Subgroups — C₃×#10612013 #14458165

Order 1920.

952 conjugacy classes of subgroups.

The subgroup lattice has 552 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66169	C₂	1	2	yes	maximal, complemented
2	C₃×#66108	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#453	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65488	C₂	1	2	yes	maximal, complemented
5	C₃×#65366	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65362	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65113	C₂	1	2	yes	maximal, complemented
8	C₃×#65111	C₂	1	2	yes	maximal, complemented
9	C₃×#65038	C₂	1	2	yes	maximal, complemented
10	#10612013	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×H(5,𝔽₂)	C₂²	1	1	yes	characteristic, complemented
12	C₃×#4149	C₂²	1	2	yes	complemented
13	C₃×#4144	C₂²	1	1	yes	characteristic, complemented
14	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	complemented
15	C₃×C₅×#127	C₂²	1	1	yes	characteristic, complemented
16	C₃×#4096	—	2	2	no	—
17	C₃×#4096	C₂²	1	2	yes	—
18	C₃×#4095	—	2	2	no	—
19	C₃×#4095	C₂²	1	2	yes	complemented
20	C₃×#4094	C₂²	1	2	yes	complemented
21	C₃×#4078	—	2	2	no	—
22	C₃×#4078	C₂²	1	2	yes	complemented
23	C₂×C₃×#686	—	2	2	no	—
24	C₂×C₃×#686	C₂²	1	2	yes	complemented
25	C₂×C₃×#686	C₂²	1	2	yes	complemented
26	C₃×#4062	—	2	2	no	—
27	C₃×#4060	—	2	2	no	—
28	C₃×#4057	—	2	2	no	—
29	C₃×D₅×D₈	—	2	2	no	—
30	C₃×#4054	C₂²	1	2	yes	complemented
31	C₃×#4053	C₂²	1	2	yes	complemented
32	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#104	C₂²	1	2	yes	complemented
34	C₃×C₅×#100	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3965	C₂²	1	1	yes	characteristic, complemented
36	C₃×#3955	C₂²	1	2	yes	complemented
37	C₃×#3954	C₂²	1	2	yes	complemented
38	C₃×#3937	C₂²	1	2	yes	complemented
39	C₃×C₄×#168	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3292	—	5	1	no	maximal, Hall
41	#66169	C₂×C₃	1	2	yes	complemented
42	#66108	C₂×C₃	1	2	yes	complemented
43	C₅×#453	C₂×C₃	1	1	yes	characteristic, complemented
44	#65488	C₂×C₃	1	2	yes	complemented
45	#65366	C₂×C₃	1	1	yes	characteristic, complemented
46	#65362	C₂×C₃	1	1	yes	characteristic, complemented
47	#65113	C₂×C₃	1	2	yes	complemented
48	#65111	C₂×C₃	1	2	yes	complemented
49	#65038	C₂×C₃	1	2	yes	complemented
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	C₂³	1	2	yes	—
52	C₂×C₃×C₅×D₄	—	2	2	no	—
