Subgroups — C₃×#10600857 #14306114

Order 1920.

792 conjugacy classes of subgroups.

The subgroup lattice has 468 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4086	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₅×#100	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#3965	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×C₃×#3955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×C₃×#3955	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×#65407	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×M₁₆×Dic₅	C₂	1	1	yes	maximal, characteristic, complemented
8	#10600857	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₂²×C₃×C₂²⋊D₅	C₄	1	4	yes	—
11	C₂²×C₃×D₂₀	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×#4086	—	2	1	no	—
15	C₃×#4086	—	2	2	no	—
16	C₃×#4086	—	2	1	no	—
17	C₂×C₃×C₄×Dic₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#681	C₂²	1	1	yes	characteristic
19	C₂×C₃×#681	C₂²	1	1	yes	characteristic
20	C₃×C₅×#100	—	2	2	no	—
21	C₃×#3965	—	2	2	no	—
22	C₃×#3955	—	2	2	no	—
23	C₃×#3955	—	2	2	no	—
24	C₃×#3947	—	2	1	no	—
25	C₃×#3946	—	2	2	no	—
26	C₃×C₈×Dic₅	—	2	1	no	—
27	C₃×#1965	—	5	1	no	maximal, Hall
28	C₂×#4086	C₂×C₃	1	1	yes	characteristic
29	C₂×C₅×#100	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×#3965	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#3955	C₂×C₃	1	1	yes	characteristic, complemented
32	C₂×#3955	C₂×C₃	1	1	yes	characteristic, complemented
33	#65407	C₂×C₃	1	1	yes	characteristic, complemented
34	M₁₆×Dic₅	C₂×C₃	1	1	yes	characteristic, complemented
35	C₂⁴×C₃×C₅	C₂×C₄	1	2	yes	—
36	C₂³×C₃×D₅	C₂×C₄	1	2	yes	—
37	C₂×C₃×C₅×D₄	—	2	1	no	—
38	C₂×C₃×C₅×D₄	—	2	1	no	—
39	C₂×C₃×C₅×D₄	—	2	1	no	—
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	1	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
44	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
45	C₂×C₃×C₂²⋊D₅	—	2	4	no	—
46	C₂×C₃×C₂²⋊D₅	—	4	8	no	—
47	C₂²×C₃×Dic₅	C₂×C₄	1	2	yes	—
48	C₂×C₃×D₂₀	—	2	1	no	—
49	C₂×C₃×D₂₀	—	2	1	no	—
50	C₂×C₃×D₂₀	—	2	1	no	—
51	C₂×C₃×D₂₀	—	2	1	no	—
52	C₂×C₃×D₂₀	—	2	1	no	—
53	C₂×C₃×D₂₀	—	2	1	no	—
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	—	2	1	no	—
56	C₃×C₅×M₁₆	—	2	1	no	—
57	C₃×C₅×M₁₆	D₄	1	2	yes	complemented
58	C₂×C₃×C₅×C₈	—	2	1	no	—
59	C₂×C₃×C₅×C₈	—	2	1	no	—
60	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
61	C₃×C₄×Dic₅	D₄	1	2	yes	—
62	C₃×C₄×Dic₅	D₄	1	1	yes	characteristic
63	C₃×#681	—	2	1	no	—
64	C₃×#681	—	2	1	no	—
65	C₃×#681	—	2	1	no	—
66	C₃×#681	D₄	1	2	yes	complemented
67	C₂×C₃×#168	—	2	1	no	—
