Subgroups — C₃×#10614674 #14439283

Order 1920.

1144 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×#4088	C₂	1	2	yes	maximal, complemented
3	C₂×C₃×#4078	C₂	1	2	yes	maximal, complemented
4	C₃×#65811	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65349	C₂	1	2	yes	maximal, complemented
6	C₃×#65348	C₂	1	4	yes	maximal, complemented
7	C₃×#65347	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×#681	C₂	1	1	yes	maximal, characteristic, complemented
9	#10614674	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
11	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
12	C₂×C₃×#709	C₂²	1	2	yes	—
13	C₃×C₅×#124	—	2	2	no	—
14	C₃×C₅×#124	C₂²	1	2	yes	—
15	C₃×C₅×#124	C₂²	1	2	yes	—
16	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
17	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
18	C₂×C₃×#689	C₂²	1	4	yes	complemented
19	C₃×#4088	—	2	8	no	—
20	C₂×C₃×#688	C₂²	1	4	yes	complemented
21	C₂×C₃×#687	C₂²	1	4	yes	—
22	C₃×#4078	—	2	8	no	—
23	C₂×C₃×#686	C₂²	1	4	yes	—
24	C₃×#4076	—	2	2	no	—
25	C₂×C₃×#681	C₂²	1	2	yes	—
26	C₃×#4021	C₂²	1	2	yes	complemented
27	C₃×#4020	C₂²	1	1	yes	characteristic, complemented
28	C₃×C₄×D₂₀	—	2	2	no	—
29	C₃×#4015	C₂²	1	1	yes	characteristic, complemented
30	C₃×#3935	C₂²	1	2	yes	complemented
31	C₃×C₄×#168	C₂²	1	2	yes	complemented
32	C₃×#3153	—	5	1	no	maximal, Hall
33	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×#4088	C₂×C₃	1	2	yes	complemented
35	C₂×#4078	C₂×C₃	1	2	yes	complemented
36	#65811	C₂×C₃	1	1	yes	characteristic, complemented
37	#65349	C₂×C₃	1	2	yes	complemented
38	#65348	C₂×C₃	1	4	yes	complemented
39	#65347	C₂×C₃	1	2	yes	complemented
40	C₄×#681	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	—	2	1	no	—
42	C₂×C₃×C₅×Q₈	—	2	1	no	—
43	C₂×C₃×C₅×Q₈	—	2	4	no	—
44	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
45	C₂×C₃×C₅×D₄	—	2	4	no	—
46	C₂×C₃×C₅×D₄	—	2	1	no	—
47	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
50	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
51	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
52	C₃×#709	—	2	4	no	—
53	C₃×#709	—	2	4	no	—
54	C₂×C₃×D₂₀	—	2	2	no	—
55	C₂×C₃×D₂₀	C₂³	1	2	yes	—
56	C₂×C₃×C₄×D₅	—	2	2	no	—
57	C₂×C₃×Dic₁₀	C₂³	1	2	yes	—
58	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
59	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
60	C₃×C₄²×C₅	D₄	1	2	yes	—
61	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
62	C₃×C₄²×C₅	C₂³	1	1	yes	characteristic
63	C₃×#689	—	2	8	no	—
64	C₃×#688	—	2	8	no	—
65	C₃×#687	—	2	8	no	—
66	C₃×#686	—	2	8	no	—
67	C₃×#685	—	2	4	no	—
68	C₃×C₄⋊Dic₅	—	2	2	no	—
69	C₃×#681	D₄	1	8	yes	complemented
70	C₂×C₃×#168	C₂³	1	4	yes	—