53	C₂×C₃×C₅×D₄	—	4	1	no	—
54	C₂×C₃×C₅×D₄	—	4	1	no	—
55	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
57	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
58	C₃×#713	—	2	2	no	—
59	C₃×#711	—	2	2	no	—
60	C₃×D₄×D₅	—	2	2	no	—
61	C₃×D₄×D₅	—	2	2	no	—
62	C₃×D₄×D₅	—	4	2	no	—
63	C₃×#709	—	2	2	no	—
64	C₃×#709	C₂³	1	2	yes	—
65	C₂×C₃×D₂₀	—	2	2	no	—
66	C₂×C₃×D₂₀	—	4	1	no	—
67	C₂×C₃×D₂₀	C₂³	1	2	yes	—
68	C₃×C₅×SD₁₆	—	2	2	no	—
69	C₃×C₅×D₈	—	2	2	no	—
70	C₃×C₅×M₁₆	C₂³	1	2	yes	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₃×#689	D₄	1	2	yes	complemented
73	C₃×#688	—	2	2	no	—
74	C₃×#688	D₄	1	2	yes	complemented
75	C₃×#687	—	2	2	no	—
76	C₃×#687	D₄	1	2	yes	complemented
77	C₃×#686	—	2	2	no	—
78	C₃×#686	—	2	2	no	—
79	C₃×#686	—	2	2	no	—
80	C₃×#686	—	2	2	no	—
81	C₃×#686	—	2	2	no	—
82	C₃×#686	—	2	2	no	—
83	C₃×#686	D₄	1	2	yes	complemented
84	C₃×#681	—	2	2	no	—
85	C₃×#681	C₂³	1	2	yes	—
86	C₂×C₃×#168	—	2	2	no	—
87	C₂×C₃×#168	C₂³	1	2	yes	—
88	C₃×D₄₀	—	2	2	no	—
89	C₃×#677	—	2	2	no	—
90	C₃×#676	—	2	2	no	—
91	C₃×C₈×D₅	—	2	2	no	—
92	C₃×#576	—	5	2	no	—
93	C₃×#576	—	5	2	no	—
94	C₃×#493	—	5	1	no	—
95	C₃×#472	—	5	2	no	—
96	C₃×#472	—	5	2	no	—
97	C₃×#453	—	5	1	no	—
98	C₃×#453	—	5	2	no	—
99	C₃×#453	D₅	1	1	yes	characteristic, complemented
100	C₃×#443	—	5	2	no	—
101	C₅×H(5,𝔽₂)	C₂²×C₃	1	1	yes	characteristic, complemented
102	#4149	C₂²×C₃	1	2	yes	complemented
103	#4144	C₂²×C₃	1	1	yes	characteristic, complemented
104	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	complemented
105	C₅×#127	C₂²×C₃	1	1	yes	characteristic, complemented
106	#4096	—	2	2	no	—
107	#4096	C₂²×C₃	1	2	yes	—
108	#4095	—	2	2	no	—
109	#4095	C₂²×C₃	1	2	yes	complemented
110	#4094	C₂²×C₃	1	2	yes	complemented
111	#4078	—	2	2	no	—
112	#4078	C₂²×C₃	1	2	yes	complemented
113	C₂×#686	—	2	2	no	—
114	C₂×#686	C₂²×C₃	1	2	yes	complemented
115	C₂×#686	C₂²×C₃	1	2	yes	complemented
116	#4062	—	2	2	no	—
117	#4060	—	2	2	no	—
118	#4057	—	2	2	no	—
119	D₅×D₈	—	2	2	no	—
120	#4054	C₂²×C₃	1	2	yes	complemented
121	#4053	C₂²×C₃	1	2	yes	complemented
122	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₅×#104	C₂²×C₃	1	2	yes	complemented
124	C₅×#100	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3965	C₂²×C₃	1	1	yes	characteristic, complemented
126	#3955	C₂²×C₃	1	2	yes	complemented
127	#3954	C₂²×C₃	1	2	yes	complemented
128	#3937	C₂²×C₃	1	2	yes	complemented
