Subgroups — C₃×#10599519 #14302328

Order 1920.

648 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4054	C₂	1	1	yes	maximal, characteristic
2	C₃×#66079	C₂	1	1	yes	maximal, characteristic, complemented
3	C₃×#65428	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65420	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#338	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#64776	C₂	1	1	yes	maximal, characteristic, complemented
8	#10599519	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂×C₃×#709	C₂²	1	1	yes	characteristic
10	C₂²×C₃×D₂₀	C₂²	1	1	yes	characteristic
11	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
13	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
14	C₃×#4072	C₂²	1	1	yes	characteristic
15	C₂×C₃×#681	C₂²	1	1	yes	characteristic
16	C₃×#4054	—	2	2	no	—
17	C₃×#4054	—	2	2	no	—
18	C₃×#4053	—	2	2	no	—
19	C₃×D₅×M₁₆	—	2	2	no	—
20	C₂×C₃×D₄₀	C₄	1	2	yes	complemented
21	C₂×C₃×#677	C₄	1	2	yes	complemented
22	C₃×#4047	—	2	2	no	—
23	C₃×#3957	—	2	2	no	—
24	C₃×#3955	—	2	2	no	—
25	C₃×#3953	—	2	2	no	—
26	C₃×#1903	—	5	1	no	maximal, Hall
27	C₂×#4054	C₂×C₃	1	1	yes	characteristic
28	#66079	C₂×C₃	1	1	yes	characteristic, complemented
29	#65428	C₂×C₃	1	1	yes	characteristic, complemented
30	#65420	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#3955	C₂×C₃	1	1	yes	characteristic, complemented
32	C₅×#338	C₂×C₃	1	1	yes	characteristic, complemented
33	#64776	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂³×C₃×D₅	—	2	1	no	—
35	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
36	C₂×C₃×C₂²⋊D₅	—	2	1	no	—
37	C₃×#709	—	2	1	no	—
38	C₃×#709	—	2	1	no	—
39	C₃×#709	D₄	1	2	yes	—
40	C₃×#709	D₄	1	2	yes	—
41	C₂×C₃×D₂₀	—	2	1	no	—
42	C₂×C₃×D₂₀	—	2	1	no	—
43	C₂×C₃×D₂₀	—	2	1	no	—
44	C₂×C₃×D₂₀	—	2	1	no	—
45	C₂×C₃×D₂₀	—	2	1	no	—
46	C₂×C₃×D₂₀	C₂×C₄	1	2	yes	—
47	C₂×C₃×D₂₀	C₂×C₄	1	1	yes	characteristic
48	C₂×C₃×C₄×D₅	—	2	1	no	—
49	C₂×C₃×Dic₁₀	C₂×C₄	1	1	yes	characteristic
50	C₃×C₅×M₁₆	—	2	1	no	—
51	C₃×C₅×M₁₆	—	2	1	no	—
52	C₃×C₅×M₁₆	—	2	1	no	—
53	C₃×C₅×M₁₆	—	2	1	no	—
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	—	2	1	no	—
56	C₂×C₃×C₅×C₈	—	2	1	no	—
57	C₂×C₃×C₅×C₈	C₂×C₄	1	2	yes	—
58	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
59	C₃×C₂²⋊Dic₅	—	2	1	no	—
60	C₃×C₄⋊Dic₅	—	2	1	no	—
61	C₃×C₄×Dic₅	—	2	1	no	—
62	C₃×#681	—	2	1	no	—
63	C₃×#681	D₄	1	2	yes	—
64	C₂×C₃×#168	—	2	1	no	—
65	C₃×D₄₀	—	2	4	no	—