71	C₂×C₃×#137	—	5	2	no	—
72	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
73	C₃×#532	—	5	1	no	—
74	C₂×C₃×#124	D₅	1	1	yes	characteristic, complemented
75	C₃×#497	—	5	2	no	—
76	C₃×#496	—	5	2	no	—
77	C₃×#495	—	5	4	no	—
78	C₃×C₄×M₁₆	—	5	1	no	—
79	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
81	C₂×#709	C₂²×C₃	1	2	yes	—
82	C₅×#124	—	2	2	no	—
83	C₅×#124	C₂²×C₃	1	2	yes	—
84	C₅×#124	C₂²×C₃	1	2	yes	—
85	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
86	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
87	C₂×#689	C₂²×C₃	1	4	yes	complemented
88	#4088	—	2	8	no	—
89	C₂×#688	C₂²×C₃	1	4	yes	complemented
90	C₂×#687	C₂²×C₃	1	4	yes	—
91	#4078	—	2	8	no	—
92	C₂×#686	C₂²×C₃	1	4	yes	—
93	#4076	—	2	2	no	—
94	C₂×#681	C₂²×C₃	1	2	yes	—
95	#4021	C₂²×C₃	1	2	yes	complemented
96	#4020	C₂²×C₃	1	1	yes	characteristic, complemented
97	C₄×D₂₀	—	2	2	no	—
98	#4015	C₂²×C₃	1	1	yes	characteristic, complemented
99	#3935	C₂²×C₃	1	2	yes	complemented
100	C₄×#168	C₂²×C₃	1	2	yes	complemented
101	#3153	—	5	1	no	Sylow
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	4	4	no	—
104	C₂³×C₃×C₅	—	4	2	no	—
105	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
106	C₂²×C₃×D₅	—	2	2	no	—
107	C₃×C₅×Q₈	—	2	4	no	—
108	C₃×C₅×Q₈	—	4	2	no	—
109	C₃×C₅×D₄	—	2	4	no	—
110	C₃×C₅×D₄	—	4	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	—	4	2	no	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
117	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
118	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
119	C₃×C₂²⋊D₅	—	4	4	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₃×D₂₀	—	2	2	no	—
122	C₃×D₂₀	—	2	2	no	—
123	C₃×D₂₀	—	4	4	no	—
124	C₃×C₄×D₅	—	4	4	no	—
125	C₃×Dic₁₀	—	2	2	no	—
126	C₃×Dic₁₀	—	2	2	no	—
127	C₃×#168	C₂×D₄	1	8	yes	—
128	C₂×C₃×#41	—	5	2	no	—
129	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
131	C₃×#137	—	10	8	no	—
132	C₃×AGL(1,ℤ/8)	—	10	8	no	—
133	C₂×C₃×Q₁₆	—	5	4	no	—
134	C₂×C₃×SD₁₆	—	5	4	no	—
135	C₂×C₃×SD₁₆	—	5	4	no	—
136	C₂×C₃×D₈	—	5	4	no	—
137	C₂×C₃×M₁₆	—	5	2	no	—
138	C₃×C₄⋊Q₈	—	5	1	no	—
139	C₃×#127	—	5	1	no	—
140	C₃×#124	—	2	2	no	—
141	C₃×#124	—	5	2	no	—
142	C₃×#124	C₂×D₅	1	2	yes	—
143	C₃×#124	C₂×D₅	1	2	yes	—
144	C₃×#121	—	10	2	no	—
145	C₃×C₄×D₄	—	10	2	no	—
146	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
147	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
148	C₃×#97	—	5	2	no	—
149	C₃×C₄×C₈	—	5	2	no	—
150	C₂⁴×C₅	—	2	1	no	—
151	C₂×C₅×Q₈	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	4	no	—
153	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
154	C₂×C₅×D₄	—	2	4	no	—
155	C₂×C₅×D₄	—	2	1	no	—
156	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