129	C₄×#168	C₂²×C₃	1	1	yes	characteristic, complemented
130	#3292	—	5	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	2	1	no	—
133	C₂³×C₃×C₅	—	4	1	no	—
134	C₂²×C₃×D₅	—	2	2	no	—
135	C₂²×C₃×D₅	—	4	1	no	—
136	C₂²×C₃×D₅	—	4	2	no	—
137	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
138	C₃×C₅×D₄	—	2	2	no	—
139	C₃×C₅×D₄	—	2	2	no	—
140	C₃×C₅×D₄	—	2	2	no	—
141	C₃×C₅×D₄	—	4	2	no	—
142	C₃×C₅×D₄	—	8	2	no	—
143	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	4	1	no	—
147	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
148	C₃×C₂²⋊D₅	—	2	2	no	—
149	C₃×C₂²⋊D₅	—	4	2	no	—
150	C₃×C₂²⋊D₅	—	4	2	no	—
151	C₂×C₃×Dic₅	—	4	1	no	—
152	C₃×D₂₀	—	2	2	no	—
153	C₃×D₂₀	—	2	2	no	—
154	C₃×D₂₀	—	4	2	no	—
155	C₃×D₂₀	—	8	2	no	—
156	C₃×D₂₀	C₂×D₄	1	2	yes	—
157	C₃×C₄×D₅	—	2	2	no	—
158	C₃×C₄×D₅	—	4	2	no	—
159	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
160	C₃×C₅×C₈	—	2	2	no	—
161	C₃×#168	—	2	2	no	—
162	C₃×#168	C₂×D₄	1	2	yes	—
163	C₃×#168	C₂×D₄	1	2	yes	—
164	C₃×H(5,𝔽₂)	—	5	2	no	—
165	C₃×H(5,𝔽₂)	—	5	1	no	—
166	C₃×H(5,𝔽₂)	C₂×D₅	1	1	yes	characteristic, complemented
167	C₃×AGL(1,ℤ/8)	—	5	2	no	—
168	C₃×AGL(1,ℤ/8)	—	5	2	no	—
169	C₃×AGL(1,ℤ/8)	—	5	2	no	—
170	C₃×AGL(1,ℤ/8)	—	10	2	no	—
171	C₃×AGL(1,ℤ/8)	—	10	2	no	—
172	C₃×AGL(1,ℤ/8)	—	10	2	no	—
173	C₃×AGL(1,ℤ/8)	—	10	2	no	—
174	C₃×AGL(1,ℤ/8)	C₂×D₅	1	2	yes	complemented
175	C₃×#135	—	5	2	no	—
176	C₃×#135	—	10	2	no	—
177	C₃×#135	—	10	2	no	—
178	C₂×C₃×D₈	—	5	2	no	—
179	C₂×C₃×D₈	—	5	2	no	—
180	C₂×C₃×D₈	—	10	2	no	—
181	C₂×C₃×D₈	—	10	2	no	—
182	C₃×#131	—	5	2	no	—
183	C₃×#131	—	5	2	no	—
184	C₃×#127	—	5	1	no	—
185	C₃×#127	C₂×D₅	1	1	yes	characteristic, complemented
186	C₃×#108	—	5	2	no	—
187	C₃×#104	—	5	2	no	—
188	C₃×#104	C₂×D₅	1	2	yes	complemented
189	C₃×#100	—	5	1	no	—
190	C₃×#100	—	5	2	no	—
191	C₃×#100	C₂×D₅	1	1	yes	characteristic, complemented
192	C₃×C₄×C₈	—	5	1	no	—
193	C₅×#41	—	2	2	no	—
194	C₅×#41	C₂³×C₃	1	2	yes	—
195	C₂×C₅×D₄	—	2	2	no	—
196	C₂×C₅×D₄	—	4	1	no	—
197	C₂×C₅×D₄	—	4	1	no	—
198	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
199	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
200	C₂×C₂²⋊D₅	—	4	1	no	—
201	#713	—	2	2	no	—
202	#711	—	2	2	no	—
203	D₄×D₅	—	2	2	no	—
204	D₄×D₅	—	2	2	no	—
205	D₄×D₅	—	4	2	no	—
206	#709	—	2	2	no	—
207	#709	C₂³×C₃	1	2	yes	—
208	C₂×D₂₀	—	2	2	no	—
209	C₂×D₂₀	—	4	1	no	—
