Subgroups — C₃×#10611559 #14416545

Order 1920.

984 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4065	C₂	1	1	yes	maximal, characteristic
2	C₃×C₄×#713	C₂	1	2	yes	maximal, complemented
3	C₃×C₅×#441	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×#65473	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65315	C₂	1	2	yes	maximal, complemented
6	C₃×#65158	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×#65149	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×#65106	C₂	1	2	yes	maximal, complemented
9	C₃×#65093	C₂	1	2	yes	maximal, complemented
10	C₃×#65000	C₂	1	1	yes	maximal, characteristic, complemented
11	C₃×D₅×#97	C₂	1	1	yes	maximal, characteristic, complemented
12	#10611559	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×#713	C₂²	1	2	yes	—
14	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic
15	C₃×C₄×C₅×Q₈	C₂²	1	2	yes	—
16	C₃×Q₈×Dic₅	C₂²	1	2	yes	—
17	C₂×C₃×#688	C₂²	1	2	yes	—
18	C₃×#4065	C₄	1	8	yes	complemented
19	C₂×C₃×D₄₀	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₈×D₅	C₂²	1	1	yes	characteristic
22	C₃×#4039	—	2	2	no	—
23	C₃×#4039	C₂²	1	2	yes	—
24	C₃×#4038	—	2	2	no	—
25	C₃×#4038	C₂²	1	2	yes	—
26	C₃×C₄×D₂₀	—	2	2	no	—
27	C₃×C₄×D₂₀	C₂²	1	2	yes	—
28	C₃×C₄²×D₅	—	2	2	no	—
29	C₃×C₄²×D₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#106	C₂²	1	1	yes	characteristic
31	C₃×C₅×#103	C₂²	1	2	yes	—
32	C₃×C₅×#97	C₂²	1	1	yes	characteristic
33	C₃×#3967	C₂²	1	2	yes	—
34	C₃×#3953	C₂²	1	2	yes	—
35	C₃×#3949	C₂²	1	1	yes	characteristic
36	C₃×#3947	C₂²	1	1	yes	characteristic
37	C₃×#3947	C₂²	1	1	yes	characteristic
38	C₃×#3941	C₂²	1	2	yes	—
39	C₃×#3939	C₂²	1	2	yes	—
40	C₃×#3935	C₂²	1	1	yes	characteristic
41	C₃×#2943	—	5	1	no	maximal, Hall
42	C₂×#4065	C₂×C₃	1	1	yes	characteristic
43	C₄×#713	C₂×C₃	1	2	yes	complemented
44	C₅×#441	C₂×C₃	1	1	yes	characteristic, complemented
45	#65473	C₂×C₃	1	1	yes	characteristic, complemented
46	#65315	C₂×C₃	1	2	yes	complemented
47	#65158	C₂×C₃	1	1	yes	characteristic, complemented
48	#65149	C₂×C₃	1	1	yes	characteristic, complemented
49	#65106	C₂×C₃	1	2	yes	complemented
50	#65093	C₂×C₃	1	2	yes	complemented
51	#65000	C₂×C₃	1	1	yes	characteristic, complemented
52	D₅×#97	C₂×C₃	1	1	yes	characteristic, complemented
53	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
