Subgroups — C₃×#10612033 #14458090

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×#66171	C₂	1	2	yes	maximal, complemented
2	C₃×#66112	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#456	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65492	C₂	1	2	yes	maximal, complemented
5	C₃×#65384	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65374	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×#65043	C₂	1	2	yes	maximal, complemented
10	#10612033	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic
12	C₃×#4149	C₂²	1	2	yes	complemented
13	C₃×#4147	C₂²	1	1	yes	characteristic
14	C₃×C₅×#137	C₂²	1	2	yes	complemented
15	C₃×C₅×C₄⋊Q₈	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	—
20	C₃×#4094	C₂²	1	2	yes	complemented
21	C₃×#4088	—	2	2	no	—
22	C₃×#4088	C₂²	1	2	yes	complemented
23	C₂×C₃×#688	—	2	2	no	—
24	C₂×C₃×#688	C₂²	1	2	yes	complemented
25	C₂×C₃×#688	C₂²	1	2	yes	complemented
26	C₃×#4065	—	2	2	no	—
27	C₃×#4064	—	2	2	no	—
28	C₃×#4060	—	2	2	no	—
29	C₃×D₅×SD₁₆	—	2	2	no	—
30	C₃×#4054	C₂²	1	2	yes	—
31	C₃×#4053	C₂²	1	2	yes	complemented
32	C₃×#4020	C₂²	1	1	yes	characteristic
33	C₃×C₅×#104	C₂²	1	2	yes	complemented
34	C₃×C₅×#101	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3968	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×#3291	—	5	1	no	maximal, Hall
41	#66171	C₂×C₃	1	2	yes	complemented
42	#66112	C₂×C₃	1	2	yes	complemented
43	C₅×#456	C₂×C₃	1	1	yes	characteristic, complemented
44	#65492	C₂×C₃	1	2	yes	complemented
45	#65384	C₂×C₃	1	1	yes	characteristic, complemented
46	#65374	C₂×C₃	1	1	yes	characteristic, complemented
47	#65113	C₂×C₃	1	2	yes	complemented
48	#65111	C₂×C₃	1	2	yes	complemented
49	#65043	C₂×C₃	1	2	yes	complemented
50	C₃×C₅×#41	—	2	2	no	—
51	C₃×C₅×#41	—	4	1	no	—
52	C₃×C₅×#41	C₂³	1	2	yes	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
55	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
56	C₃×#713	—	2	2	no	—
57	C₃×#713	—	2	2	no	—
58	C₃×Q₈×D₅	—	2	2	no	—
59	C₃×D₄×D₅	—	2	2	no	—
60	C₃×D₄×D₅	—	4	2	no	—
61	C₃×#709	—	2	2	no	—
62	C₃×#709	—	4	1	no	—
63	C₃×#709	C₂³	1	2	yes	—
64	C₂×C₃×D₂₀	—	2	2	no	—
65	C₂×C₃×D₂₀	—	4	1	no	—
66	C₂×C₃×D₂₀	C₂³	1	2	yes	—
67	C₃×C₅×Q₁₆	—	2	2	no	—
68	C₃×C₅×SD₁₆	—	2	2	no	—
69	C₃×C₅×M₁₆	C₂³	1	2	yes	—
70	C₃×C₅×C₄⋊C₄	—	4	1	no	—
71	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
72	C₃×#689	—	2	2	no	—
73	C₃×#689	D₄	1	2	yes	complemented
74	C₃×#688	—	2	2	no	—
75	C₃×#688	—	2	2	no	—
76	C₃×#688	—	2	2	no	—
77	C₃×#688	—	2	2	no	—
78	C₃×#688	—	2	2	no	—
79	C₃×#688	—	2	2	no	—
80	C₃×#688	D₄	1	2	yes	complemented
81	C₃×#687	D₄	1	2	yes	complemented