210	C₂×D₂₀	C₂³×C₃	1	2	yes	—
211	C₅×SD₁₆	—	2	2	no	—
212	C₅×D₈	—	2	2	no	—
213	C₅×M₁₆	C₂³×C₃	1	2	yes	—
214	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
215	#689	C₃×D₄	1	2	yes	complemented
216	#688	—	2	2	no	—
217	#688	C₃×D₄	1	2	yes	complemented
218	#687	—	2	2	no	—
219	#687	C₃×D₄	1	2	yes	complemented
220	#686	—	2	2	no	—
221	#686	—	2	2	no	—
222	#686	—	2	2	no	—
223	#686	—	2	2	no	—
224	#686	—	2	2	no	—
225	#686	—	2	2	no	—
226	#686	C₃×D₄	1	2	yes	complemented
227	#681	—	2	2	no	—
228	#681	C₂³×C₃	1	2	yes	—
229	C₂×#168	—	2	2	no	—
230	C₂×#168	C₂³×C₃	1	2	yes	—
231	D₄₀	—	2	2	no	—
232	#677	—	2	2	no	—
233	#676	—	2	2	no	—
234	C₈×D₅	—	2	2	no	—
235	#576	—	5	2	no	—
236	#576	—	5	2	no	—
237	#493	—	5	1	no	—
238	#472	—	5	2	no	—
239	#472	—	5	2	no	—
240	#453	—	5	1	no	—
241	#453	—	5	2	no	—
242	#453	C₃×D₅	1	1	yes	characteristic, complemented
243	#443	—	5	2	no	—
244	C₂²×C₃×C₅	—	2	2	no	—
245	C₂²×C₃×C₅	—	4	1	no	—
246	C₂²×C₃×C₅	—	4	1	no	—
247	C₂²×C₃×C₅	—	8	1	no	—
248	C₂²×C₃×C₅	—	8	1	no	—
249	C₂²×C₃×C₅	—	16	1	no	—
250	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
251	C₂×C₃×D₅	—	2	2	no	—
252	C₂×C₃×D₅	—	4	2	no	—
253	C₂×C₃×D₅	—	8	2	no	—
254	C₂×C₃×D₅	—	16	1	no	—
255	C₂×C₃×D₅	—	16	2	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	2	2	no	—
258	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
259	C₃×Dic₅	—	2	2	no	—
260	C₃×#41	—	2	2	no	—
261	C₃×#41	—	5	2	no	—
262	C₃×#41	—	10	2	no	—
263	C₃×#41	—	10	2	no	—
264	C₃×#41	—	10	2	no	—
265	C₃×#41	C₂²×D₅	1	2	yes	—
266	C₂×C₃×D₄	—	2	2	no	—
267	C₂×C₃×D₄	—	4	1	no	—
268	C₂×C₃×D₄	—	4	1	no	—
269	C₂×C₃×D₄	—	5	2	no	—
270	C₂×C₃×D₄	—	10	2	no	—
271	C₂×C₃×D₄	—	10	2	no	—
272	C₂×C₃×D₄	—	10	2	no	—
273	C₂×C₃×D₄	—	20	1	no	—
274	C₂×C₃×D₄	—	20	2	no	—
275	C₂×C₃×D₄	—	20	1	no	—
276	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
277	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
278	C₃×Q₁₆	—	5	2	no	—
279	C₃×SD₁₆	—	2	2	no	—
280	C₃×SD₁₆	—	5	2	no	—
281	C₃×SD₁₆	—	5	2	no	—
282	C₃×SD₁₆	—	10	2	no	—
283	C₃×SD₁₆	—	10	2	no	—
284	C₃×SD₁₆	—	10	2	no	—
285	C₃×D₈	—	2	2	no	—
286	C₃×D₈	—	5	2	no	—
287	C₃×D₈	—	10	2	no	—
288	C₃×D₈	—	10	2	no	—
289	C₃×D₈	—	10	2	no	—
290	C₃×D₈	—	10	2	no	—
291	C₃×D₈	—	10	2	no	—
292	C₃×D₈	—	10	2	no	—
293	C₃×D₈	—	10	2	no	—
294	C₃×M₁₆	—	5	2	no	—
295	C₃×M₁₆	—	10	2	no	—
296	C₃×M₁₆	—	10	2	no	—
297	C₃×M₁₆	C₂²×D₅	1	2	yes	—
298	C₂×C₃×C₈	—	5	2	no	—
299	C₂×C₃×C₈	—	10	2	no	—