54	C₃×#713	—	2	4	no	—
55	C₃×#713	C₂×C₄	1	8	yes	complemented
56	C₂×C₃×D₂₀	—	2	2	no	—
57	C₂×C₃×D₂₀	C₂³	1	2	yes	—
58	C₂×C₃×C₄×D₅	—	2	2	no	—
59	C₂×C₃×C₄×D₅	—	2	2	no	—
60	C₂×C₃×C₄×D₅	—	2	2	no	—
61	C₂×C₃×C₄×D₅	D₄	1	2	yes	—
62	C₂×C₃×C₄×D₅	C₂³	1	1	yes	characteristic
63	C₃×C₅×Q₁₆	C₂×C₄	1	4	yes	complemented
64	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
65	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
66	C₃×C₅×C₄⋊C₄	—	2	2	no	—
67	C₃×C₅×C₄⋊C₄	C₂³	1	2	yes	—
68	C₃×C₄²×C₅	—	2	2	no	—
69	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
70	C₃×#688	C₂×C₄	1	8	yes	complemented
71	C₃×#685	—	2	2	no	—
72	C₃×#685	—	2	2	no	—
73	C₃×#685	—	2	2	no	—
74	C₃×C₄⋊Dic₅	—	2	2	no	—
75	C₃×C₄⋊Dic₅	C₂³	1	2	yes	—
76	C₃×C₄×Dic₅	—	2	2	no	—
77	C₃×C₄×Dic₅	—	2	2	no	—
78	C₃×C₄×Dic₅	D₄	1	2	yes	—
79	C₃×C₄×Dic₅	C₂³	1	1	yes	characteristic
80	C₂×C₃×#168	C₂³	1	1	yes	characteristic
81	C₂×C₃×#168	C₂³	1	1	yes	characteristic
82	C₃×D₄₀	C₂×C₄	1	4	yes	complemented
83	C₃×C₈×D₅	—	2	2	no	—
84	C₃×C₈×D₅	C₂×C₄	1	4	yes	complemented
85	C₂×C₃×#135	—	5	1	no	—
86	C₃×C₄×#41	—	5	2	no	—
87	C₃×#442	—	5	1	no	—
88	C₃×#442	—	5	1	no	—
89	C₃×#441	—	5	1	no	—
90	C₃×#441	D₅	1	1	yes	characteristic, complemented
91	C₃×#440	—	5	2	no	—
92	C₃×#440	—	5	2	no	—
93	C₃×#427	—	5	1	no	—
94	C₃×#416	—	5	2	no	—
95	C₂×C₃×#97	—	5	1	no	—
96	C₂×#713	C₂²×C₃	1	2	yes	—
97	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic
98	C₄×C₅×Q₈	C₂²×C₃	1	2	yes	—
99	Q₈×Dic₅	C₂²×C₃	1	2	yes	—
100	C₂×#688	C₂²×C₃	1	2	yes	—
101	#4065	C₃×C₄	1	8	yes	complemented
102	C₂×D₄₀	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₈×D₅	C₂²×C₃	1	1	yes	characteristic
105	#4039	—	2	2	no	—
106	#4039	C₂²×C₃	1	2	yes	—
107	#4038	—	2	2	no	—
108	#4038	C₂²×C₃	1	2	yes	—
109	C₄×D₂₀	—	2	2	no	—
110	C₄×D₂₀	C₂²×C₃	1	2	yes	—
111	C₄²×D₅	—	2	2	no	—
112	C₄²×D₅	C₂²×C₃	1	1	yes	characteristic
113	C₅×#106	C₂²×C₃	1	1	yes	characteristic
114	C₅×#103	C₂²×C₃	1	2	yes	—
115	C₅×#97	C₂²×C₃	1	1	yes	characteristic
116	#3967	C₂²×C₃	1	2	yes	—
117	#3953	C₂²×C₃	1	2	yes	—
118	#3949	C₂²×C₃	1	1	yes	characteristic
119	#3947	C₂²×C₃	1	1	yes	characteristic
120	#3947	C₂²×C₃	1	1	yes	characteristic
121	#3941	C₂²×C₃	1	2	yes	—
122	#3939	C₂²×C₃	1	2	yes	—
123	#3935	C₂²×C₃	1	1	yes	characteristic
124	#2943	—	5	1	no	Sylow
