Subgroups — C₃×#10612019 #14457817

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 520 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₃×#66172	C₂	1	2	yes	maximal, complemented
2	C₃×#66109	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#454	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65489	C₂	1	2	yes	maximal, complemented
5	C₃×#65350	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65349	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65115	C₂	1	2	yes	maximal, complemented
8	C₃×#65112	C₂	1	2	yes	maximal, complemented
9	C₃×#65044	C₂	1	2	yes	maximal, complemented
10	#10612019	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₃×C₅×2₋¹⁺⁴	C₂²	1	1	yes	characteristic, complemented
12	C₃×#4150	C₂²	1	2	yes	—
13	C₃×#4144	C₂²	1	1	yes	characteristic
14	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	2	yes	—
15	C₃×C₅×#124	C₂²	1	1	yes	characteristic
16	C₃×#4097	—	2	2	no	—
17	C₃×#4097	C₂²	1	2	yes	complemented
18	C₃×#4096	—	2	2	no	—
19	C₃×#4096	C₂²	1	2	yes	—
20	C₃×#4094	C₂²	1	2	yes	complemented
21	C₂×C₃×#689	—	2	2	no	—
22	C₂×C₃×#689	C₂²	1	2	yes	complemented
23	C₃×#4088	—	2	2	no	—
24	C₃×#4088	C₂²	1	2	yes	—
25	C₂×C₃×#687	C₂²	1	2	yes	—
26	C₃×#4061	—	2	2	no	—
27	C₃×D₅×SD₁₆	—	2	2	no	—
28	C₃×#4058	—	2	2	no	—
29	C₃×#4057	—	2	2	no	—
30	C₃×#4055	C₂²	1	2	yes	—
31	C₃×#4053	C₂²	1	2	yes	—
32	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
33	C₃×C₅×#104	C₂²	1	2	yes	complemented
34	C₃×C₅×#101	C₂²	1	1	yes	characteristic, complemented
35	C₃×#3965	C₂²	1	1	yes	characteristic
36	C₃×#3956	C₂²	1	2	yes	complemented
37	C₃×#3954	C₂²	1	2	yes	complemented
38	C₃×#3937	C₂²	1	2	yes	—
39	C₃×#3935	C₂²	1	1	yes	characteristic, complemented
40	C₃×#3289	—	5	1	no	maximal, Hall
41	#66172	C₂×C₃	1	2	yes	complemented
42	#66109	C₂×C₃	1	2	yes	complemented
43	C₅×#454	C₂×C₃	1	1	yes	characteristic, complemented
44	#65489	C₂×C₃	1	2	yes	complemented
45	#65350	C₂×C₃	1	1	yes	characteristic, complemented
46	#65349	C₂×C₃	1	1	yes	characteristic, complemented
47	#65115	C₂×C₃	1	2	yes	complemented
48	#65112	C₂×C₃	1	2	yes	complemented
49	#65044	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×D₄	C₂³	1	1	yes	characteristic
56	C₂×C₃×C₂²⋊D₅	—	4	1	no	—
57	C₃×Q₈×D₅	—	2	2	no	—
58	C₃×#711	—	2	2	no	—
59	C₃×#711	—	2	2	no	—
60	C₃×#711	—	4	2	no	—