300	C₂×C₃×C₈	—	10	2	no	—
301	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
302	C₂³×C₅	—	2	1	no	—
303	C₂³×C₅	—	2	1	no	—
304	C₂³×C₅	—	4	1	no	—
305	C₂²×D₅	—	2	2	no	—
306	C₂²×D₅	—	4	1	no	—
307	C₂²×D₅	—	4	2	no	—
308	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
309	C₅×D₄	—	2	2	no	—
310	C₅×D₄	—	2	2	no	—
311	C₅×D₄	—	2	2	no	—
312	C₅×D₄	—	4	2	no	—
313	C₅×D₄	—	8	2	no	—
314	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	4	1	no	—
318	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
319	C₂²⋊D₅	—	2	2	no	—
320	C₂²⋊D₅	—	4	2	no	—
321	C₂²⋊D₅	—	4	2	no	—
322	C₂×Dic₅	—	4	1	no	—
323	D₂₀	—	2	2	no	—
324	D₂₀	—	2	2	no	—
325	D₂₀	—	4	2	no	—
326	D₂₀	—	8	2	no	—
327	D₂₀	C₂×C₃×D₄	1	2	yes	—
328	C₄×D₅	—	2	2	no	—
329	C₄×D₅	—	4	2	no	—
330	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
331	C₅×C₈	—	2	2	no	—
332	#168	—	2	2	no	—
333	#168	C₂×C₃×D₄	1	2	yes	—
334	#168	C₂×C₃×D₄	1	2	yes	—
335	H(5,𝔽₂)	—	5	2	no	—
336	H(5,𝔽₂)	—	5	1	no	—
337	H(5,𝔽₂)	C₂×C₃×D₅	1	1	yes	characteristic, complemented
338	AGL(1,ℤ/8)	—	5	2	no	—
339	AGL(1,ℤ/8)	—	5	2	no	—
340	AGL(1,ℤ/8)	—	5	2	no	—
341	AGL(1,ℤ/8)	—	10	2	no	—
342	AGL(1,ℤ/8)	—	10	2	no	—
343	AGL(1,ℤ/8)	—	10	2	no	—
344	AGL(1,ℤ/8)	—	10	2	no	—
345	AGL(1,ℤ/8)	C₂×C₃×D₅	1	2	yes	complemented
346	#135	—	5	2	no	—
347	#135	—	10	2	no	—
348	#135	—	10	2	no	—
349	C₂×D₈	—	5	2	no	—
350	C₂×D₈	—	5	2	no	—
351	C₂×D₈	—	10	2	no	—
352	C₂×D₈	—	10	2	no	—
353	#131	—	5	2	no	—
354	#131	—	5	2	no	—
355	#127	—	5	1	no	—
356	#127	C₂×C₃×D₅	1	1	yes	characteristic, complemented
357	#108	—	5	2	no	—
358	#104	—	5	2	no	—
359	#104	C₂×C₃×D₅	1	2	yes	complemented
360	#100	—	5	1	no	—
361	#100	—	5	2	no	—
362	#100	C₂×C₃×D₅	1	1	yes	characteristic, complemented
363	C₄×C₈	—	5	1	no	—
364	C₂×C₃×C₅	—	2	1	no	—
365	C₂×C₃×C₅	—	4	2	no	—
366	C₂×C₃×C₅	—	8	1	no	—
367	C₂×C₃×C₅	—	8	1	no	—
368	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
369	C₃×D₅	—	4	2	no	—
370	C₃×D₅	—	8	2	no	—
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	—	4	1	no	—
374	C₂³×C₃	—	10	2	no	—
375	C₂³×C₃	—	20	2	no	—
376	C₂³×C₃	—	20	1	no	—
377	C₃×Q₈	—	5	2	no	—
378	C₃×Q₈	D₄×D₅	1	2	yes	—
379	C₃×D₄	—	2	2	no	—
380	C₃×D₄	—	2	2	no	—
381	C₃×D₄	—	2	2	no	—
382	C₃×D₄	—	4	2	no	—
383	C₃×D₄	—	5	2	no	—
384	C₃×D₄	—	8	2	no	—
385	C₃×D₄	—	10	2	no	—
386	C₃×D₄	—	10	2	no	—
387	C₃×D₄	—	10	2	no	—
388	C₃×D₄	—	20	2	no	—
389	C₃×D₄	—	20	2	no	—