125	C₂²×C₃×D₅	—	2	2	no	—
126	C₂²×C₃×D₅	C₂×D₄	1	1	yes	characteristic
127	C₃×C₅×Q₈	—	2	2	no	—
128	C₃×C₅×Q₈	C₂²×C₄	1	4	yes	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	2	no	—
131	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
132	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
133	C₂×C₃×Dic₅	—	2	2	no	—
134	C₂×C₃×Dic₅	C₂×D₄	1	2	yes	—
135	C₂×C₃×Dic₅	C₂×D₄	1	1	yes	characteristic
136	C₃×D₂₀	—	2	8	no	—
137	C₃×D₂₀	—	2	2	no	—
138	C₃×D₂₀	C₂²×C₄	1	4	yes	—
139	C₃×C₄×D₅	—	2	8	no	—
140	C₃×C₄×D₅	—	4	2	no	—
141	C₃×C₄×D₅	—	4	4	no	—
142	C₃×C₄×D₅	—	4	4	no	—
143	C₃×C₄×D₅	C₂²×C₄	1	2	yes	—
144	C₃×C₄×D₅	#41	1	2	yes	—
145	C₃×C₅×C₈	—	2	1	no	—
146	C₃×C₅×C₈	C₂²×C₄	1	2	yes	—
147	C₃×#168	—	2	1	no	—
148	C₃×#168	C₂²×C₄	1	2	yes	—
149	C₂×C₃×#41	—	5	2	no	—
150	C₃×#135	—	5	8	no	—
151	C₂×C₃×Q₁₆	C₂×D₅	1	1	yes	characteristic
152	C₂×C₃×SD₁₆	—	5	2	no	—
153	C₂×C₃×D₈	—	5	1	no	—
154	C₂²×C₃×C₈	—	5	1	no	—
155	C₂²×C₃×C₈	—	5	1	no	—
156	C₃×C₄×Q₈	—	5	2	no	—
157	C₃×C₄×Q₈	C₂×D₅	1	2	yes	—
158	C₃×C₄×D₄	—	5	2	no	—
159	C₃×C₄×D₄	—	5	2	no	—
160	C₃×C₄×D₄	—	10	2	no	—
161	C₃×C₄×D₄	—	10	2	no	—
162	C₃×#117	—	5	2	no	—
163	C₃×#117	—	10	2	no	—
164	C₂×C₃×C₄²	—	5	1	no	—
165	C₂×C₃×C₄²	—	10	2	no	—
166	C₃×#107	—	5	2	no	—
167	C₃×#106	—	5	1	no	—
168	C₃×#106	C₂×D₅	1	1	yes	characteristic
169	C₃×#103	—	5	2	no	—
170	C₃×#103	C₂×D₅	1	2	yes	—
171	C₃×#102	—	5	2	no	—
172	C₃×#102	—	5	2	no	—
173	C₃×#97	—	5	1	no	—
174	C₃×#97	—	5	1	no	—
175	C₃×#97	—	5	1	no	—
176	C₃×#97	C₂×D₅	1	1	yes	characteristic
177	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
178	#713	—	2	4	no	—
179	#713	C₂×C₃×C₄	1	8	yes	complemented
180	C₂×D₂₀	—	2	2	no	—
181	C₂×D₂₀	C₂³×C₃	1	2	yes	—
182	C₂×C₄×D₅	—	2	2	no	—
183	C₂×C₄×D₅	—	2	2	no	—
184	C₂×C₄×D₅	—	2	2	no	—
185	C₂×C₄×D₅	C₃×D₄	1	2	yes	—
186	C₂×C₄×D₅	C₂³×C₃	1	1	yes	characteristic
187	C₅×Q₁₆	C₂×C₃×C₄	1	4	yes	complemented
188	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
189	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
190	C₅×C₄⋊C₄	—	2	2	no	—
191	C₅×C₄⋊C₄	C₂³×C₃	1	2	yes	—
192	C₄²×C₅	—	2	2	no	—
193	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
194	#688	C₂×C₃×C₄	1	8	yes	complemented
195	#685	—	2	2	no	—
196	#685	—	2	2	no	—
197	#685	—	2	2	no	—
198	C₄⋊Dic₅	—	2	2	no	—
199	C₄⋊Dic₅	C₂³×C₃	1	2	yes	—
200	C₄×Dic₅	—	2	2	no	—