68	C₂×C₃×#168	—	2	1	no	—
69	C₂×C₃×#127	—	5	1	no	—
70	C₃×#423	—	5	1	no	—
71	C₂×C₃×#100	—	5	1	no	—
72	C₂×C₃×#100	—	5	1	no	—
73	C₂×C₃×#100	—	5	1	no	—
74	C₂×C₃×#100	D₅	1	1	yes	characteristic, complemented
75	C₃×C₄×M₁₆	—	5	1	no	—
76	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
77	C₂²×C₂²⋊D₅	C₃×C₄	1	4	yes	—
78	C₂²×D₂₀	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	#4086	—	2	1	no	—
82	#4086	—	2	2	no	—
83	#4086	—	2	1	no	—
84	C₂×C₄×Dic₅	C₂²×C₃	1	1	yes	characteristic
85	C₂×#681	C₂²×C₃	1	1	yes	characteristic
86	C₂×#681	C₂²×C₃	1	1	yes	characteristic
87	C₅×#100	—	2	2	no	—
88	#3965	—	2	2	no	—
89	#3955	—	2	2	no	—
90	#3955	—	2	2	no	—
91	#3947	—	2	1	no	—
92	#3946	—	2	2	no	—
93	C₈×Dic₅	—	2	1	no	—
94	#1965	—	5	1	no	Sylow
95	C₂³×C₃×C₅	—	2	2	no	—
96	C₂³×C₃×C₅	—	2	2	no	—
97	C₂³×C₃×C₅	—	2	2	no	—
98	C₂³×C₃×C₅	—	4	4	no	—
99	C₂³×C₃×C₅	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₃×D₅	—	2	2	no	—
101	C₂²×C₃×D₅	—	2	2	no	—
102	C₂²×C₃×D₅	—	2	2	no	—
103	C₂²×C₃×D₅	—	4	4	no	—
104	C₃×C₅×D₄	—	4	1	no	—
105	C₃×C₅×D₄	—	4	1	no	—
106	C₃×C₅×D₄	—	4	1	no	—
107	C₃×C₅×D₄	—	4	1	no	—
108	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
109	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
110	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
114	C₃×C₂²⋊D₅	—	4	8	no	—
115	C₃×C₂²⋊D₅	—	4	8	no	—
116	C₂×C₃×Dic₅	—	2	4	no	—
117	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
118	C₂×C₃×Dic₅	C₂²⋊C₄	1	2	yes	—
119	C₃×D₂₀	—	4	1	no	—
120	C₃×D₂₀	—	4	1	no	—
121	C₃×D₂₀	—	4	1	no	—
122	C₃×D₂₀	—	4	1	no	—
123	C₃×C₅×C₈	—	2	2	no	—
124	C₃×C₅×C₈	—	4	1	no	—
125	C₃×#168	—	2	2	no	—
126	C₃×#168	—	4	1	no	—
127	C₂²×C₃×D₄	—	5	4	no	—
128	C₂²×C₃×D₄	—	5	1	no	—
129	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
130	C₂×C₃×M₁₆	—	5	1	no	—
131	C₂×C₃×M₁₆	—	5	1	no	—
132	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
133	C₂×C₃×M₁₆	C₂×D₅	1	1	yes	characteristic
134	C₃×#127	—	10	1	no	—
135	C₃×#127	—	10	1	no	—
136	C₃×#127	—	10	2	no	—
137	C₂×C₃×C₄²	—	5	1	no	—
138	C₃×C₄⋊C₈	—	10	2	no	—
139	C₃×#100	—	2	2	no	—
140	C₃×#100	—	10	2	no	—
141	C₃×#100	—	10	2	no	—
142	C₃×#100	—	10	2	no	—
143	C₃×#97	—	10	1	no	—
144	C₃×C₄×C₈	—	10	1	no	—
145	C₂⁴×C₅	C₂×C₃×C₄	1	2	yes	—
146	C₂³×D₅	C₂×C₃×C₄	1	2	yes	—
147	C₂×C₅×D₄	—	2	1	no	—
148	C₂×C₅×D₄	—	2	1	no	—
149	C₂×C₅×D₄	—	2	1	no	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	—	2	1	no	—
152	C₂×C₅×D₄	—	2	1	no	—
153	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
154	C₂×C₂²⋊D₅	—	2	4	no	—
155	C₂×C₂²⋊D₅	—	2	4	no	—
156	C₂×C₂²⋊D₅	—	4	8	no	—