390	C₃×D₄	—	20	2	no	—
391	C₃×D₄	—	40	2	no	—
392	C₃×D₄	D₄×D₅	1	2	yes	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	4	1	no	—
396	C₂×C₃×C₄	—	10	2	no	—
397	C₂×C₃×C₄	—	20	2	no	—
398	C₂×C₃×C₄	—	20	1	no	—
399	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
400	C₃×C₈	—	2	2	no	—
401	C₃×C₈	—	5	2	no	—
402	C₃×C₈	—	5	2	no	—
403	C₃×C₈	—	10	2	no	—
404	C₂²×C₅	—	2	2	no	—
405	C₂²×C₅	—	4	1	no	—
406	C₂²×C₅	—	4	1	no	—
407	C₂²×C₅	—	8	1	no	—
408	C₂²×C₅	—	8	1	no	—
409	C₂²×C₅	—	16	1	no	—
410	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
411	C₂×D₅	—	2	2	no	—
412	C₂×D₅	—	4	2	no	—
413	C₂×D₅	—	8	2	no	—
414	C₂×D₅	—	16	1	no	—
415	C₂×D₅	—	16	2	no	—
416	C₄×C₅	—	2	2	no	—
417	C₄×C₅	—	2	2	no	—
418	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
419	Dic₅	—	2	2	no	—
420	#41	—	2	2	no	—
421	#41	—	5	2	no	—
422	#41	—	10	2	no	—
423	#41	—	10	2	no	—
424	#41	—	10	2	no	—
425	#41	C₂²×C₃×D₅	1	2	yes	—
426	C₂×D₄	—	2	2	no	—
427	C₂×D₄	—	4	1	no	—
428	C₂×D₄	—	4	1	no	—
429	C₂×D₄	—	5	2	no	—
430	C₂×D₄	—	10	2	no	—
431	C₂×D₄	—	10	2	no	—
432	C₂×D₄	—	10	2	no	—
433	C₂×D₄	—	20	1	no	—
434	C₂×D₄	—	20	2	no	—
435	C₂×D₄	—	20	1	no	—
436	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
437	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
438	Q₁₆	—	5	2	no	—
439	SD₁₆	—	2	2	no	—
440	SD₁₆	—	5	2	no	—
441	SD₁₆	—	5	2	no	—
442	SD₁₆	—	10	2	no	—
443	SD₁₆	—	10	2	no	—
444	SD₁₆	—	10	2	no	—
445	D₈	—	2	2	no	—
446	D₈	—	5	2	no	—
447	D₈	—	10	2	no	—
448	D₈	—	10	2	no	—
449	D₈	—	10	2	no	—
450	D₈	—	10	2	no	—
451	D₈	—	10	2	no	—
452	D₈	—	10	2	no	—
453	D₈	—	10	2	no	—
454	M₁₆	—	5	2	no	—
455	M₁₆	—	10	2	no	—
456	M₁₆	—	10	2	no	—
457	M₁₆	C₂²×C₃×D₅	1	2	yes	—
458	C₂×C₈	—	5	2	no	—
459	C₂×C₈	—	10	2	no	—
460	C₂×C₈	—	10	2	no	—
461	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
462	C₃×C₅	#3292	1	1	yes	characteristic, complemented, Hall
463	C₂²×C₃	—	2	2	no	—
464	C₂²×C₃	—	4	1	no	—
465	C₂²×C₃	—	4	1	no	—
466	C₂²×C₃	—	8	1	no	—
467	C₂²×C₃	—	8	1	no	—
468	C₂²×C₃	—	10	2	no	—
469	C₂²×C₃	—	16	1	no	—
470	C₂²×C₃	—	20	2	no	—
471	C₂²×C₃	—	40	2	no	—
472	C₂²×C₃	—	80	2	no	—
473	C₂²×C₃	—	80	1	no	—
474	C₂²×C₃	#4144	1	1	yes	characteristic
475	C₃×C₄	—	2	2	no	—
476	C₃×C₄	—	2	2	no	—
477	C₃×C₄	—	10	2	no	—
478	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
479	C₂×C₅	—	2	1	no	—
480	C₂×C₅	—	4	2	no	—
481	C₂×C₅	—	8	1	no	—
482	C₂×C₅	—	8	1	no	—