201	C₄×Dic₅	—	2	2	no	—
202	C₄×Dic₅	C₃×D₄	1	2	yes	—
203	C₄×Dic₅	C₂³×C₃	1	1	yes	characteristic
204	C₂×#168	C₂³×C₃	1	1	yes	characteristic
205	C₂×#168	C₂³×C₃	1	1	yes	characteristic
206	D₄₀	C₂×C₃×C₄	1	4	yes	complemented
207	C₈×D₅	—	2	2	no	—
208	C₈×D₅	C₂×C₃×C₄	1	4	yes	complemented
209	C₂×#135	—	5	1	no	—
210	C₄×#41	—	5	2	no	—
211	#442	—	5	1	no	—
212	#442	—	5	1	no	—
213	#441	—	5	1	no	—
214	#441	C₃×D₅	1	1	yes	characteristic, complemented
215	#440	—	5	2	no	—
216	#440	—	5	2	no	—
217	#427	—	5	1	no	—
218	#416	—	5	2	no	—
219	C₂×#97	—	5	1	no	—
220	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
221	C₂×C₃×D₅	—	2	2	no	—
222	C₂×C₃×D₅	—	2	4	no	—
223	C₂×C₃×D₅	—	4	2	no	—
224	C₂×C₃×D₅	—	4	2	no	—
225	C₂×C₃×D₅	C₄×D₄	1	2	yes	—
226	C₃×C₄×C₅	—	2	4	no	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	4	2	no	—
229	C₃×C₄×C₅	C₂³×C₄	1	1	yes	characteristic
230	C₃×C₄×C₅	C₂×#41	1	1	yes	characteristic
231	C₃×Dic₅	—	2	2	no	—
232	C₃×Dic₅	—	4	2	no	—
233	C₃×Dic₅	C₄×D₄	1	2	yes	—
234	C₃×#41	—	5	8	no	—
235	C₃×#41	—	10	4	no	—
236	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
237	C₂×C₃×D₄	—	5	2	no	—
238	C₂×C₃×D₄	—	10	2	no	—
239	C₂²×C₃×C₄	—	5	1	no	—
240	C₂²×C₃×C₄	—	5	2	no	—
241	C₂²×C₃×C₄	—	10	2	no	—
242	C₂²×C₃×C₄	—	10	2	no	—
243	C₂²×C₃×C₄	—	10	2	no	—
244	C₃×Q₁₆	C₄×D₅	1	4	yes	complemented
245	C₃×SD₁₆	—	5	8	no	—
246	C₃×D₈	—	5	4	no	—
247	C₂×C₃×C₈	—	5	1	no	—
248	C₂×C₃×C₈	—	5	4	no	—
249	C₂×C₃×C₈	—	5	1	no	—
250	C₂×C₃×C₈	—	10	2	no	—
251	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
252	C₂×C₃×C₈	C₂²×D₅	1	1	yes	characteristic
253	C₃×C₄⋊C₄	—	2	2	no	—
254	C₃×C₄⋊C₄	—	5	2	no	—
255	C₃×C₄⋊C₄	—	10	2	no	—
256	C₃×C₄⋊C₄	C₂²×D₅	1	2	yes	—
257	C₃×C₂²⋊C₄	—	10	2	no	—
258	C₃×C₂²⋊C₄	—	10	2	no	—
259	C₃×C₂²⋊C₄	—	10	2	no	—
260	C₃×C₄²	—	2	2	no	—
261	C₃×C₄²	—	5	2	no	—
262	C₃×C₄²	—	5	1	no	—
263	C₃×C₄²	—	10	2	no	—
264	C₃×C₄²	—	10	2	no	—
265	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
266	C₂²×D₅	—	2	2	no	—
267	C₂²×D₅	C₂×C₃×D₄	1	1	yes	characteristic
268	C₅×Q₈	—	2	2	no	—
269	C₅×Q₈	C₂²×C₃×C₄	1	4	yes	—
270	C₂×C₄×C₅	—	2	2	no	—
271	C₂×C₄×C₅	—	2	2	no	—
272	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
273	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
274	C₂×Dic₅	—	2	2	no	—
275	C₂×Dic₅	C₂×C₃×D₄	1	2	yes	—
276	C₂×Dic₅	C₂×C₃×D₄	1	1	yes	characteristic