157	C₂²×C₄×C₅	—	2	1	no	—
158	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
160	C₂×C₂²⋊D₅	—	2	2	no	—
161	#709	—	2	4	no	—
162	#709	—	2	4	no	—
163	C₂×D₂₀	—	2	2	no	—
164	C₂×D₂₀	C₂³×C₃	1	2	yes	—
165	C₂×C₄×D₅	—	2	2	no	—
166	C₂×Dic₁₀	C₂³×C₃	1	2	yes	—
167	C₅×C₂²⋊C₄	—	2	4	no	—
168	C₅×C₂²⋊C₄	—	2	4	no	—
169	C₄²×C₅	C₃×D₄	1	2	yes	—
170	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
171	C₄²×C₅	C₂³×C₃	1	1	yes	characteristic
172	#689	—	2	8	no	—
173	#688	—	2	8	no	—
174	#687	—	2	8	no	—
175	#686	—	2	8	no	—
176	#685	—	2	4	no	—
177	C₄⋊Dic₅	—	2	2	no	—
178	#681	C₃×D₄	1	8	yes	complemented
179	C₂×#168	C₂³×C₃	1	4	yes	—
180	C₂×#137	—	5	2	no	—
181	C₂×AGL(1,ℤ/8)	—	5	2	no	—
182	#532	—	5	1	no	—
183	C₂×#124	C₃×D₅	1	1	yes	characteristic, complemented
184	#497	—	5	2	no	—
185	#496	—	5	2	no	—
186	#495	—	5	4	no	—
187	C₄×M₁₆	—	5	1	no	—
188	C₂²×C₃×C₅	—	2	2	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	4	no	—
191	C₂²×C₃×C₅	—	8	4	no	—
192	C₂²×C₃×C₅	#127	1	2	yes	—
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂×C₃×D₅	—	4	2	no	—
195	C₂×C₃×D₅	—	4	4	no	—
196	C₃×C₄×C₅	—	2	2	no	—
197	C₃×C₄×C₅	—	2	2	no	—
198	C₃×C₄×C₅	—	4	2	no	—
199	C₃×C₄×C₅	#127	1	2	yes	—
200	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
201	C₃×Dic₅	—	4	2	no	—
202	C₂⁴×C₃	—	2	1	no	—
203	C₃×#41	—	10	4	no	—
204	C₃×#41	—	10	4	no	—
205	C₂×C₃×Q₈	—	2	1	no	—
206	C₂×C₃×Q₈	—	2	4	no	—
207	C₂×C₃×Q₈	—	5	2	no	—
208	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
209	C₂×C₃×D₄	—	2	4	no	—
210	C₂×C₃×D₄	—	2	1	no	—
211	C₂×C₃×D₄	—	5	2	no	—
212	C₂×C₃×D₄	—	10	2	no	—
213	C₂×C₃×D₄	—	10	2	no	—
214	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
215	C₂²×C₃×C₄	—	2	1	no	—
216	C₂²×C₃×C₄	—	10	2	no	—
217	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
218	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
219	C₃×Q₁₆	—	10	8	no	—
220	C₃×SD₁₆	—	10	8	no	—
221	C₃×SD₁₆	—	10	8	no	—
222	C₃×D₈	—	10	8	no	—
223	C₃×M₁₆	—	5	8	no	—
224	C₂×C₃×C₈	—	5	4	no	—
225	C₃×C₄⋊C₄	—	10	2	no	—
226	C₃×C₂²⋊C₄	—	2	4	no	—
227	C₃×C₂²⋊C₄	—	2	4	no	—
228	C₃×C₂²⋊C₄	—	10	4	no	—
229	C₃×C₄²	C₂²⋊D₅	1	2	yes	—
230	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
231	C₃×C₄²	C₂²×D₅	1	1	yes	characteristic
232	C₂³×C₅	—	2	2	no	—
233	C₂³×C₅	—	4	4	no	—
234	C₂³×C₅	—	4	2	no	—
235	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
236	C₂²×D₅	—	2	2	no	—
237	C₅×Q₈	—	2	4	no	—
238	C₅×Q₈	—	4	2	no	—
239	C₅×D₄	—	2	4	no	—
240	C₅×D₄	—	4	2	no	—
241	C₂×C₄×C₅	—	2	2	no	—
242	C₂×C₄×C₅	—	4	2	no	—
243	C₂×C₄×C₅	—	4	2	no	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
245	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