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×#577	—	5	2	no	—
93	C₃×#577	—	5	2	no	—
94	C₃×#492	—	5	1	no	—
95	C₃×#471	—	5	2	no	—
96	C₃×#471	—	5	2	no	—
97	C₃×#456	—	5	1	no	—
98	C₃×#456	D₅	1	1	yes	characteristic, complemented
99	C₃×#453	—	5	2	no	—
100	C₃×#443	—	5	2	no	—
101	C₅×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic
102	#4149	C₂²×C₃	1	2	yes	complemented
103	#4147	C₂²×C₃	1	1	yes	characteristic
104	C₅×#137	C₂²×C₃	1	2	yes	complemented
105	C₅×C₄⋊Q₈	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	—
110	#4094	C₂²×C₃	1	2	yes	complemented
111	#4088	—	2	2	no	—
112	#4088	C₂²×C₃	1	2	yes	complemented
113	C₂×#688	—	2	2	no	—
114	C₂×#688	C₂²×C₃	1	2	yes	complemented
115	C₂×#688	C₂²×C₃	1	2	yes	complemented
116	#4065	—	2	2	no	—
117	#4064	—	2	2	no	—
118	#4060	—	2	2	no	—
119	D₅×SD₁₆	—	2	2	no	—
120	#4054	C₂²×C₃	1	2	yes	—
121	#4053	C₂²×C₃	1	2	yes	complemented
122	#4020	C₂²×C₃	1	1	yes	characteristic
123	C₅×#104	C₂²×C₃	1	2	yes	complemented
124	C₅×#101	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3968	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	#3291	—	5	1	no	Sylow
131	C₂²×C₃×D₅	—	2	2	no	—
132	C₂²×C₃×D₅	—	4	2	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	2	2	no	—
135	C₃×C₅×Q₈	—	4	1	no	—
136	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
137	C₃×C₅×D₄	—	2	2	no	—
138	C₃×C₅×D₄	—	4	1	no	—
139	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	4	2	no	—
145	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
146	C₃×C₂²⋊D₅	—	2	2	no	—
147	C₃×C₂²⋊D₅	—	4	2	no	—
148	C₃×D₂₀	—	2	2	no	—
149	C₃×D₂₀	—	2	2	no	—
150	C₃×D₂₀	—	4	2	no	—
151	C₃×D₂₀	—	4	1	no	—
152	C₃×D₂₀	—	8	2	no	—
153	C₃×D₂₀	C₂×D₄	1	2	yes	—
154	C₃×C₄×D₅	—	2	2	no	—
155	C₃×C₄×D₅	—	4	2	no	—
156	C₃×C₄×D₅	—	4	2	no	—
157	C₃×Dic₁₀	—	4	1	no	—
158	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
159	C₃×C₅×C₈	—	2	2	no	—
160	C₃×#168	—	2	2	no	—
161	C₃×#168	C₂×D₄	1	2	yes	—
162	C₃×#168	C₂×D₄	1	2	yes	—
163	C₃×2₋¹⁺⁴	—	5	1	no	—
164	C₃×2₋¹⁺⁴	C₂×D₅	1	1	yes	characteristic
165	C₃×H(5,𝔽₂)	—	5	2	no	—
166	C₃×#137	—	5	2	no	—
167	C₃×#137	—	10	2	no	—
168	C₃×#137	—	10	2	no	—
169	C₃×#137	C₂×D₅	1	2	yes	complemented
170	C₃×AGL(1,ℤ/8)	—	5	2	no	—
171	C₃×AGL(1,ℤ/8)	—	5	2	no	—
172	C₃×AGL(1,ℤ/8)	—	10	2	no	—
173	C₃×AGL(1,ℤ/8)	—	10	2	no	—
174	C₃×#135	—	5	2	no	—
175	C₃×#135	—	10	2	no	—
176	C₃×#135	—	10	2	no	—
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	—	5	2	no	—
183	C₃×C₄⋊Q₈	C₂×D₅	1	1	yes	characteristic, complemented
184	C₃×#127	—	5	1	no	—
185	C₃×#108	—	5	2	no	—
186	C₃×#104	—	5	2	no	—
187	C₃×#104	C₂×D₅	1	2	yes	complemented
188	C₃×#101	—	5	1	no	—
189	C₃×#101	C₂×D₅	1	1	yes	characteristic, complemented