61	C₃×D₄×D₅	—	2	2	no	—
62	C₃×#709	—	2	2	no	—
63	C₃×#709	C₂³	1	2	yes	—
64	C₂×C₃×Dic₁₀	—	2	2	no	—
65	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
66	C₃×C₅×SD₁₆	—	2	2	no	—
67	C₃×C₅×D₈	—	2	2	no	—
68	C₃×C₅×M₁₆	C₂³	1	2	yes	—
69	C₃×C₅×C₂²⋊C₄	—	4	1	no	—
70	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
71	C₃×#689	—	2	2	no	—
72	C₃×#689	—	2	2	no	—
73	C₃×#689	—	2	2	no	—
74	C₃×#689	—	2	2	no	—
75	C₃×#689	D₄	1	2	yes	—
76	C₃×#688	—	2	2	no	—
77	C₃×#688	D₄	1	2	yes	—
78	C₃×#687	—	2	2	no	—
79	C₃×#687	—	2	2	no	—
80	C₃×#687	—	2	2	no	—
81	C₃×#687	D₄	1	2	yes	—
82	C₃×#686	D₄	1	2	yes	—
83	C₃×C₄⋊Dic₅	—	4	1	no	—
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×Dic₂₀	—	2	2	no	—
89	C₃×#677	—	2	2	no	—
90	C₃×#676	—	2	2	no	—
91	C₃×C₈×D₅	—	2	2	no	—
92	C₃×#578	—	5	2	no	—
93	C₃×#577	—	5	2	no	—
94	C₃×#497	—	5	1	no	—
95	C₃×#473	—	5	2	no	—
96	C₃×#471	—	5	2	no	—
97	C₃×#456	—	5	2	no	—
98	C₃×#455	—	5	1	no	—
99	C₃×#454	D₅	1	1	yes	characteristic, complemented
100	C₃×#444	—	5	2	no	—
101	C₅×2₋¹⁺⁴	C₂²×C₃	1	1	yes	characteristic, complemented
102	#4150	C₂²×C₃	1	2	yes	—
103	#4144	C₂²×C₃	1	1	yes	characteristic
104	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	2	yes	—
105	C₅×#124	C₂²×C₃	1	1	yes	characteristic
106	#4097	—	2	2	no	—
107	#4097	C₂²×C₃	1	2	yes	complemented
108	#4096	—	2	2	no	—
109	#4096	C₂²×C₃	1	2	yes	—
110	#4094	C₂²×C₃	1	2	yes	complemented
111	C₂×#689	—	2	2	no	—
112	C₂×#689	C₂²×C₃	1	2	yes	complemented
113	#4088	—	2	2	no	—
114	#4088	C₂²×C₃	1	2	yes	—
115	C₂×#687	C₂²×C₃	1	2	yes	—
116	#4061	—	2	2	no	—
117	D₅×SD₁₆	—	2	2	no	—
118	#4058	—	2	2	no	—
119	#4057	—	2	2	no	—
120	#4055	C₂²×C₃	1	2	yes	—
121	#4053	C₂²×C₃	1	2	yes	—
122	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
123	C₅×#104	C₂²×C₃	1	2	yes	complemented
124	C₅×#101	C₂²×C₃	1	1	yes	characteristic, complemented
125	#3965	C₂²×C₃	1	1	yes	characteristic
126	#3956	C₂²×C₃	1	2	yes	complemented
127	#3954	C₂²×C₃	1	2	yes	complemented
128	#3937	C₂²×C₃	1	2	yes	—
129	#3935	C₂²×C₃	1	1	yes	characteristic, complemented
130	#3289	—	5	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂²×C₃×D₅	—	4	1	no	—
133	C₃×C₅×Q₈	—	2	2	no	—
134	C₃×C₅×Q₈	—	4	1	no	—
135	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
136	C₃×C₅×D₄	—	2	2	no	—
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	2	no	—