157	C₂²×Dic₅	C₂×C₃×C₄	1	2	yes	—
158	C₂×D₂₀	—	2	1	no	—
159	C₂×D₂₀	—	2	1	no	—
160	C₂×D₂₀	—	2	1	no	—
161	C₂×D₂₀	—	2	1	no	—
162	C₂×D₂₀	—	2	1	no	—
163	C₂×D₂₀	—	2	1	no	—
164	C₅×M₁₆	—	2	1	no	—
165	C₅×M₁₆	—	2	1	no	—
166	C₅×M₁₆	—	2	1	no	—
167	C₅×M₁₆	C₃×D₄	1	2	yes	complemented
168	C₂×C₅×C₈	—	2	1	no	—
169	C₂×C₅×C₈	—	2	1	no	—
170	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
171	C₄×Dic₅	C₃×D₄	1	2	yes	—
172	C₄×Dic₅	C₃×D₄	1	1	yes	characteristic
173	#681	—	2	1	no	—
174	#681	—	2	1	no	—
175	#681	—	2	1	no	—
176	#681	C₃×D₄	1	2	yes	complemented
177	C₂×#168	—	2	1	no	—
178	C₂×#168	—	2	1	no	—
179	C₂×#127	—	5	1	no	—
180	#423	—	5	1	no	—
181	C₂×#100	—	5	1	no	—
182	C₂×#100	—	5	1	no	—
183	C₂×#100	—	5	1	no	—
184	C₂×#100	C₃×D₅	1	1	yes	characteristic, complemented
185	C₄×M₁₆	—	5	1	no	—
186	C₂²×C₃×C₅	—	2	2	no	—
187	C₂²×C₃×C₅	—	4	2	no	—
188	C₂²×C₃×C₅	—	4	4	no	—
189	C₂²×C₃×C₅	—	8	2	no	—
190	C₂²×C₃×C₅	—	8	2	no	—
191	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
193	C₂²×C₃×C₅	C₄×D₄	1	1	yes	characteristic
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	4	no	—
196	C₂×C₃×D₅	—	8	2	no	—
197	C₂×C₃×D₅	—	8	2	no	—
198	C₃×C₄×C₅	#121	1	1	yes	characteristic
199	C₃×C₄×C₅	#121	1	1	yes	characteristic
200	C₃×C₄×C₅	#124	1	1	yes	characteristic
201	C₃×C₄×C₅	#127	1	1	yes	characteristic
202	C₃×Dic₅	—	2	2	no	—
203	C₃×Dic₅	#100	1	4	yes	complemented
204	C₂⁴×C₃	—	5	2	no	—
205	C₂⁴×C₃	C₄×D₅	1	2	yes	—
206	C₂×C₃×D₄	—	2	1	no	—
207	C₂×C₃×D₄	—	2	1	no	—
208	C₂×C₃×D₄	—	2	1	no	—
209	C₂×C₃×D₄	—	2	1	no	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	2	1	no	—
212	C₂×C₃×D₄	—	10	4	no	—
213	C₂×C₃×D₄	—	10	4	no	—
214	C₂×C₃×D₄	—	10	1	no	—
215	C₂×C₃×D₄	—	10	1	no	—
216	C₂×C₃×D₄	—	10	1	no	—
217	C₂×C₃×D₄	—	10	1	no	—
218	C₂×C₃×D₄	—	10	1	no	—
219	C₂×C₃×D₄	—	10	1	no	—
220	C₂×C₃×D₄	—	20	8	no	—
221	C₂²×C₃×C₄	—	5	2	no	—
222	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
223	C₃×M₁₆	—	2	1	no	—
224	C₃×M₁₆	—	2	1	no	—
225	C₃×M₁₆	—	2	1	no	—
226	C₃×M₁₆	—	5	2	no	—
227	C₃×M₁₆	—	10	1	no	—
228	C₃×M₁₆	—	10	1	no	—
229	C₃×M₁₆	—	10	1	no	—
230	C₃×M₁₆	C₂²⋊D₅	1	2	yes	complemented
231	C₂×C₃×C₈	—	2	1	no	—
232	C₂×C₃×C₈	—	2	1	no	—
233	C₂×C₃×C₈	—	10	1	no	—
234	C₂×C₃×C₈	—	10	1	no	—
235	C₃×C₄²	—	5	1	no	—
236	C₃×C₄²	—	5	1	no	—
237	C₃×C₄²	—	5	2	no	—
238	C₂³×C₅	—	2	2	no	—
239	C₂³×C₅	—	2	2	no	—
240	C₂³×C₅	—	2	2	no	—
241	C₂³×C₅	—	4	4	no	—
242	C₂³×C₅	C₂²×C₃×C₄	1	1	yes	characteristic
243	C₂²×D₅	—	2	2	no	—
244	C₂²×D₅	—	2	2	no	—
245	C₂²×D₅	—	2	2	no	—
246	C₂²×D₅	—	4	4	no	—
247	C₅×D₄	—	4	1	no	—
248	C₅×D₄	—	4	1	no	—
249	C₅×D₄	—	4	1	no	—