190	C₃×#100	—	5	2	no	—
191	C₃×C₄×C₈	—	5	1	no	—
192	C₅×#41	—	2	2	no	—
193	C₅×#41	—	4	1	no	—
194	C₅×#41	C₂³×C₃	1	2	yes	—
195	C₂×C₅×Q₈	—	2	2	no	—
196	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
198	#713	—	2	2	no	—
199	#713	—	2	2	no	—
200	Q₈×D₅	—	2	2	no	—
201	D₄×D₅	—	2	2	no	—
202	D₄×D₅	—	4	2	no	—
203	#709	—	2	2	no	—
204	#709	—	4	1	no	—
205	#709	C₂³×C₃	1	2	yes	—
206	C₂×D₂₀	—	2	2	no	—
207	C₂×D₂₀	—	4	1	no	—
208	C₂×D₂₀	C₂³×C₃	1	2	yes	—
209	C₅×Q₁₆	—	2	2	no	—
210	C₅×SD₁₆	—	2	2	no	—
211	C₅×M₁₆	C₂³×C₃	1	2	yes	—
212	C₅×C₄⋊C₄	—	4	1	no	—
213	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
214	#689	—	2	2	no	—
215	#689	C₃×D₄	1	2	yes	complemented
216	#688	—	2	2	no	—
217	#688	—	2	2	no	—
218	#688	—	2	2	no	—
219	#688	—	2	2	no	—
220	#688	—	2	2	no	—
221	#688	—	2	2	no	—
222	#688	C₃×D₄	1	2	yes	complemented
223	#687	C₃×D₄	1	2	yes	complemented
224	#686	—	2	2	no	—
225	#686	C₃×D₄	1	2	yes	complemented
226	#681	—	2	2	no	—
227	#681	C₂³×C₃	1	2	yes	—
228	C₂×#168	—	2	2	no	—
229	C₂×#168	C₂³×C₃	1	2	yes	—
230	D₄₀	—	2	2	no	—
231	#677	—	2	2	no	—
232	#676	—	2	2	no	—
233	C₈×D₅	—	2	2	no	—
234	#577	—	5	2	no	—
235	#577	—	5	2	no	—
236	#492	—	5	1	no	—
237	#471	—	5	2	no	—
238	#471	—	5	2	no	—
239	#456	—	5	1	no	—
240	#456	C₃×D₅	1	1	yes	characteristic, complemented
241	#453	—	5	2	no	—
242	#443	—	5	2	no	—
243	C₂²×C₃×C₅	—	2	2	no	—
244	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
245	C₂×C₃×D₅	—	2	2	no	—
246	C₂×C₃×D₅	—	4	2	no	—
247	C₂×C₃×D₅	—	8	2	no	—
248	C₂×C₃×D₅	—	16	2	no	—
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	2	no	—
251	C₃×C₄×C₅	—	4	1	no	—
252	C₃×C₄×C₅	—	4	1	no	—
253	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
254	C₃×Dic₅	—	2	2	no	—
255	C₃×#41	—	2	2	no	—
256	C₃×#41	—	4	1	no	—
257	C₃×#41	—	5	2	no	—
258	C₃×#41	—	10	2	no	—
259	C₃×#41	—	10	2	no	—
260	C₃×#41	—	10	2	no	—
261	C₃×#41	—	20	1	no	—
262	C₃×#41	C₂²×D₅	1	2	yes	—
263	C₂×C₃×Q₈	—	2	2	no	—
264	C₂×C₃×Q₈	—	10	2	no	—
265	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
266	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
267	C₂×C₃×D₄	—	5	2	no	—
268	C₂×C₃×D₄	—	10	2	no	—
269	C₂×C₃×D₄	—	10	2	no	—
270	C₂×C₃×D₄	—	20	1	no	—
271	C₂×C₃×D₄	—	20	2	no	—
272	C₃×Q₁₆	—	2	2	no	—
273	C₃×Q₁₆	—	5	2	no	—
274	C₃×Q₁₆	—	10	2	no	—
275	C₃×SD₁₆	—	2	2	no	—
276	C₃×SD₁₆	—	5	2	no	—
277	C₃×SD₁₆	—	5	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	—	10	2	no	—
285	C₃×D₈	—	5	2	no	—
286	C₃×D₈	—	10	2	no	—
287	C₃×D₈	—	10	2	no	—
288	C₃×M₁₆	—	5	2	no	—
289	C₃×M₁₆	—	10	2	no	—
290	C₃×M₁₆	—	10	2	no	—
291	C₃×M₁₆	C₂²×D₅	1	2	yes	—
292	C₂×C₃×C₈	—	5	2	no	—
293	C₂×C₃×C₈	—	10	2	no	—