141	C₂×C₃×C₄×C₅	—	2	1	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	4	2	no	—
144	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
145	C₃×C₂²⋊D₅	—	2	2	no	—
146	C₃×C₂²⋊D₅	—	4	2	no	—
147	C₃×C₂²⋊D₅	—	4	2	no	—
148	C₂×C₃×Dic₅	—	2	2	no	—
149	C₂×C₃×Dic₅	—	4	1	no	—
150	C₂×C₃×Dic₅	—	4	2	no	—
151	C₃×D₂₀	C₂×D₄	1	2	yes	—
152	C₃×C₄×D₅	—	2	2	no	—
153	C₃×C₄×D₅	—	4	2	no	—
154	C₃×Dic₁₀	—	2	2	no	—
155	C₃×Dic₁₀	—	2	2	no	—
156	C₃×Dic₁₀	—	4	2	no	—
157	C₃×Dic₁₀	C₂×D₄	1	2	yes	—
158	C₃×C₅×C₈	—	2	2	no	—
159	C₃×#168	—	2	2	no	—
160	C₃×#168	C₂×D₄	1	2	yes	—
161	C₃×#168	C₂×D₄	1	2	yes	—
162	C₃×2₋¹⁺⁴	—	5	2	no	—
163	C₃×2₋¹⁺⁴	C₂×D₅	1	1	yes	characteristic, complemented
164	C₃×H(5,𝔽₂)	—	5	1	no	—
165	C₃×#137	—	5	2	no	—
166	C₃×#137	—	5	2	no	—
167	C₃×#137	—	5	2	no	—
168	C₃×#137	—	10	2	no	—
169	C₃×#137	—	10	2	no	—
170	C₃×#137	—	10	2	no	—
171	C₃×AGL(1,ℤ/8)	—	10	2	no	—
172	C₃×AGL(1,ℤ/8)	C₂×D₅	1	2	yes	—
173	C₃×#135	—	5	2	no	—
174	C₃×#135	—	10	2	no	—
175	C₃×#135	—	10	2	no	—
176	C₂×C₃×Q₁₆	—	5	2	no	—
177	C₂×C₃×Q₁₆	—	10	2	no	—
178	C₂×C₃×SD₁₆	—	5	2	no	—
179	C₂×C₃×SD₁₆	—	10	2	no	—
180	C₃×#131	—	5	2	no	—
181	C₃×#131	—	5	2	no	—
182	C₃×C₄⋊Q₈	—	5	1	no	—
183	C₃×#124	C₂×D₅	1	1	yes	characteristic
184	C₃×#108	—	5	2	no	—
185	C₃×#104	—	5	2	no	—
186	C₃×#104	C₂×D₅	1	2	yes	complemented
187	C₃×#101	—	5	2	no	—
188	C₃×#101	C₂×D₅	1	1	yes	characteristic, complemented
189	C₃×#100	—	5	1	no	—
190	C₃×#97	—	5	1	no	—
191	C₅×#41	—	2	2	no	—
192	C₅×#41	—	4	1	no	—
193	C₅×#41	C₂³×C₃	1	2	yes	—
194	C₂×C₅×Q₈	—	2	2	no	—
195	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
196	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
197	C₂×C₂²⋊D₅	—	4	1	no	—
198	Q₈×D₅	—	2	2	no	—
199	#711	—	2	2	no	—
200	#711	—	2	2	no	—
201	#711	—	4	2	no	—
202	D₄×D₅	—	2	2	no	—
203	#709	—	2	2	no	—
204	#709	C₂³×C₃	1	2	yes	—
205	C₂×Dic₁₀	—	2	2	no	—
206	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
207	C₅×SD₁₆	—	2	2	no	—
208	C₅×D₈	—	2	2	no	—
209	C₅×M₁₆	C₂³×C₃	1	2	yes	—
210	C₅×C₂²⋊C₄	—	4	1	no	—
211	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
212	#689	—	2	2	no	—
213	#689	—	2	2	no	—
214	#689	—	2	2	no	—
215	#689	—	2	2	no	—
216	#689	C₃×D₄	1	2	yes	—
217	#688	—	2	2	no	—
218	#688	C₃×D₄	1	2	yes	—
219	#687	—	2	2	no	—
220	#687	—	2	2	no	—
221	#687	—	2	2	no	—
222	#687	C₃×D₄	1	2	yes	—
223	#686	C₃×D₄	1	2	yes	—
224	C₄⋊Dic₅	—	4	1	no	—