250	C₅×D₄	—	4	1	no	—
251	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
252	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
253	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
254	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
255	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
256	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
257	C₂²⋊D₅	—	4	8	no	—
258	C₂²⋊D₅	—	4	8	no	—
259	C₂×Dic₅	—	2	4	no	—
260	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
261	C₂×Dic₅	C₃×C₂²⋊C₄	1	2	yes	—
262	D₂₀	—	4	1	no	—
263	D₂₀	—	4	1	no	—
264	D₂₀	—	4	1	no	—
265	D₂₀	—	4	1	no	—
266	C₅×C₈	—	2	2	no	—
267	C₅×C₈	—	4	1	no	—
268	#168	—	2	2	no	—
269	#168	—	4	1	no	—
270	C₂²×D₄	—	5	4	no	—
271	C₂²×D₄	—	5	1	no	—
272	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
273	C₂×M₁₆	—	5	1	no	—
274	C₂×M₁₆	—	5	1	no	—
275	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
276	C₂×M₁₆	C₂×C₃×D₅	1	1	yes	characteristic
277	#127	—	10	1	no	—
278	#127	—	10	1	no	—
279	#127	—	10	2	no	—
280	C₂×C₄²	—	5	1	no	—
281	C₄⋊C₈	—	10	2	no	—
282	#100	—	2	2	no	—
283	#100	—	10	2	no	—
284	#100	—	10	2	no	—
285	#100	—	10	2	no	—
286	#97	—	10	1	no	—
287	C₄×C₈	—	10	1	no	—
288	C₂×C₃×C₅	—	2	1	no	—
289	C₂×C₃×C₅	—	2	1	no	—
290	C₂×C₃×C₅	—	8	2	no	—
291	C₂×C₃×C₅	#390	1	1	yes	characteristic
292	C₂×C₃×C₅	C₂×#100	1	2	yes	—
293	C₃×D₅	—	8	2	no	—
294	C₂³×C₃	—	2	2	no	—
295	C₂³×C₃	—	2	2	no	—
296	C₂³×C₃	—	2	2	no	—
297	C₂³×C₃	—	4	4	no	—
298	C₂³×C₃	—	10	2	no	—
299	C₂³×C₃	—	10	2	no	—
300	C₂³×C₃	—	10	2	no	—
301	C₂³×C₃	—	20	4	no	—
302	C₂³×C₃	C₂×C₄×D₅	1	1	yes	characteristic
303	C₃×D₄	—	4	1	no	—
304	C₃×D₄	—	4	1	no	—
305	C₃×D₄	—	4	1	no	—
306	C₃×D₄	—	4	1	no	—
307	C₃×D₄	—	20	8	no	—
308	C₃×D₄	—	20	8	no	—
309	C₃×D₄	—	20	1	no	—
310	C₃×D₄	—	20	1	no	—
311	C₃×D₄	—	20	1	no	—
312	C₃×D₄	—	20	1	no	—
313	C₂×C₃×C₄	—	5	2	no	—
314	C₂×C₃×C₄	—	5	2	no	—
315	C₂×C₃×C₄	—	10	4	no	—
316	C₂×C₃×C₄	#709	1	1	yes	characteristic
317	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
318	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
319	C₂×C₃×C₄	D₄×D₅	1	1	yes	characteristic
320	C₂×C₃×C₄	#711	1	1	yes	characteristic
321	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
322	C₃×C₈	—	2	2	no	—
323	C₃×C₈	—	4	1	no	—
324	C₃×C₈	—	10	2	no	—
325	C₃×C₈	—	20	1	no	—
326	C₂²×C₅	—	2	2	no	—
327	C₂²×C₅	—	4	2	no	—
328	C₂²×C₅	—	4	4	no	—
329	C₂²×C₅	—	8	2	no	—
330	C₂²×C₅	—	8	2	no	—
331	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	1	yes	characteristic
332	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