66	C₃×#677	—	2	4	no	—
67	C₃×#676	—	2	4	no	—
68	C₃×C₈×D₅	—	2	4	no	—
69	C₂×C₃×AGL(1,ℤ/8)	—	5	1	no	—
70	C₃×#568	—	5	1	no	—
71	C₃×#421	—	5	1	no	—
72	C₃×#418	—	5	1	no	—
73	C₂×C₃×#100	—	5	1	no	—
74	C₃×#344	—	5	1	no	—
75	C₃×#338	D₅	1	1	yes	characteristic, complemented
76	C₂×#709	C₂²×C₃	1	1	yes	characteristic
77	C₂²×D₂₀	C₂²×C₃	1	1	yes	characteristic
78	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
79	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
80	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
81	#4072	C₂²×C₃	1	1	yes	characteristic
82	C₂×#681	C₂²×C₃	1	1	yes	characteristic
83	#4054	—	2	2	no	—
84	#4054	—	2	2	no	—
85	#4053	—	2	2	no	—
86	D₅×M₁₆	—	2	2	no	—
87	C₂×D₄₀	C₃×C₄	1	2	yes	complemented
88	C₂×#677	C₃×C₄	1	2	yes	complemented
89	#4047	—	2	2	no	—
90	#3957	—	2	2	no	—
91	#3955	—	2	2	no	—
92	#3953	—	2	2	no	—
93	#1903	—	5	1	no	Sylow
94	C₂³×C₃×C₅	#41	1	1	yes	characteristic
95	C₂²×C₃×D₅	—	2	1	no	—
96	C₂²×C₃×D₅	—	2	2	no	—
97	C₂²×C₃×D₅	—	4	1	no	—
98	C₂²×C₃×D₅	—	4	1	no	—
99	C₂²×C₃×D₅	—	8	2	no	—
100	C₂×C₃×C₄×C₅	C₂²×C₄	1	1	yes	characteristic
101	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
102	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
103	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
105	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
106	C₃×C₂²⋊D₅	—	2	2	no	—
107	C₃×C₂²⋊D₅	—	2	2	no	—
108	C₂×C₃×Dic₅	—	2	1	no	—
109	C₂×C₃×Dic₅	—	4	1	no	—
110	C₃×D₂₀	—	2	2	no	—
111	C₃×D₂₀	—	2	1	no	—
112	C₃×D₂₀	—	2	2	no	—
113	C₃×D₂₀	—	4	1	no	—
114	C₃×D₂₀	—	4	1	no	—
115	C₃×D₂₀	C₂²⋊C₄	1	2	yes	—
116	C₃×C₄×D₅	—	2	2	no	—
117	C₃×C₄×D₅	—	2	2	no	—
118	C₃×Dic₁₀	—	2	1	no	—
119	C₃×Dic₁₀	C₂²⋊C₄	1	2	yes	—
120	C₃×C₅×C₈	—	2	2	no	—
121	C₃×C₅×C₈	—	2	2	no	—
122	C₃×C₅×C₈	—	4	1	no	—
123	C₃×#168	—	2	2	no	—
124	C₂×C₃×#41	—	5	1	no	—
125	C₂²×C₃×D₄	—	5	1	no	—
126	C₃×AGL(1,ℤ/8)	—	10	2	no	—
127	C₃×AGL(1,ℤ/8)	—	10	2	no	—
128	C₂×C₃×SD₁₆	—	5	2	no	—
129	C₂×C₃×D₈	—	5	2	no	—
130	C₃×#131	—	10	2	no	—
131	C₃×#131	—	10	2	no	—
132	C₂×C₃×M₁₆	—	5	1	no	—
133	C₂×C₃×M₁₆	—	10	2	no	—
134	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
135	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
136	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
137	C₃×#117	—	5	1	no	—
138	C₃×#104	—	10	2	no	—
139	C₃×#102	—	10	2	no	—
140	C₃×#100	—	10	2	no	—
141	C₂³×D₅	—	2	1	no	—
142	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
143	C₂×C₂²⋊D₅	—	2	1	no	—