225	#681	—	2	2	no	—
226	#681	C₂³×C₃	1	2	yes	—
227	C₂×#168	—	2	2	no	—
228	C₂×#168	C₂³×C₃	1	2	yes	—
229	Dic₂₀	—	2	2	no	—
230	#677	—	2	2	no	—
231	#676	—	2	2	no	—
232	C₈×D₅	—	2	2	no	—
233	#578	—	5	2	no	—
234	#577	—	5	2	no	—
235	#497	—	5	1	no	—
236	#473	—	5	2	no	—
237	#471	—	5	2	no	—
238	#456	—	5	2	no	—
239	#455	—	5	1	no	—
240	#454	C₃×D₅	1	1	yes	characteristic, complemented
241	#444	—	5	2	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	—	4	1	no	—
244	C₂²×C₃×C₅	—	8	1	no	—
245	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
246	C₂×C₃×D₅	—	2	2	no	—
247	C₂×C₃×D₅	—	16	1	no	—
248	C₃×C₄×C₅	—	2	2	no	—
249	C₃×C₄×C₅	—	4	1	no	—
250	C₃×C₄×C₅	—	4	1	no	—
251	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
252	C₃×Dic₅	—	2	2	no	—
253	C₃×Dic₅	—	4	2	no	—
254	C₃×#41	—	2	2	no	—
255	C₃×#41	—	4	1	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	—	20	2	no	—
261	C₃×#41	C₂²×D₅	1	2	yes	—
262	C₂×C₃×Q₈	—	2	2	no	—
263	C₂×C₃×Q₈	—	5	2	no	—
264	C₂×C₃×Q₈	—	10	2	no	—
265	C₂×C₃×Q₈	—	10	2	no	—
266	C₂×C₃×Q₈	C₂²×D₅	1	1	yes	characteristic
267	C₂×C₃×D₄	—	10	2	no	—
268	C₂×C₃×D₄	—	20	1	no	—
269	C₂×C₃×D₄	C₂²×D₅	1	1	yes	characteristic
270	C₃×Q₁₆	—	5	2	no	—
271	C₃×Q₁₆	—	10	2	no	—
272	C₃×Q₁₆	—	10	2	no	—
273	C₃×Q₁₆	—	10	2	no	—
274	C₃×Q₁₆	—	10	2	no	—
275	C₃×Q₁₆	—	10	2	no	—
276	C₃×SD₁₆	—	2	2	no	—
277	C₃×SD₁₆	—	5	2	no	—
278	C₃×SD₁₆	—	5	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×D₈	—	2	2	no	—
285	C₃×D₈	—	5	2	no	—
286	C₃×M₁₆	—	5	2	no	—
287	C₃×M₁₆	—	10	2	no	—
288	C₃×M₁₆	—	10	2	no	—
289	C₃×M₁₆	C₂²×D₅	1	2	yes	—
290	C₂×C₃×C₈	—	5	2	no	—
291	C₂×C₃×C₈	—	10	2	no	—
292	C₂×C₃×C₈	—	10	2	no	—
293	C₃×C₄⋊C₄	—	20	1	no	—
294	C₃×C₂²⋊C₄	—	4	1	no	—
295	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
296	C₂³×C₅	—	2	1	no	—
297	C₂²×D₅	—	4	1	no	—
298	C₅×Q₈	—	2	2	no	—
299	C₅×Q₈	—	4	1	no	—
300	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
301	C₅×D₄	—	2	2	no	—
302	C₅×D₄	—	2	2	no	—
303	C₅×D₄	—	4	1	no	—
304	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
305	C₂×C₄×C₅	—	2	2	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	4	2	no	—
309	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
310	C₂²⋊D₅	—	2	2	no	—
311	C₂²⋊D₅	—	4	2	no	—
312	C₂²⋊D₅	—	4	2	no	—
313	C₂×Dic₅	—	2	2	no	—
314	C₂×Dic₅	—	4	1	no	—
315	C₂×Dic₅	—	4	2	no	—
316	D₂₀	C₂×C₃×D₄	1	2	yes	—