277	D₂₀	—	2	8	no	—
278	D₂₀	—	2	2	no	—
279	D₂₀	C₂²×C₃×C₄	1	4	yes	—
280	C₄×D₅	—	2	8	no	—
281	C₄×D₅	—	4	2	no	—
282	C₄×D₅	—	4	4	no	—
283	C₄×D₅	—	4	4	no	—
284	C₄×D₅	C₂²×C₃×C₄	1	2	yes	—
285	C₄×D₅	C₃×#41	1	2	yes	—
286	C₅×C₈	—	2	1	no	—
287	C₅×C₈	C₂²×C₃×C₄	1	2	yes	—
288	#168	—	2	1	no	—
289	#168	C₂²×C₃×C₄	1	2	yes	—
290	C₂×#41	—	5	2	no	—
291	#135	—	5	8	no	—
292	C₂×Q₁₆	C₂×C₃×D₅	1	1	yes	characteristic
293	C₂×SD₁₆	—	5	2	no	—
294	C₂×D₈	—	5	1	no	—
295	C₂²×C₈	—	5	1	no	—
296	C₂²×C₈	—	5	1	no	—
297	C₄×Q₈	—	5	2	no	—
298	C₄×Q₈	C₂×C₃×D₅	1	2	yes	—
299	C₄×D₄	—	5	2	no	—
300	C₄×D₄	—	5	2	no	—
301	C₄×D₄	—	10	2	no	—
302	C₄×D₄	—	10	2	no	—
303	#117	—	5	2	no	—
304	#117	—	10	2	no	—
305	C₂×C₄²	—	5	1	no	—
306	C₂×C₄²	—	10	2	no	—
307	#107	—	5	2	no	—
308	#106	—	5	1	no	—
309	#106	C₂×C₃×D₅	1	1	yes	characteristic
310	#103	—	5	2	no	—
311	#103	C₂×C₃×D₅	1	2	yes	—
312	#102	—	5	2	no	—
313	#102	—	5	2	no	—
314	#97	—	5	1	no	—
315	#97	—	5	1	no	—
316	#97	—	5	1	no	—
317	#97	C₂×C₃×D₅	1	1	yes	characteristic
318	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
319	C₂×C₃×C₅	#575	1	2	yes	—
320	C₃×D₅	—	2	2	no	—
321	C₃×D₅	—	4	4	no	—
322	C₂³×C₃	—	5	1	no	—
323	C₂³×C₃	—	10	2	no	—
324	C₃×Q₈	—	2	2	no	—
325	C₃×Q₈	C₂×C₄×D₅	1	4	yes	—
326	C₃×D₄	—	5	4	no	—
327	C₃×D₄	—	10	8	no	—
328	C₃×D₄	—	10	2	no	—
329	C₂×C₃×C₄	—	2	2	no	—
330	C₂×C₃×C₄	—	2	2	no	—
331	C₂×C₃×C₄	—	5	1	no	—
332	C₂×C₃×C₄	—	5	2	no	—
333	C₂×C₃×C₄	—	5	2	no	—
334	C₂×C₃×C₄	—	5	2	no	—
335	C₂×C₃×C₄	—	10	8	no	—
336	C₂×C₃×C₄	—	10	2	no	—
337	C₂×C₃×C₄	—	20	2	no	—
338	C₂×C₃×C₄	—	20	4	no	—
339	C₂×C₃×C₄	—	20	4	no	—
340	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
341	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
342	C₃×C₈	—	2	1	no	—
343	C₃×C₈	—	5	2	no	—
344	C₃×C₈	—	10	1	no	—
345	C₃×C₈	C₂×C₄×D₅	1	2	yes	—
346	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
347	C₂×D₅	—	2	2	no	—
348	C₂×D₅	—	2	4	no	—
349	C₂×D₅	—	4	2	no	—
350	C₂×D₅	—	4	2	no	—
351	C₂×D₅	C₃×C₄×D₄	1	2	yes	—
352	C₄×C₅	—	2	2	no	—
353	C₄×C₅	—	2	4	no	—
354	C₄×C₅	—	4	2	no	—
355	C₄×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
356	C₄×C₅	C₂×C₃×#41	1	1	yes	characteristic
357	Dic₅	—	2	2	no	—
358	Dic₅	—	4	2	no	—
359	Dic₅	C₃×C₄×D₄	1	2	yes	—
360	#41	—	5	8	no	—
361	#41	—	10	4	no	—
362	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