294	C₂×C₃×C₈	—	10	2	no	—
295	C₃×C₄⋊C₄	—	4	1	no	—
296	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
297	C₂²×D₅	—	2	2	no	—
298	C₂²×D₅	—	4	2	no	—
299	C₅×Q₈	—	2	2	no	—
300	C₅×Q₈	—	2	2	no	—
301	C₅×Q₈	—	4	1	no	—
302	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
303	C₅×D₄	—	2	2	no	—
304	C₅×D₄	—	4	1	no	—
305	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	1	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	4	2	no	—
311	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
312	C₂²⋊D₅	—	2	2	no	—
313	C₂²⋊D₅	—	4	2	no	—
314	D₂₀	—	2	2	no	—
315	D₂₀	—	2	2	no	—
316	D₂₀	—	4	2	no	—
317	D₂₀	—	4	1	no	—
318	D₂₀	—	8	2	no	—
319	D₂₀	C₂×C₃×D₄	1	2	yes	—
320	C₄×D₅	—	2	2	no	—
321	C₄×D₅	—	4	2	no	—
322	C₄×D₅	—	4	2	no	—
323	Dic₁₀	—	4	1	no	—
324	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
325	C₅×C₈	—	2	2	no	—
326	#168	—	2	2	no	—
327	#168	C₂×C₃×D₄	1	2	yes	—
328	#168	C₂×C₃×D₄	1	2	yes	—
329	2₋¹⁺⁴	—	5	1	no	—
330	2₋¹⁺⁴	C₂×C₃×D₅	1	1	yes	characteristic
331	H(5,𝔽₂)	—	5	2	no	—
332	#137	—	5	2	no	—
333	#137	—	10	2	no	—
334	#137	—	10	2	no	—
335	#137	C₂×C₃×D₅	1	2	yes	complemented
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	2	no	—
341	#135	—	10	2	no	—
342	#135	—	10	2	no	—
343	C₂×SD₁₆	—	5	2	no	—
344	C₂×SD₁₆	—	5	2	no	—
345	C₂×SD₁₆	—	10	2	no	—
346	C₂×SD₁₆	—	10	2	no	—
347	#131	—	5	2	no	—
348	#131	—	5	2	no	—
349	C₄⋊Q₈	C₂×C₃×D₅	1	1	yes	characteristic, complemented
350	#127	—	5	1	no	—
351	#108	—	5	2	no	—
352	#104	—	5	2	no	—
353	#104	C₂×C₃×D₅	1	2	yes	complemented
354	#101	—	5	1	no	—
355	#101	C₂×C₃×D₅	1	1	yes	characteristic, complemented
356	#100	—	5	2	no	—
357	C₄×C₈	—	5	1	no	—
358	C₂×C₃×C₅	—	2	1	no	—
359	C₂×C₃×C₅	—	4	2	no	—
360	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
361	C₃×D₅	—	4	2	no	—
362	C₃×D₅	—	8	2	no	—
363	C₂³×C₃	—	10	2	no	—
364	C₂³×C₃	—	20	2	no	—
365	C₃×Q₈	—	2	2	no	—
366	C₃×Q₈	—	2	2	no	—
367	C₃×Q₈	—	4	1	no	—
368	C₃×Q₈	—	5	2	no	—
369	C₃×Q₈	—	20	1	no	—
370	C₃×Q₈	D₄×D₅	1	2	yes	—
371	C₃×D₄	—	2	2	no	—
372	C₃×D₄	—	4	1	no	—
373	C₃×D₄	—	5	2	no	—
374	C₃×D₄	—	10	2	no	—
375	C₃×D₄	—	10	2	no	—
376	C₃×D₄	—	10	2	no	—
377	C₃×D₄	—	20	2	no	—
378	C₃×D₄	—	20	1	no	—
379	C₃×D₄	—	20	2	no	—
380	C₃×D₄	—	40	2	no	—
381	C₃×D₄	D₄×D₅	1	2	yes	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	4	2	no	—
387	C₂×C₃×C₄	—	10	2	no	—
388	C₂×C₃×C₄	—	20	2	no	—
389	C₂×C₃×C₄	—	20	2	no	—
390	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
391	C₃×C₈	—	2	2	no	—
392	C₃×C₈	—	5	2	no	—
393	C₃×C₈	—	5	2	no	—
394	C₃×C₈	—	10	2	no	—
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	—	4	1	no	—
404	C₄×C₅	—	4	1	no	—
405	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