317	C₄×D₅	—	2	2	no	—
318	C₄×D₅	—	4	2	no	—
319	Dic₁₀	—	2	2	no	—
320	Dic₁₀	—	2	2	no	—
321	Dic₁₀	—	4	2	no	—
322	Dic₁₀	C₂×C₃×D₄	1	2	yes	—
323	C₅×C₈	—	2	2	no	—
324	#168	—	2	2	no	—
325	#168	C₂×C₃×D₄	1	2	yes	—
326	#168	C₂×C₃×D₄	1	2	yes	—
327	2₋¹⁺⁴	—	5	2	no	—
328	2₋¹⁺⁴	C₂×C₃×D₅	1	1	yes	characteristic, complemented
329	H(5,𝔽₂)	—	5	1	no	—
330	#137	—	5	2	no	—
331	#137	—	5	2	no	—
332	#137	—	5	2	no	—
333	#137	—	10	2	no	—
334	#137	—	10	2	no	—
335	#137	—	10	2	no	—
336	AGL(1,ℤ/8)	—	10	2	no	—
337	AGL(1,ℤ/8)	C₂×C₃×D₅	1	2	yes	—
338	#135	—	5	2	no	—
339	#135	—	10	2	no	—
340	#135	—	10	2	no	—
341	C₂×Q₁₆	—	5	2	no	—
342	C₂×Q₁₆	—	10	2	no	—
343	C₂×SD₁₆	—	5	2	no	—
344	C₂×SD₁₆	—	10	2	no	—
345	#131	—	5	2	no	—
346	#131	—	5	2	no	—
347	C₄⋊Q₈	—	5	1	no	—
348	#124	C₂×C₃×D₅	1	1	yes	characteristic
349	#108	—	5	2	no	—
350	#104	—	5	2	no	—
351	#104	C₂×C₃×D₅	1	2	yes	complemented
352	#101	—	5	2	no	—
353	#101	C₂×C₃×D₅	1	1	yes	characteristic, complemented
354	#100	—	5	1	no	—
355	#97	—	5	1	no	—
356	C₂×C₃×C₅	—	2	1	no	—
357	C₂×C₃×C₅	—	4	2	no	—
358	C₂×C₃×C₅	—	8	1	no	—
359	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
360	C₃×D₅	—	4	2	no	—
361	C₂³×C₃	—	2	1	no	—
362	C₂³×C₃	—	20	1	no	—
363	C₃×Q₈	—	2	2	no	—
364	C₃×Q₈	—	4	1	no	—
365	C₃×Q₈	—	5	2	no	—
366	C₃×Q₈	—	10	2	no	—
367	C₃×Q₈	—	10	2	no	—
368	C₃×Q₈	—	20	2	no	—
369	C₃×Q₈	D₄×D₅	1	2	yes	—
370	C₃×D₄	—	2	2	no	—
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	—	20	2	no	—
376	C₃×D₄	—	20	2	no	—
377	C₃×D₄	D₄×D₅	1	2	yes	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	4	2	no	—
382	C₂×C₃×C₄	—	10	2	no	—
383	C₂×C₃×C₄	—	10	2	no	—
384	C₂×C₃×C₄	—	20	2	no	—
385	C₂×C₃×C₄	—	20	1	no	—
386	C₂×C₃×C₄	—	20	2	no	—
387	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
388	C₃×C₈	—	2	2	no	—
389	C₃×C₈	—	5	2	no	—
390	C₃×C₈	—	5	2	no	—
391	C₃×C₈	—	10	2	no	—
392	C₂²×C₅	—	2	2	no	—
393	C₂²×C₅	—	4	1	no	—
394	C₂²×C₅	—	8	1	no	—
395	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
396	C₂×D₅	—	2	2	no	—
397	C₂×D₅	—	16	1	no	—
398	C₄×C₅	—	2	2	no	—
399	C₄×C₅	—	4	1	no	—
400	C₄×C₅	—	4	1	no	—
401	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
402	Dic₅	—	2	2	no	—
403	Dic₅	—	4	2	no	—
404	#41	—	2	2	no	—
405	#41	—	4	1	no	—
406	#41	—	5	2	no	—
407	#41	—	10	2	no	—
408	#41	—	10	2	no	—
409	#41	—	10	2	no	—
410	#41	—	20	2	no	—
411	#41	C₂²×C₃×D₅	1	2	yes	—