144	#709	—	2	1	no	—
145	#709	—	2	1	no	—
146	#709	C₃×D₄	1	2	yes	—
147	#709	C₃×D₄	1	2	yes	—
148	C₂×D₂₀	—	2	1	no	—
149	C₂×D₂₀	—	2	1	no	—
150	C₂×D₂₀	—	2	1	no	—
151	C₂×D₂₀	—	2	1	no	—
152	C₂×D₂₀	—	2	1	no	—
153	C₂×D₂₀	C₂×C₃×C₄	1	2	yes	—
154	C₂×D₂₀	C₂×C₃×C₄	1	1	yes	characteristic
155	C₂×C₄×D₅	—	2	1	no	—
156	C₂×Dic₁₀	C₂×C₃×C₄	1	1	yes	characteristic
157	C₅×M₁₆	—	2	1	no	—
158	C₅×M₁₆	—	2	1	no	—
159	C₅×M₁₆	—	2	1	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	1	no	—
162	C₅×M₁₆	—	2	1	no	—
163	C₂×C₅×C₈	—	2	1	no	—
164	C₂×C₅×C₈	C₂×C₃×C₄	1	2	yes	—
165	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
166	C₂²⋊Dic₅	—	2	1	no	—
167	C₄⋊Dic₅	—	2	1	no	—
168	C₄×Dic₅	—	2	1	no	—
169	#681	—	2	1	no	—
170	#681	C₃×D₄	1	2	yes	—
171	C₂×#168	—	2	1	no	—
172	D₄₀	—	2	4	no	—
173	#677	—	2	4	no	—
174	#676	—	2	4	no	—
175	C₈×D₅	—	2	4	no	—
176	C₂×AGL(1,ℤ/8)	—	5	1	no	—
177	#568	—	5	1	no	—
178	#421	—	5	1	no	—
179	#418	—	5	1	no	—
180	C₂×#100	—	5	1	no	—
181	#344	—	5	1	no	—
182	#338	C₃×D₅	1	1	yes	characteristic, complemented
183	C₂²×C₃×C₅	—	4	1	no	—
184	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
185	C₂²×C₃×C₅	#121	1	1	yes	characteristic
186	C₂²×C₃×C₅	#123	1	1	yes	characteristic
187	C₂×C₃×D₅	—	2	2	no	—
188	C₂×C₃×D₅	—	4	2	no	—
189	C₂×C₃×D₅	—	8	1	no	—
190	C₂×C₃×D₅	—	8	2	no	—
191	C₂×C₃×D₅	—	8	2	no	—
192	C₂×C₃×D₅	—	8	2	no	—
193	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₃×C₄×C₅	C₄×D₄	1	1	yes	characteristic
195	C₃×C₄×C₅	#120	1	1	yes	characteristic
196	C₃×C₄×C₅	#121	1	1	yes	characteristic
197	C₃×Dic₅	—	2	2	no	—
198	C₃×Dic₅	—	8	1	no	—
199	C₂⁴×C₃	—	10	1	no	—
200	C₃×#41	—	5	2	no	—
201	C₃×#41	—	5	2	no	—
202	C₃×#41	—	10	1	no	—
203	C₃×#41	—	10	1	no	—
204	C₂×C₃×Q₈	—	5	1	no	—
205	C₂×C₃×D₄	—	5	1	no	—
206	C₂×C₃×D₄	—	5	2	no	—
207	C₂×C₃×D₄	—	10	1	no	—
208	C₂×C₃×D₄	—	10	1	no	—
209	C₂×C₃×D₄	—	10	1	no	—
210	C₂×C₃×D₄	—	10	1	no	—
211	C₂×C₃×D₄	—	10	1	no	—
212	C₂×C₃×D₄	—	10	1	no	—
213	C₂²×C₃×C₄	—	10	1	no	—
214	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
215	C₃×SD₁₆	—	10	4	no	—
216	C₃×D₈	—	10	4	no	—
217	C₃×M₁₆	—	2	1	no	—
218	C₃×M₁₆	—	2	1	no	—
219	C₃×M₁₆	—	2	1	no	—
220	C₃×M₁₆	—	2	1	no	—
221	C₃×M₁₆	—	2	1	no	—
222	C₃×M₁₆	—	2	1	no	—
223	C₃×M₁₆	—	5	2	no	—
224	C₃×M₁₆	—	10	4	no	—
225	C₃×M₁₆	—	10	1	no	—
226	C₂×C₃×C₈	—	2	1	no	—
227	C₂×C₃×C₈	—	10	4	no	—
228	C₂×C₃×C₈	—	10	1	no	—
229	C₂×C₃×C₈	C₄×D₅	1	2	yes	—
230	C₂×C₃×C₈	D₂₀	1	2	yes	—
231	C₃×C₄⋊C₄	—	10	1	no	—
232	C₃×C₂²⋊C₄	—	10	1	no	—
