no	—
484	D₄	C₂×C₃×D₂₀	1	2	yes	—
485	C₂×C₄	—	2	1	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	10	2	no	—
488	C₂×C₄	—	10	2	no	—
489	C₂×C₄	—	20	2	no	—
490	C₂×C₄	—	20	2	no	—
491	C₂×C₄	—	20	2	no	—
492	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
493	C₈	—	2	2	no	—
494	C₈	—	10	2	no	—
495	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
496	C₈	C₂×C₃×D₂₀	1	1	yes	characteristic
497	C₈	C₃×D₄×D₅	1	1	yes	characteristic
498	C₈	C₃×D₄×D₅	1	1	yes	characteristic
499	C₂×C₃	—	2	1	no	—
500	C₂×C₃	—	4	2	no	—
501	C₂×C₃	—	20	2	no	—
502	C₂×C₃	—	40	2	no	—
503	C₂×C₃	D₄×D₂₀	1	1	yes	characteristic
504	C₅	C₃×#3291	1	1	yes	characteristic, complemented, Sylow
505	C₂²	—	2	2	no	—
506	C₂²	—	10	2	no	—
507	C₂²	—	20	2	no	—
508	C₂²	—	40	2	no	—
509	C₂²	—	80	2	no	—
510	C₂²	C₃×#4149	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	10	2	no	—
514	C₄	—	20	2	no	—
515	C₄	C₂²×C₃×D₂₀	1	1	yes	characteristic
516	C₄	C₂×C₃×D₄×D₅	1	1	yes	characteristic
517	C₃	#10611624	1	1	yes	characteristic, direct product factor, Sylow
518	C₂	—	2	1	no	—
519	C₂	—	4	2	no	—
520	C₂	—	20	2	no	—
521	C₂	—	40	2	no	—
522	C₂	C₃×D₄×D₂₀	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	D₄×D₂₀
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#443	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₃×#443	D₅
hypocenter	C₅	C₃×#3291
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#443

Complements

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

N	H ≅ G/N	type
1. C₃×#66104	C₂	semidirect
2. C₃×#66085	C₂	semidirect
3. C₃×C₅×#443	C₂	semidirect
4. C₃×#65430	C₂	semidirect
5. C₃×#65187	C₂	semidirect
6. C₃×#65115	C₂	semidirect
7. C₃×#65111	C₂	semidirect
8. C₃×#64989	C₂	semidirect
9. C₃×#64982	C₂	semidirect
10. #10611624	C₃	direct (N × H)
12. C₃×#4149	C₂²	semidirect
14. C₃×C₅×#131	C₂²	semidirect
15. C₃×#4097	C₂²	semidirect
22. C₃×#4055	C₂²	semidirect
28. C₂×C₃×#677	C₂²	semidirect
29. C₂×C₃×#677	C₂²	semidirect
30. C₃×#4047	C₂²	semidirect
32. C₃×#4015	C₂²	semidirect
33. C₃×C₅×#108	C₂²	semidirect
34. C₃×C₅×#104	C₂²	semidirect
35. C₃×C₄×C₅×C₈	C₂²	semidirect
36. C₃×#3956	C₂²	semidirect
37. C₃×#3955	C₂²	semidirect
38. C₃×#3951	C₂²	semidirect
39. C₃×#3937	C₂²	semidirect
41. #66104	C₂×C₃	semidirect
42. #66085	C₂×C₃	semidirect
43. C₅×#443	C₂×C₃	semidirect
44. #65430	C₂×C₃	semidirect
45. #65187	C₂×C₃	semidirect
46. #65115	C₂×C₃	semidirect
47. #65111	C₂×C₃	semidirect
48. #64989	C₂×C₃	semidirect
49. #64982	C₂×C₃	semidirect
65. C₃×C₅×Q₁₆	D₄	semidirect
66. C₃×C₅×SD₁₆	D₄	semidirect
67. C₃×C₅×D₈	D₄	semidirect
81. C₃×Dic₂₀	D₄	semidirect
83. C₃×D₄₀	D₄	semidirect
90. C₃×#677	D₄	semidirect
101. C₃×#443	D₅	semidirect
103. #4149	C₂²×C₃	semidirect
105. C₅×#131	C₂²×C₃	semidirect
106. #4097	C₂²×C₃	semidirect
113. #4055	C₂²×C₃	semidirect
119. C₂×#677	C₂²×C₃	semidirect
120. C₂×#677	C₂²×C₃	semidirect
121. #4047	C₂²×C₃	semidirect
123. #4015	C₂²×C₃	semidirect
124. C₅×#108	C₂²×C₃	semidirect
125. C₅×#104	C₂²×C₃	semidirect
126. C₄×C₅×C₈	C₂²×C₃	semidirect
127. #3956	C₂²×C₃	semidirect
128. #3955	C₂²×C₃	semidirect
129. #3951	C₂²×C₃	semidirect
130. #3937	C₂²×C₃	semidirect
182. C₃×#131	C₂×D₅	semidirect
186. C₃×#108	C₂×D₅	semidirect
188. C₃×#104	C₂×D₅	semidirect
191. C₃×C₄×C₈	C₂×D₅	semidirect
207. C₅×Q₁₆	C₃×D₄	semidirect
208. C₅×SD₁₆	C₃×D₄	semidirect
209. C₅×D₈	C₃×D₄	semidirect
223. Dic₂₀	C₃×D₄	semidirect
225. D₄₀	C₃×D₄	semidirect
232. #677	C₃×D₄	semidirect
243. #443	C₃×D₅	semidirect
274. C₃×Q₁₆	D₂₀	semidirect
284. C₃×SD₁₆	D₂₀	semidirect
288. C₃×D₈	D₂₀	semidirect
349. #131	C₂×C₃×D₅	semidirect
353. #108	C₂×C₃×D₅	semidirect
355. #104	C₂×C₃×D₅	semidirect
358. C₄×C₈	C₂×C₃×D₅	semidirect
425. Q₁₆	C₃×D₂₀	semidirect
435. SD₁₆	C₃×D₂₀	semidirect
439. D₈	C₃×D₂₀	semidirect
450. C₃×C₅	#3291	semidirect
504. C₅	C₃×#3291	semidirect
517. C₃	#10611624	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×#66104	2
C₃×#66085	2
C₃×C₅×#443	2
C₃×#65430	2
C₃×#65187	2
C₃×#65115	2
C₃×#65111	2
C₃×#64989	2
C₃×#64982	2
#10611624	3
C₃×#3291	5

Subgroups — C3×#10611624 #14458102

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611624 #14458102