412	C₂×Q₈	—	2	2	no	—
413	C₂×Q₈	—	5	2	no	—
414	C₂×Q₈	—	10	2	no	—
415	C₂×Q₈	—	10	2	no	—
416	C₂×Q₈	C₂²×C₃×D₅	1	1	yes	characteristic
417	C₂×D₄	—	10	2	no	—
418	C₂×D₄	—	20	1	no	—
419	C₂×D₄	C₂²×C₃×D₅	1	1	yes	characteristic
420	Q₁₆	—	5	2	no	—
421	Q₁₆	—	10	2	no	—
422	Q₁₆	—	10	2	no	—
423	Q₁₆	—	10	2	no	—
424	Q₁₆	—	10	2	no	—
425	Q₁₆	—	10	2	no	—
426	SD₁₆	—	2	2	no	—
427	SD₁₆	—	5	2	no	—
428	SD₁₆	—	5	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	D₈	—	2	2	no	—
435	D₈	—	5	2	no	—
436	M₁₆	—	5	2	no	—
437	M₁₆	—	10	2	no	—
438	M₁₆	—	10	2	no	—
439	M₁₆	C₂²×C₃×D₅	1	2	yes	—
440	C₂×C₈	—	5	2	no	—
441	C₂×C₈	—	10	2	no	—
442	C₂×C₈	—	10	2	no	—
443	C₄⋊C₄	—	20	1	no	—
444	C₂²⋊C₄	—	4	1	no	—
445	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
446	C₃×C₅	#3289	1	1	yes	characteristic, complemented, Hall
447	C₂²×C₃	—	2	2	no	—
448	C₂²×C₃	—	4	1	no	—
449	C₂²×C₃	—	8	1	no	—
450	C₂²×C₃	—	10	2	no	—
451	C₂²×C₃	—	80	1	no	—
452	C₂²×C₃	#4144	1	1	yes	characteristic
453	C₃×C₄	—	2	2	no	—
454	C₃×C₄	—	4	1	no	—
455	C₃×C₄	—	4	1	no	—
456	C₃×C₄	—	10	2	no	—
457	C₃×C₄	—	20	2	no	—
458	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
459	C₂×C₅	—	2	1	no	—
460	C₂×C₅	—	4	2	no	—
461	C₂×C₅	—	8	1	no	—
462	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
463	D₅	—	4	2	no	—
464	C₂³	—	2	1	no	—
465	C₂³	—	20	1	no	—
466	Q₈	—	2	2	no	—
467	Q₈	—	4	1	no	—
468	Q₈	—	5	2	no	—
469	Q₈	—	10	2	no	—
470	Q₈	—	10	2	no	—
471	Q₈	—	20	2	no	—
472	Q₈	C₃×D₄×D₅	1	2	yes	—
473	D₄	—	2	2	no	—
474	D₄	—	2	2	no	—
475	D₄	—	4	1	no	—
476	D₄	—	5	2	no	—
477	D₄	—	10	2	no	—
478	D₄	—	20	2	no	—
479	D₄	—	20	2	no	—
480	D₄	C₃×D₄×D₅	1	2	yes	—
481	C₂×C₄	—	2	2	no	—
482	C₂×C₄	—	2	1	no	—
483	C₂×C₄	—	2	1	no	—
484	C₂×C₄	—	4	2	no	—
485	C₂×C₄	—	10	2	no	—
486	C₂×C₄	—	10	2	no	—
487	C₂×C₄	—	20	2	no	—
488	C₂×C₄	—	20	1	no	—
489	C₂×C₄	—	20	2	no	—
490	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
491	C₈	—	2	2	no	—
492	C₈	—	5	2	no	—
493	C₈	—	5	2	no	—
494	C₈	—	10	2	no	—
495	C₂×C₃	—	2	1	no	—
496	C₂×C₃	—	4	2	no	—
497	C₂×C₃	—	8	1	no	—
498	C₂×C₃	—	20	2	no	—
499	C₂×C₃	#65924	1	1	yes	characteristic
500	C₅	C₃×#3289	1	1	yes	characteristic, complemented, Sylow
501	C₂²	—	2	2	no	—
502	C₂²	—	4	1	no	—
503	C₂²	—	8	1	no	—
504	C₂²	—	10	2	no	—
505	C₂²	—	80	1	no	—
506	C₂²	C₃×#4144	1	1	yes	characteristic
507	C₄	—	2	2	no	—
508	C₄	—	4	1	no	—