363	C₂×D₄	—	5	2	no	—
364	C₂×D₄	—	10	2	no	—
365	C₂²×C₄	—	5	1	no	—
366	C₂²×C₄	—	5	2	no	—
367	C₂²×C₄	—	10	2	no	—
368	C₂²×C₄	—	10	2	no	—
369	C₂²×C₄	—	10	2	no	—
370	Q₁₆	C₃×C₄×D₅	1	4	yes	complemented
371	SD₁₆	—	5	8	no	—
372	D₈	—	5	4	no	—
373	C₂×C₈	—	5	1	no	—
374	C₂×C₈	—	5	4	no	—
375	C₂×C₈	—	5	1	no	—
376	C₂×C₈	—	10	2	no	—
377	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
378	C₂×C₈	C₂²×C₃×D₅	1	1	yes	characteristic
379	C₄⋊C₄	—	2	2	no	—
380	C₄⋊C₄	—	5	2	no	—
381	C₄⋊C₄	—	10	2	no	—
382	C₄⋊C₄	C₂²×C₃×D₅	1	2	yes	—
383	C₂²⋊C₄	—	10	2	no	—
384	C₂²⋊C₄	—	10	2	no	—
385	C₂²⋊C₄	—	10	2	no	—
386	C₄²	—	2	2	no	—
387	C₄²	—	5	2	no	—
388	C₄²	—	5	1	no	—
389	C₄²	—	10	2	no	—
390	C₄²	—	10	2	no	—
391	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
392	C₃×C₅	#2943	1	1	yes	characteristic, complemented, Hall
393	C₂²×C₃	—	5	2	no	—
394	C₂²×C₃	—	10	2	no	—
395	C₂²×C₃	—	10	4	no	—
396	C₂²×C₃	—	20	2	no	—
397	C₂²×C₃	—	20	2	no	—
398	C₂²×C₃	C₂×D₄×D₅	1	1	yes	characteristic
399	C₃×C₄	—	2	2	no	—
400	C₃×C₄	—	2	4	no	—
401	C₃×C₄	—	4	2	no	—
402	C₃×C₄	—	5	2	no	—
403	C₃×C₄	—	10	2	no	—
404	C₃×C₄	—	20	2	no	—
405	C₃×C₄	C₂²×C₄×D₅	1	1	yes	characteristic
406	C₃×C₄	D₅×#41	1	1	yes	characteristic
407	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
408	C₂×C₅	C₃×#575	1	2	yes	—
409	D₅	—	2	2	no	—
410	D₅	—	4	4	no	—
411	C₂³	—	5	1	no	—
412	C₂³	—	10	2	no	—
413	Q₈	—	2	2	no	—
414	Q₈	C₂×C₃×C₄×D₅	1	4	yes	—
415	D₄	—	5	4	no	—
416	D₄	—	10	8	no	—
417	D₄	—	10	2	no	—
418	C₂×C₄	—	2	2	no	—
419	C₂×C₄	—	2	2	no	—
420	C₂×C₄	—	5	1	no	—
421	C₂×C₄	—	5	2	no	—
422	C₂×C₄	—	5	2	no	—
423	C₂×C₄	—	5	2	no	—
424	C₂×C₄	—	10	8	no	—
425	C₂×C₄	—	10	2	no	—
426	C₂×C₄	—	20	2	no	—
427	C₂×C₄	—	20	4	no	—
428	C₂×C₄	—	20	4	no	—
429	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
430	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
431	C₈	—	2	1	no	—
432	C₈	—	5	2	no	—
433	C₈	—	10	1	no	—
434	C₈	C₂×C₃×C₄×D₅	1	2	yes	—
435	C₂×C₃	—	10	2	no	—
436	C₂×C₃	—	20	4	no	—
437	C₂×C₃	C₄×D₄×D₅	1	1	yes	characteristic
438	C₂×C₃	#66111	1	2	yes	—
439	C₅	C₃×#2943	1	1	yes	characteristic, complemented, Sylow
440	C₂²	—	5	2	no	—
441	C₂²	—	10	2	no	—
442	C₂²	—	10	4	no	—
443	C₂²	—	20	2	no	—
444	C₂²	—	20	2	no	—
445	C₂²	C₂×C₃×D₄×D₅	1	1	yes	characteristic
446	C₄	—	2	2	no	—
447	C₄	—	2	4	no	—