406	Dic₅	—	2	2	no	—
407	#41	—	2	2	no	—
408	#41	—	4	1	no	—
409	#41	—	5	2	no	—
410	#41	—	10	2	no	—
411	#41	—	10	2	no	—
412	#41	—	10	2	no	—
413	#41	—	20	1	no	—
414	#41	C₂²×C₃×D₅	1	2	yes	—
415	C₂×Q₈	—	2	2	no	—
416	C₂×Q₈	—	10	2	no	—
417	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
418	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
419	C₂×D₄	—	5	2	no	—
420	C₂×D₄	—	10	2	no	—
421	C₂×D₄	—	10	2	no	—
422	C₂×D₄	—	20	1	no	—
423	C₂×D₄	—	20	2	no	—
424	Q₁₆	—	2	2	no	—
425	Q₁₆	—	5	2	no	—
426	Q₁₆	—	10	2	no	—
427	SD₁₆	—	2	2	no	—
428	SD₁₆	—	5	2	no	—
429	SD₁₆	—	5	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	—	10	2	no	—
436	SD₁₆	—	10	2	no	—
437	D₈	—	5	2	no	—
438	D₈	—	10	2	no	—
439	D₈	—	10	2	no	—
440	M₁₆	—	5	2	no	—
441	M₁₆	—	10	2	no	—
442	M₁₆	—	10	2	no	—
443	M₁₆	C₂²×C₃×D₅	1	2	yes	—
444	C₂×C₈	—	5	2	no	—
445	C₂×C₈	—	10	2	no	—
446	C₂×C₈	—	10	2	no	—
447	C₄⋊C₄	—	4	1	no	—
448	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
449	C₃×C₅	#3291	1	1	yes	characteristic, complemented, Hall
450	C₂²×C₃	—	2	2	no	—
451	C₂²×C₃	—	10	2	no	—
452	C₂²×C₃	—	20	2	no	—
453	C₂²×C₃	—	40	2	no	—
454	C₂²×C₃	—	80	2	no	—
455	C₂²×C₃	#4144	1	1	yes	characteristic
456	C₃×C₄	—	2	2	no	—
457	C₃×C₄	—	2	2	no	—
458	C₃×C₄	—	4	1	no	—
459	C₃×C₄	—	4	1	no	—
460	C₃×C₄	—	10	2	no	—
461	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
462	C₂×C₅	—	2	1	no	—
463	C₂×C₅	—	4	2	no	—
464	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
465	D₅	—	4	2	no	—
466	D₅	—	8	2	no	—
467	C₂³	—	10	2	no	—
468	C₂³	—	20	2	no	—
469	Q₈	—	2	2	no	—
470	Q₈	—	2	2	no	—
471	Q₈	—	4	1	no	—
472	Q₈	—	5	2	no	—
473	Q₈	—	20	1	no	—
474	Q₈	C₃×D₄×D₅	1	2	yes	—
475	D₄	—	2	2	no	—
476	D₄	—	4	1	no	—
477	D₄	—	5	2	no	—
478	D₄	—	10	2	no	—
479	D₄	—	10	2	no	—
480	D₄	—	10	2	no	—
481	D₄	—	20	2	no	—
482	D₄	—	20	1	no	—
483	D₄	—	20	2	no	—
484	D₄	—	40	2	no	—
485	D₄	C₃×D₄×D₅	1	2	yes	—
486	C₂×C₄	—	2	1	no	—
487	C₂×C₄	—	2	2	no	—
488	C₂×C₄	—	2	1	no	—
489	C₂×C₄	—	2	1	no	—
490	C₂×C₄	—	4	2	no	—
491	C₂×C₄	—	10	2	no	—
492	C₂×C₄	—	20	2	no	—
493	C₂×C₄	—	20	2	no	—
494	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
495	C₈	—	2	2	no	—
496	C₈	—	5	2	no	—
497	C₈	—	5	2	no	—
498	C₈	—	10	2	no	—
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	#65924	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×#4144	1	1	yes	characteristic
511	C₄	—	2	2	no	—
512	C₄	—	2	2	no	—
513	C₄	—	4	1	no	—
514	C₄	—	4	1	no	—
515	C₄	—	10	2	no	—
516	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
517	C₃	#10612033	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×#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×#456	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₃×#456	D₅