483	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
484	D₅	—	4	2	no	—
485	D₅	—	8	2	no	—
486	C₂³	—	2	1	no	—
487	C₂³	—	2	1	no	—
488	C₂³	—	4	1	no	—
489	C₂³	—	10	2	no	—
490	C₂³	—	20	2	no	—
491	C₂³	—	20	1	no	—
492	Q₈	—	5	2	no	—
493	Q₈	C₃×D₄×D₅	1	2	yes	—
494	D₄	—	2	2	no	—
495	D₄	—	2	2	no	—
496	D₄	—	2	2	no	—
497	D₄	—	4	2	no	—
498	D₄	—	5	2	no	—
499	D₄	—	8	2	no	—
500	D₄	—	10	2	no	—
501	D₄	—	10	2	no	—
502	D₄	—	10	2	no	—
503	D₄	—	20	2	no	—
504	D₄	—	20	2	no	—
505	D₄	—	20	2	no	—
506	D₄	—	40	2	no	—
507	D₄	C₃×D₄×D₅	1	2	yes	—
508	C₂×C₄	—	2	1	no	—
509	C₂×C₄	—	2	2	no	—
510	C₂×C₄	—	4	1	no	—
511	C₂×C₄	—	10	2	no	—
512	C₂×C₄	—	20	2	no	—
513	C₂×C₄	—	20	1	no	—
514	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
515	C₈	—	2	2	no	—
516	C₈	—	5	2	no	—
517	C₈	—	5	2	no	—
518	C₈	—	10	2	no	—
519	C₂×C₃	—	2	1	no	—
520	C₂×C₃	—	4	2	no	—
521	C₂×C₃	—	8	1	no	—
522	C₂×C₃	—	8	1	no	—
523	C₂×C₃	—	20	2	no	—
524	C₂×C₃	—	40	2	no	—
525	C₂×C₃	#65924	1	1	yes	characteristic
526	C₅	C₃×#3292	1	1	yes	characteristic, complemented, Sylow
527	C₂²	—	2	2	no	—
528	C₂²	—	4	1	no	—
529	C₂²	—	4	1	no	—
530	C₂²	—	8	1	no	—
531	C₂²	—	8	1	no	—
532	C₂²	—	10	2	no	—
533	C₂²	—	16	1	no	—
534	C₂²	—	20	2	no	—
535	C₂²	—	40	2	no	—
536	C₂²	—	80	2	no	—
537	C₂²	—	80	1	no	—
538	C₂²	C₃×#4144	1	1	yes	characteristic
539	C₄	—	2	2	no	—
540	C₄	—	2	2	no	—
541	C₄	—	10	2	no	—
542	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
543	C₃	#10612013	1	1	yes	characteristic, direct product factor, Sylow
544	C₂	—	2	1	no	—
545	C₂	—	4	2	no	—
546	C₂	—	8	1	no	—
547	C₂	—	8	1	no	—
548	C₂	—	20	2	no	—
549	C₂	—	40	2	no	—
550	C₂	C₃×#65924	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#65924
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#453	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₃×#453	D₅
hypocenter	C₅	C₃×#3292
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#453

Complements

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

N	H ≅ G/N	type
1. C₃×#66169	C₂	semidirect
2. C₃×#66108	C₂	semidirect
3. C₃×C₅×#453	C₂	semidirect
4. C₃×#65488	C₂	semidirect
5. C₃×#65366	C₂	semidirect
6. C₃×#65362	C₂	semidirect
7. C₃×#65113	C₂	semidirect
8. C₃×#65111	C₂	semidirect
9. C₃×#65038	C₂	semidirect
10. #10612013	C₃	direct (N × H)
11. C₃×C₅×H(5,𝔽₂)	C₂²	semidirect
12. C₃×#4149	C₂²	semidirect
13. C₃×#4144	C₂²	semidirect
14. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