233	C₃×C₄²	—	10	1	no	—
234	C₂³×C₅	C₃×#41	1	1	yes	characteristic
235	C₂²×D₅	—	2	1	no	—
236	C₂²×D₅	—	2	2	no	—
237	C₂²×D₅	—	4	1	no	—
238	C₂²×D₅	—	4	1	no	—
239	C₂²×D₅	—	8	2	no	—
240	C₂×C₄×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
246	C₂²⋊D₅	—	2	2	no	—
247	C₂²⋊D₅	—	2	2	no	—
248	C₂×Dic₅	—	2	1	no	—
249	C₂×Dic₅	—	4	1	no	—
250	D₂₀	—	2	2	no	—
251	D₂₀	—	2	1	no	—
252	D₂₀	—	2	2	no	—
253	D₂₀	—	4	1	no	—
254	D₂₀	—	4	1	no	—
255	D₂₀	C₃×C₂²⋊C₄	1	2	yes	—
256	C₄×D₅	—	2	2	no	—
257	C₄×D₅	—	2	2	no	—
258	Dic₁₀	—	2	1	no	—
259	Dic₁₀	C₃×C₂²⋊C₄	1	2	yes	—
260	C₅×C₈	—	2	2	no	—
261	C₅×C₈	—	2	2	no	—
262	C₅×C₈	—	4	1	no	—
263	#168	—	2	2	no	—
264	C₂×#41	—	5	1	no	—
265	C₂²×D₄	—	5	1	no	—
266	AGL(1,ℤ/8)	—	10	2	no	—
267	AGL(1,ℤ/8)	—	10	2	no	—
268	C₂×SD₁₆	—	5	2	no	—
269	C₂×D₈	—	5	2	no	—
270	#131	—	10	2	no	—
271	#131	—	10	2	no	—
272	C₂×M₁₆	—	5	1	no	—
273	C₂×M₁₆	—	10	2	no	—
274	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
275	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
276	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
277	#117	—	5	1	no	—
278	#104	—	10	2	no	—
279	#102	—	10	2	no	—
280	#100	—	10	2	no	—
281	C₂×C₃×C₅	—	2	1	no	—
282	C₂×C₃×C₅	—	2	1	no	—
283	C₂×C₃×C₅	—	2	1	no	—
284	C₂×C₃×C₅	#386	1	1	yes	characteristic
285	C₃×D₅	—	4	2	no	—
286	C₃×D₅	—	8	2	no	—
287	C₂³×C₃	—	10	1	no	—
288	C₂³×C₃	—	10	2	no	—
289	C₂³×C₃	—	20	1	no	—
290	C₂³×C₃	—	20	1	no	—
291	C₂³×C₃	—	40	2	no	—
292	C₂³×C₃	#713	1	1	yes	characteristic
293	C₃×Q₈	—	5	2	no	—
294	C₃×Q₈	—	10	1	no	—
295	C₃×D₄	—	5	2	no	—
296	C₃×D₄	—	10	2	no	—
297	C₃×D₄	—	10	2	no	—
298	C₃×D₄	—	10	1	no	—
299	C₃×D₄	—	10	2	no	—
300	C₃×D₄	—	10	2	no	—
301	C₃×D₄	—	20	1	no	—
302	C₃×D₄	—	20	1	no	—
303	C₂×C₃×C₄	—	10	1	no	—
304	C₂×C₃×C₄	—	10	2	no	—
305	C₂×C₃×C₄	—	10	2	no	—
306	C₂×C₃×C₄	—	20	1	no	—
307	C₂×C₃×C₄	C₂×C₄×D₅	1	1	yes	characteristic
308	C₂×C₃×C₄	C₂×D₂₀	1	1	yes	characteristic
309	C₂×C₃×C₄	#709	1	1	yes	characteristic
310	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
311	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
312	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
313	C₃×C₈	—	2	2	no	—
314	C₃×C₈	—	2	2	no	—
315	C₃×C₈	—	4	1	no	—
316	C₃×C₈	—	10	2	no	—
317	C₂²×C₅	—	4	1	no	—
318	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
319	C₂²×C₅	C₃×#121	1	1	yes	characteristic
320	C₂²×C₅	C₃×#123	1	1	yes	characteristic
321	C₂×D₅	—	2	2	no	—
322	C₂×D₅	—	4	2	no	—
323	C₂×D₅	—	8	1	no	—