hypocenter	C₅	C₃×#3291
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#456

Complements

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

N	H ≅ G/N	type
1. C₃×#66171	C₂	semidirect
2. C₃×#66112	C₂	semidirect
3. C₃×C₅×#456	C₂	semidirect
4. C₃×#65492	C₂	semidirect
5. C₃×#65384	C₂	semidirect
6. C₃×#65374	C₂	semidirect
7. C₃×#65113	C₂	semidirect
8. C₃×#65111	C₂	semidirect
9. C₃×#65043	C₂	semidirect
10. #10612033	C₃	direct (N × H)
12. C₃×#4149	C₂²	semidirect
14. C₃×C₅×#137	C₂²	semidirect
15. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
20. C₃×#4094	C₂²	semidirect
22. C₃×#4088	C₂²	semidirect
24. C₂×C₃×#688	C₂²	semidirect
25. C₂×C₃×#688	C₂²	semidirect
31. C₃×#4053	C₂²	semidirect
33. C₃×C₅×#104	C₂²	semidirect
34. C₃×C₅×#101	C₂²	semidirect
35. C₃×#3968	C₂²	semidirect
36. C₃×#3955	C₂²	semidirect
37. C₃×#3954	C₂²	semidirect
38. C₃×#3937	C₂²	semidirect
39. C₃×C₄×#168	C₂²	semidirect
41. #66171	C₂×C₃	semidirect
42. #66112	C₂×C₃	semidirect
43. C₅×#456	C₂×C₃	semidirect
44. #65492	C₂×C₃	semidirect
45. #65384	C₂×C₃	semidirect
46. #65374	C₂×C₃	semidirect
47. #65113	C₂×C₃	semidirect
48. #65111	C₂×C₃	semidirect
49. #65043	C₂×C₃	semidirect
73. C₃×#689	D₄	semidirect
80. C₃×#688	D₄	semidirect
81. C₃×#687	D₄	semidirect
83. C₃×#686	D₄	semidirect
98. C₃×#456	D₅	semidirect
102. #4149	C₂²×C₃	semidirect
104. C₅×#137	C₂²×C₃	semidirect
105. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
110. #4094	C₂²×C₃	semidirect
112. #4088	C₂²×C₃	semidirect
114. C₂×#688	C₂²×C₃	semidirect
115. C₂×#688	C₂²×C₃	semidirect
121. #4053	C₂²×C₃	semidirect
123. C₅×#104	C₂²×C₃	semidirect
124. C₅×#101	C₂²×C₃	semidirect
125. #3968	C₂²×C₃	semidirect
126. #3955	C₂²×C₃	semidirect
127. #3954	C₂²×C₃	semidirect
128. #3937	C₂²×C₃	semidirect
129. C₄×#168	C₂²×C₃	semidirect
169. C₃×#137	C₂×D₅	semidirect
183. C₃×C₄⋊Q₈	C₂×D₅	semidirect
187. C₃×#104	C₂×D₅	semidirect
189. C₃×#101	C₂×D₅	semidirect
215. #689	C₃×D₄	semidirect
222. #688	C₃×D₄	semidirect
223. #687	C₃×D₄	semidirect
225. #686	C₃×D₄	semidirect
240. #456	C₃×D₅	semidirect
335. #137	C₂×C₃×D₅	semidirect
349. C₄⋊Q₈	C₂×C₃×D₅	semidirect
353. #104	C₂×C₃×D₅	semidirect
355. #101	C₂×C₃×D₅	semidirect
449. C₃×C₅	#3291	semidirect
504. C₅	C₃×#3291	semidirect
517. C₃	#10612033	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×#66171	2
C₃×#66112	2
C₃×C₅×#456	2
C₃×#65492	2
C₃×#65384	2
C₃×#65374	2
C₃×#65113	2
C₃×#65111	2
C₃×#65043	2
#10612033	3
C₃×#3291	5

Subgroups — C3×#10612033 #14458090

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612033 #14458090