15. C₃×C₅×#127	C₂²	semidirect
19. C₃×#4095	C₂²	semidirect
20. C₃×#4094	C₂²	semidirect
22. C₃×#4078	C₂²	semidirect
24. C₂×C₃×#686	C₂²	semidirect
25. C₂×C₃×#686	C₂²	semidirect
30. C₃×#4054	C₂²	semidirect
31. C₃×#4053	C₂²	semidirect
32. C₃×#4020	C₂²	semidirect
33. C₃×C₅×#104	C₂²	semidirect
34. C₃×C₅×#100	C₂²	semidirect
35. C₃×#3965	C₂²	semidirect
36. C₃×#3955	C₂²	semidirect
37. C₃×#3954	C₂²	semidirect
38. C₃×#3937	C₂²	semidirect
39. C₃×C₄×#168	C₂²	semidirect
41. #66169	C₂×C₃	semidirect
42. #66108	C₂×C₃	semidirect
43. C₅×#453	C₂×C₃	semidirect
44. #65488	C₂×C₃	semidirect
45. #65366	C₂×C₃	semidirect
46. #65362	C₂×C₃	semidirect
47. #65113	C₂×C₃	semidirect
48. #65111	C₂×C₃	semidirect
49. #65038	C₂×C₃	semidirect
72. C₃×#689	D₄	semidirect
74. C₃×#688	D₄	semidirect
76. C₃×#687	D₄	semidirect
83. C₃×#686	D₄	semidirect
99. C₃×#453	D₅	semidirect
101. C₅×H(5,𝔽₂)	C₂²×C₃	semidirect
102. #4149	C₂²×C₃	semidirect
103. #4144	C₂²×C₃	semidirect
104. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
105. C₅×#127	C₂²×C₃	semidirect
109. #4095	C₂²×C₃	semidirect
110. #4094	C₂²×C₃	semidirect
112. #4078	C₂²×C₃	semidirect
114. C₂×#686	C₂²×C₃	semidirect
115. C₂×#686	C₂²×C₃	semidirect
120. #4054	C₂²×C₃	semidirect
121. #4053	C₂²×C₃	semidirect
122. #4020	C₂²×C₃	semidirect
123. C₅×#104	C₂²×C₃	semidirect
124. C₅×#100	C₂²×C₃	semidirect
125. #3965	C₂²×C₃	semidirect
126. #3955	C₂²×C₃	semidirect
127. #3954	C₂²×C₃	semidirect
128. #3937	C₂²×C₃	semidirect
129. C₄×#168	C₂²×C₃	semidirect
166. C₃×H(5,𝔽₂)	C₂×D₅	semidirect
174. C₃×AGL(1,ℤ/8)	C₂×D₅	semidirect
185. C₃×#127	C₂×D₅	semidirect
188. C₃×#104	C₂×D₅	semidirect
191. C₃×#100	C₂×D₅	semidirect
215. #689	C₃×D₄	semidirect
217. #688	C₃×D₄	semidirect
219. #687	C₃×D₄	semidirect
226. #686	C₃×D₄	semidirect
242. #453	C₃×D₅	semidirect
337. H(5,𝔽₂)	C₂×C₃×D₅	semidirect
345. AGL(1,ℤ/8)	C₂×C₃×D₅	semidirect
356. #127	C₂×C₃×D₅	semidirect
359. #104	C₂×C₃×D₅	semidirect
362. #100	C₂×C₃×D₅	semidirect
462. C₃×C₅	#3292	semidirect
526. C₅	C₃×#3292	semidirect
543. C₃	#10612013	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×#66169	2
C₃×#66108	2
C₃×C₅×#453	2
C₃×#65488	2
C₃×#65366	2
C₃×#65362	2
C₃×#65113	2
C₃×#65111	2
C₃×#65038	2
#10612013	3
C₃×#3292	5

Subgroups — C3×#10612013 #14458165

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612013 #14458165