324	C₂×D₅	—	8	2	no	—
325	C₂×D₅	—	8	2	no	—
326	C₂×D₅	—	8	2	no	—
327	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
328	C₄×C₅	C₃×C₄×D₄	1	1	yes	characteristic
329	C₄×C₅	C₃×#120	1	1	yes	characteristic
330	C₄×C₅	C₃×#121	1	1	yes	characteristic
331	Dic₅	—	2	2	no	—
332	Dic₅	—	8	1	no	—
333	C₂⁴	—	10	1	no	—
334	#41	—	5	2	no	—
335	#41	—	5	2	no	—
336	#41	—	10	1	no	—
337	#41	—	10	1	no	—
338	C₂×Q₈	—	5	1	no	—
339	C₂×D₄	—	5	1	no	—
340	C₂×D₄	—	5	2	no	—
341	C₂×D₄	—	10	1	no	—
342	C₂×D₄	—	10	1	no	—
343	C₂×D₄	—	10	1	no	—
344	C₂×D₄	—	10	1	no	—
345	C₂×D₄	—	10	1	no	—
346	C₂×D₄	—	10	1	no	—
347	C₂²×C₄	—	10	1	no	—
348	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
349	SD₁₆	—	10	4	no	—
350	D₈	—	10	4	no	—
351	M₁₆	—	2	1	no	—
352	M₁₆	—	2	1	no	—
353	M₁₆	—	2	1	no	—
354	M₁₆	—	2	1	no	—
355	M₁₆	—	2	1	no	—
356	M₁₆	—	2	1	no	—
357	M₁₆	—	5	2	no	—
358	M₁₆	—	10	4	no	—
359	M₁₆	—	10	1	no	—
360	C₂×C₈	—	2	1	no	—
361	C₂×C₈	—	10	4	no	—
362	C₂×C₈	—	10	1	no	—
363	C₂×C₈	C₃×C₄×D₅	1	2	yes	—
364	C₂×C₈	C₃×D₂₀	1	2	yes	—
365	C₄⋊C₄	—	10	1	no	—
366	C₂²⋊C₄	—	10	1	no	—
367	C₄²	—	10	1	no	—
368	C₃×C₅	#1903	1	1	yes	characteristic, complemented, Hall
369	C₂²×C₃	—	4	1	no	—
370	C₂²×C₃	—	10	2	no	—
371	C₂²×C₃	—	20	2	no	—
372	C₂²×C₃	—	40	1	no	—
373	C₂²×C₃	—	40	2	no	—
374	C₂²×C₃	—	40	2	no	—
375	C₂²×C₃	—	40	2	no	—
376	C₂²×C₃	#4039	1	1	yes	characteristic
377	C₂²×C₃	#4040	1	1	yes	characteristic
378	C₂²×C₃	#4041	1	1	yes	characteristic
379	C₃×C₄	—	10	2	no	—
380	C₃×C₄	—	40	1	no	—
381	C₃×C₄	C₄×D₂₀	1	1	yes	characteristic
382	C₃×C₄	D₅×C₂²⋊C₄	1	1	yes	characteristic
383	C₃×C₄	#4028	1	1	yes	characteristic
384	C₃×C₄	#4030	1	1	yes	characteristic
385	C₂×C₅	—	2	1	no	—
386	C₂×C₅	—	2	1	no	—
387	C₂×C₅	—	2	1	no	—
388	C₂×C₅	C₃×#386	1	1	yes	characteristic
389	D₅	—	4	2	no	—
390	D₅	—	8	2	no	—
391	C₂³	—	10	1	no	—
392	C₂³	—	10	2	no	—
393	C₂³	—	20	1	no	—
394	C₂³	—	20	1	no	—
395	C₂³	—	40	2	no	—
396	C₂³	C₃×#713	1	1	yes	characteristic
397	Q₈	—	5	2	no	—
398	Q₈	—	10	1	no	—
399	D₄	—	5	2	no	—
400	D₄	—	10	2	no	—
401	D₄	—	10	2	no	—
402	D₄	—	10	1	no	—
403	D₄	—	10	2	no	—
404	D₄	—	10	2	no	—
405	D₄	—	20	1	no	—
406	D₄	—	20	1	no	—
407	C₂×C₄	—	10	1	no	—
408	C₂×C₄	—	10	2	no	—
409	C₂×C₄	—	10	2	no	—
410	C₂×C₄	—	20	1	no	—
411	C₂×C₄	C₂×C₃×C₄×D₅	1	1	yes	characteristic
412	C₂×C₄	C₂×C₃×D₂₀	1	1	yes	characteristic
413	C₂×C₄	C₃×#709	1	1	yes	characteristic
414	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