333	C₂²×C₅	C₃×C₄×D₄	1	1	yes	characteristic
334	C₂×D₅	—	4	2	no	—
335	C₂×D₅	—	4	4	no	—
336	C₂×D₅	—	8	2	no	—
337	C₂×D₅	—	8	2	no	—
338	C₄×C₅	C₃×#121	1	1	yes	characteristic
339	C₄×C₅	C₃×#121	1	1	yes	characteristic
340	C₄×C₅	C₃×#124	1	1	yes	characteristic
341	C₄×C₅	C₃×#127	1	1	yes	characteristic
342	Dic₅	—	2	2	no	—
343	Dic₅	C₃×#100	1	4	yes	complemented
344	C₂⁴	—	5	2	no	—
345	C₂⁴	C₃×C₄×D₅	1	2	yes	—
346	C₂×D₄	—	2	1	no	—
347	C₂×D₄	—	2	1	no	—
348	C₂×D₄	—	2	1	no	—
349	C₂×D₄	—	2	1	no	—
350	C₂×D₄	—	2	1	no	—
351	C₂×D₄	—	2	1	no	—
352	C₂×D₄	—	10	4	no	—
353	C₂×D₄	—	10	4	no	—
354	C₂×D₄	—	10	1	no	—
355	C₂×D₄	—	10	1	no	—
356	C₂×D₄	—	10	1	no	—
357	C₂×D₄	—	10	1	no	—
358	C₂×D₄	—	10	1	no	—
359	C₂×D₄	—	10	1	no	—
360	C₂×D₄	—	20	8	no	—
361	C₂²×C₄	—	5	2	no	—
362	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
363	M₁₆	—	2	1	no	—
364	M₁₆	—	2	1	no	—
365	M₁₆	—	2	1	no	—
366	M₁₆	—	5	2	no	—
367	M₁₆	—	10	1	no	—
368	M₁₆	—	10	1	no	—
369	M₁₆	—	10	1	no	—
370	M₁₆	C₃×C₂²⋊D₅	1	2	yes	complemented
371	C₂×C₈	—	2	1	no	—
372	C₂×C₈	—	2	1	no	—
373	C₂×C₈	—	10	1	no	—
374	C₂×C₈	—	10	1	no	—
375	C₄²	—	5	1	no	—
376	C₄²	—	5	1	no	—
377	C₄²	—	5	2	no	—
378	C₃×C₅	#1965	1	1	yes	characteristic, complemented, Hall
379	C₂²×C₃	—	2	2	no	—
380	C₂²×C₃	—	4	4	no	—
381	C₂²×C₃	—	4	2	no	—
382	C₂²×C₃	—	8	2	no	—
383	C₂²×C₃	—	8	2	no	—
384	C₂²×C₃	—	20	4	no	—
385	C₂²×C₃	—	20	2	no	—
386	C₂²×C₃	—	40	2	no	—
387	C₂²×C₃	—	40	2	no	—
388	C₂²×C₃	D₅×C₂²⋊C₄	1	1	yes	characteristic
389	C₂²×C₃	#4027	1	1	yes	characteristic
390	C₂²×C₃	C₄×C₂²⋊D₅	1	1	yes	characteristic
391	C₃×C₄	—	5	4	no	—
392	C₃×C₄	—	10	2	no	—
393	C₃×C₄	#4030	1	1	yes	characteristic
394	C₃×C₄	#4031	1	1	yes	characteristic
395	C₃×C₄	#4085	1	1	yes	characteristic
396	C₃×C₄	#4086	1	1	yes	characteristic
397	C₂×C₅	—	2	1	no	—
398	C₂×C₅	—	2	1	no	—
399	C₂×C₅	—	8	2	no	—
400	C₂×C₅	C₃×#390	1	1	yes	characteristic
401	C₂×C₅	C₂×C₃×#100	1	2	yes	—
402	D₅	—	8	2	no	—
403	C₂³	—	2	2	no	—
404	C₂³	—	2	2	no	—
405	C₂³	—	2	2	no	—
406	C₂³	—	4	4	no	—
407	C₂³	—	10	2	no	—
408	C₂³	—	10	2	no	—
409	C₂³	—	10	2	no	—
410	C₂³	—	20	4	no	—
411	C₂³	C₂×C₃×C₄×D₅	1	1	yes	characteristic
412	D₄	—	4	1	no	—
413	D₄	—	4	1	no	—
414	D₄	—	4	1	no	—
415	D₄	—	4	1	no	—
416	D₄	—	20	8	no	—
417	D₄	—	20	8	no	—
418	D₄	—	20	1	no	—
419	D₄	—	20	1	no	—
420	D₄	—	20	1	no	—
421	D₄	—	20	1	no	—
422	C₂×C₄	—	5	2	no	—
423	C₂×C₄	—	5	2	no	—
424	C₂×C₄	—	10	4	no	—
425	C₂×C₄	C₃×#709	1	1	yes	characteristic
426	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
427	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
428	C₂×C₄	C₃×D₄×D₅	1	1	yes	characteristic