448	C₄	—	4	2	no	—
449	C₄	—	5	2	no	—
450	C₄	—	10	2	no	—
451	C₄	—	20	2	no	—
452	C₄	C₂²×C₃×C₄×D₅	1	1	yes	characteristic
453	C₄	C₃×D₅×#41	1	1	yes	characteristic
454	C₃	#10611559	1	1	yes	characteristic, direct product factor, Sylow
455	C₂	—	10	2	no	—
456	C₂	—	20	4	no	—
457	C₂	C₃×C₄×D₄×D₅	1	1	yes	characteristic
458	C₂	C₃×#66111	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂×D₄×D₅
commutator	C₄×C₅	C₂³×C₃×C₄
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₃×C₅×#441	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
prime radical	C₂×C₃×#4065	C₂
cosocle	C₂×C₄×C₅	C₂⁴×C₃
hypercenter	C₃×#441	D₅
hypocenter	C₅	C₃×#2943
LCS	G ▷ C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₃×C₄² ◁ C₃×#441

Complements

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

N	H ≅ G/N	type
2. C₃×C₄×#713	C₂	semidirect
3. C₃×C₅×#441	C₂	semidirect
4. C₃×#65473	C₂	semidirect
5. C₃×#65315	C₂	semidirect
6. C₃×#65158	C₂	semidirect
7. C₃×#65149	C₂	semidirect
8. C₃×#65106	C₂	semidirect
9. C₃×#65093	C₂	semidirect
10. C₃×#65000	C₂	semidirect
11. C₃×D₅×#97	C₂	semidirect
12. #10611559	C₃	direct (N × H)
18. C₃×#4065	C₄	semidirect
43. C₄×#713	C₂×C₃	semidirect
44. C₅×#441	C₂×C₃	semidirect
45. #65473	C₂×C₃	semidirect
46. #65315	C₂×C₃	semidirect
47. #65158	C₂×C₃	semidirect
48. #65149	C₂×C₃	semidirect
49. #65106	C₂×C₃	semidirect
50. #65093	C₂×C₃	semidirect
51. #65000	C₂×C₃	semidirect
52. D₅×#97	C₂×C₃	semidirect
55. C₃×#713	C₂×C₄	semidirect
63. C₃×C₅×Q₁₆	C₂×C₄	semidirect
70. C₃×#688	C₂×C₄	semidirect
82. C₃×D₄₀	C₂×C₄	semidirect
84. C₃×C₈×D₅	C₂×C₄	semidirect
90. C₃×#441	D₅	semidirect
101. #4065	C₃×C₄	semidirect
179. #713	C₂×C₃×C₄	semidirect
187. C₅×Q₁₆	C₂×C₃×C₄	semidirect
194. #688	C₂×C₃×C₄	semidirect
206. D₄₀	C₂×C₃×C₄	semidirect
208. C₈×D₅	C₂×C₃×C₄	semidirect
214. #441	C₃×D₅	semidirect
244. C₃×Q₁₆	C₄×D₅	semidirect
370. Q₁₆	C₃×C₄×D₅	semidirect
392. C₃×C₅	#2943	semidirect
439. C₅	C₃×#2943	semidirect
454. C₃	#10611559	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×#4065	2
C₃×C₄×#713	2
C₃×C₅×#441	2
C₃×#65473	2
C₃×#65315	2
C₃×#65158	2
C₃×#65149	2
C₃×#65106	2
C₃×#65093	2
C₃×#65000	2
C₃×D₅×#97	2
#10611559	3
C₃×#2943	5

Subgroups — C3×#10611559 #14416545

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10611559 #14416545