415	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
416	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
417	C₈	—	2	2	no	—
418	C₈	—	2	2	no	—
419	C₈	—	4	1	no	—
420	C₈	—	10	2	no	—
421	C₂×C₃	—	2	1	no	—
422	C₂×C₃	—	2	1	no	—
423	C₂×C₃	—	2	1	no	—
424	C₂×C₃	—	20	2	no	—
425	C₂×C₃	—	40	2	no	—
426	C₂×C₃	#64954	1	1	yes	characteristic
427	C₅	C₃×#1903	1	1	yes	characteristic, complemented, Sylow
428	C₂²	—	4	1	no	—
429	C₂²	—	10	2	no	—
430	C₂²	—	20	2	no	—
431	C₂²	—	40	1	no	—
432	C₂²	—	40	2	no	—
433	C₂²	—	40	2	no	—
434	C₂²	—	40	2	no	—
435	C₂²	C₃×#4039	1	1	yes	characteristic
436	C₂²	C₃×#4040	1	1	yes	characteristic
437	C₂²	C₃×#4041	1	1	yes	characteristic
438	C₄	—	10	2	no	—
439	C₄	—	40	1	no	—
440	C₄	C₃×C₄×D₂₀	1	1	yes	characteristic
441	C₄	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
442	C₄	C₃×#4028	1	1	yes	characteristic
443	C₄	C₃×#4030	1	1	yes	characteristic
444	C₃	#10599519	1	1	yes	characteristic, direct product factor, Sylow
445	C₂	—	2	1	no	—
446	C₂	—	2	1	no	—
447	C₂	—	2	1	no	—
448	C₂	—	20	2	no	—
449	C₂	—	40	2	no	—
450	C₂	C₃×#64954	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₃	#64954
commutator	C₂×C₄×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₃×C₅×#338	C₂
socle	C₂×C₃×C₅	#386
prime radical	C₂×C₃×#4054	C₂
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₃×#338	D₅
hypocenter	C₅	C₃×#1903
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂×C₃ ◁ C₂²×C₃×C₄ ◁ C₃×#338

Complements

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

N	H ≅ G/N	type
2. C₃×#66079	C₂	semidirect
3. C₃×#65428	C₂	semidirect
4. C₃×#65420	C₂	semidirect
5. C₂×C₃×#3955	C₂	semidirect
6. C₃×C₅×#338	C₂	semidirect
7. C₃×#64776	C₂	semidirect
8. #10599519	C₃	direct (N × H)
20. C₂×C₃×D₄₀	C₄	semidirect
21. C₂×C₃×#677	C₄	semidirect
28. #66079	C₂×C₃	semidirect
29. #65428	C₂×C₃	semidirect
30. #65420	C₂×C₃	semidirect
31. C₂×#3955	C₂×C₃	semidirect
32. C₅×#338	C₂×C₃	semidirect
33. #64776	C₂×C₃	semidirect
75. C₃×#338	D₅	semidirect
87. C₂×D₄₀	C₃×C₄	semidirect
88. C₂×#677	C₃×C₄	semidirect
182. #338	C₃×D₅	semidirect
368. C₃×C₅	#1903	semidirect
427. C₅	C₃×#1903	semidirect
444. C₃	#10599519	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂×C₃×#4054	2
C₃×#66079	2
C₃×#65428	2
C₃×#65420	2
C₂×C₃×#3955	2
C₃×C₅×#338	2
C₃×#64776	2
#10599519	3
C₃×#1903	5

Subgroups — C3×#10599519 #14302328

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10599519 #14302328