429	C₂×C₄	C₃×#711	1	1	yes	characteristic
430	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
431	C₈	—	2	2	no	—
432	C₈	—	4	1	no	—
433	C₈	—	10	2	no	—
434	C₈	—	20	1	no	—
435	C₂×C₃	—	2	1	no	—
436	C₂×C₃	—	2	1	no	—
437	C₂×C₃	—	8	2	no	—
438	C₂×C₃	—	40	2	no	—
439	C₂×C₃	D₅×#100	1	2	yes	—
440	C₂×C₃	#65246	1	1	yes	characteristic
441	C₅	C₃×#1965	1	1	yes	characteristic, complemented, Sylow
442	C₂²	—	2	2	no	—
443	C₂²	—	4	4	no	—
444	C₂²	—	4	2	no	—
445	C₂²	—	8	2	no	—
446	C₂²	—	8	2	no	—
447	C₂²	—	20	4	no	—
448	C₂²	—	20	2	no	—
449	C₂²	—	40	2	no	—
450	C₂²	—	40	2	no	—
451	C₂²	C₃×D₅×C₂²⋊C₄	1	1	yes	characteristic
452	C₂²	C₃×#4027	1	1	yes	characteristic
453	C₂²	C₃×C₄×C₂²⋊D₅	1	1	yes	characteristic
454	C₄	—	5	4	no	—
455	C₄	—	10	2	no	—
456	C₄	C₃×#4030	1	1	yes	characteristic
457	C₄	C₃×#4031	1	1	yes	characteristic
458	C₄	C₃×#4085	1	1	yes	characteristic
459	C₄	C₃×#4086	1	1	yes	characteristic
460	C₃	#10600857	1	1	yes	characteristic, direct product factor, Sylow
461	C₂	—	2	1	no	—
462	C₂	—	2	1	no	—
463	C₂	—	8	2	no	—
464	C₂	—	40	2	no	—
465	C₂	C₃×D₅×#100	1	2	yes	—
466	C₂	C₃×#65246	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	D₅×C₂²⋊C₄
commutator	C₂³×C₅	C₂²×C₃×C₄
Frattini	C₂²×C₄	C₂²×C₃×D₅
Fitting	C₂×C₃×C₅×#100	C₂
socle	C₂²×C₃×C₅	C₂×C₂²⋊C₄
prime radical	C₂×C₃×#4086	C₂
cosocle	C₂²×C₄×C₅	C₂³×C₃
hypercenter	C₂×C₃×#100	D₅
hypocenter	C₅	C₃×#1965
LCS	G ▷ C₂³×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#100

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₅×#100	C₂	semidirect
3. C₂×C₃×#3965	C₂	semidirect
4. C₂×C₃×#3955	C₂	semidirect
5. C₂×C₃×#3955	C₂	semidirect
6. C₃×#65407	C₂	semidirect
7. C₃×M₁₆×Dic₅	C₂	semidirect
8. #10600857	C₃	direct (N × H)
29. C₂×C₅×#100	C₂×C₃	semidirect
30. C₂×#3965	C₂×C₃	semidirect
31. C₂×#3955	C₂×C₃	semidirect
32. C₂×#3955	C₂×C₃	semidirect
33. #65407	C₂×C₃	semidirect
34. M₁₆×Dic₅	C₂×C₃	semidirect
57. C₃×C₅×M₁₆	D₄	semidirect
66. C₃×#681	D₄	semidirect
74. C₂×C₃×#100	D₅	semidirect
167. C₅×M₁₆	C₃×D₄	semidirect
176. #681	C₃×D₄	semidirect
184. C₂×#100	C₃×D₅	semidirect
203. C₃×Dic₅	#100	semidirect
230. C₃×M₁₆	C₂²⋊D₅	semidirect
343. Dic₅	C₃×#100	semidirect
370. M₁₆	C₃×C₂²⋊D₅	semidirect
378. C₃×C₅	#1965	semidirect
441. C₅	C₃×#1965	semidirect
460. C₃	#10600857	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×#4086	2
C₂×C₃×C₅×#100	2
C₂×C₃×#3965	2
C₂×C₃×#3955	2
C₃×#65407	2
C₃×M₁₆×Dic₅	2
#10600857	3
C₃×#1965	5

Subgroups — C3×#10600857 #14306114

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10600857 #14306114