509	C₄	—	4	1	no	—
510	C₄	—	10	2	no	—
511	C₄	—	20	2	no	—
512	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
513	C₃	#10612019	1	1	yes	characteristic, direct product factor, Sylow
514	C₂	—	2	1	no	—
515	C₂	—	4	2	no	—
516	C₂	—	8	1	no	—
517	C₂	—	20	2	no	—
518	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×#454	C₂
socle	C₂×C₃×C₅	D₄²
hypercenter	C₃×#454	D₅
hypocenter	C₅	C₃×#3289
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂×C₃×C₄ ◁ C₃×#454

Complements

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

N	H ≅ G/N	type
1. C₃×#66172	C₂	semidirect
2. C₃×#66109	C₂	semidirect
3. C₃×C₅×#454	C₂	semidirect
4. C₃×#65489	C₂	semidirect
5. C₃×#65350	C₂	semidirect
6. C₃×#65349	C₂	semidirect
7. C₃×#65115	C₂	semidirect
8. C₃×#65112	C₂	semidirect
9. C₃×#65044	C₂	semidirect
10. #10612019	C₃	direct (N × H)
11. C₃×C₅×2₋¹⁺⁴	C₂²	semidirect
17. C₃×#4097	C₂²	semidirect
20. C₃×#4094	C₂²	semidirect
22. C₂×C₃×#689	C₂²	semidirect
32. C₃×#4015	C₂²	semidirect
33. C₃×C₅×#104	C₂²	semidirect
34. C₃×C₅×#101	C₂²	semidirect
36. C₃×#3956	C₂²	semidirect
37. C₃×#3954	C₂²	semidirect
39. C₃×#3935	C₂²	semidirect
41. #66172	C₂×C₃	semidirect
42. #66109	C₂×C₃	semidirect
43. C₅×#454	C₂×C₃	semidirect
44. #65489	C₂×C₃	semidirect
45. #65350	C₂×C₃	semidirect
46. #65349	C₂×C₃	semidirect
47. #65115	C₂×C₃	semidirect
48. #65112	C₂×C₃	semidirect
49. #65044	C₂×C₃	semidirect
99. C₃×#454	D₅	semidirect
101. C₅×2₋¹⁺⁴	C₂²×C₃	semidirect
107. #4097	C₂²×C₃	semidirect
110. #4094	C₂²×C₃	semidirect
112. C₂×#689	C₂²×C₃	semidirect
122. #4015	C₂²×C₃	semidirect
123. C₅×#104	C₂²×C₃	semidirect
124. C₅×#101	C₂²×C₃	semidirect
126. #3956	C₂²×C₃	semidirect
127. #3954	C₂²×C₃	semidirect
129. #3935	C₂²×C₃	semidirect
163. C₃×2₋¹⁺⁴	C₂×D₅	semidirect
186. C₃×#104	C₂×D₅	semidirect
188. C₃×#101	C₂×D₅	semidirect
240. #454	C₃×D₅	semidirect
328. 2₋¹⁺⁴	C₂×C₃×D₅	semidirect
351. #104	C₂×C₃×D₅	semidirect
353. #101	C₂×C₃×D₅	semidirect
446. C₃×C₅	#3289	semidirect
500. C₅	C₃×#3289	semidirect
513. C₃	#10612019	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×#66172	2
C₃×#66109	2
C₃×C₅×#454	2
C₃×#65489	2
C₃×#65350	2
C₃×#65349	2
C₃×#65115	2
C₃×#65112	2
C₃×#65044	2
#10612019	3
C₃×#3289	5

Subgroups — C3×#10612019 #14457817

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10612019 #14457817