246	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
247	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
249	C₂²⋊D₅	—	4	4	no	—
250	C₂×Dic₅	—	2	2	no	—
251	D₂₀	—	2	2	no	—
252	D₂₀	—	2	2	no	—
253	D₂₀	—	4	4	no	—
254	C₄×D₅	—	4	4	no	—
255	Dic₁₀	—	2	2	no	—
256	Dic₁₀	—	2	2	no	—
257	#168	C₂×C₃×D₄	1	8	yes	—
258	C₂×#41	—	5	2	no	—
259	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
260	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
261	#137	—	10	8	no	—
262	AGL(1,ℤ/8)	—	10	8	no	—
263	C₂×Q₁₆	—	5	4	no	—
264	C₂×SD₁₆	—	5	4	no	—
265	C₂×SD₁₆	—	5	4	no	—
266	C₂×D₈	—	5	4	no	—
267	C₂×M₁₆	—	5	2	no	—
268	C₄⋊Q₈	—	5	1	no	—
269	#127	—	5	1	no	—
270	#124	—	2	2	no	—
271	#124	—	5	2	no	—
272	#124	C₂×C₃×D₅	1	2	yes	—
273	#124	C₂×C₃×D₅	1	2	yes	—
274	#121	—	10	2	no	—
275	C₄×D₄	—	10	2	no	—
276	C₂×C₂²⋊C₄	—	2	2	no	—
277	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
278	#97	—	5	2	no	—
279	C₄×C₈	—	5	2	no	—
280	C₂×C₃×C₅	—	2	2	no	—
281	C₂×C₃×C₅	—	8	2	no	—
282	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
283	C₂×C₃×C₅	#575	1	2	yes	—
284	C₃×D₅	—	8	2	no	—
285	C₂³×C₃	—	2	2	no	—
286	C₂³×C₃	—	4	4	no	—
287	C₂³×C₃	—	4	2	no	—
288	C₂³×C₃	—	10	2	no	—
289	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
290	C₃×Q₈	—	2	4	no	—
291	C₃×Q₈	—	4	2	no	—
292	C₃×Q₈	—	10	2	no	—
293	C₃×Q₈	—	10	2	no	—
294	C₃×D₄	—	2	4	no	—
295	C₃×D₄	—	4	2	no	—
296	C₃×D₄	—	10	2	no	—
297	C₃×D₄	—	10	2	no	—
298	C₃×D₄	—	20	4	no	—
299	C₃×D₄	—	20	4	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	4	2	no	—
302	C₂×C₃×C₄	—	4	2	no	—
303	C₂×C₃×C₄	—	10	2	no	—
304	C₂×C₃×C₄	—	20	4	no	—
305	C₂×C₃×C₄	D₄×D₅	1	4	yes	—
306	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
307	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	2	yes	—
308	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
309	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
310	C₃×C₈	—	5	8	no	—
311	C₂²×C₅	—	2	2	no	—
312	C₂²×C₅	—	4	4	no	—
313	C₂²×C₅	—	4	2	no	—
314	C₂²×C₅	—	8	4	no	—
315	C₂²×C₅	C₃×#127	1	2	yes	—
316	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
317	C₂×D₅	—	4	4	no	—
318	C₂×D₅	—	4	2	no	—
319	C₄×C₅	—	2	2	no	—
320	C₄×C₅	—	2	2	no	—
321	C₄×C₅	—	4	2	no	—
322	C₄×C₅	C₃×#127	1	2	yes	—
323	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
324	Dic₅	—	4	2	no	—
325	C₂⁴	—	2	1	no	—
326	#41	—	10	4	no	—
327	#41	—	10	4	no	—
328	C₂×Q₈	—	2	1	no	—
329	C₂×Q₈	—	2	4	no	—
330	C₂×Q₈	—	5	2	no	—
331	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
332	C₂×D₄	—	2	4	no	—
333	C₂×D₄	—	2	1	no	—
334	C₂×D₄	—	5	2	no	—
335	C₂×D₄	—	10	2	no	—
336	C₂×D₄	—	10	2	no	—
337	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
338	C₂²×C₄	—	2	1	no	—
339	C₂²×C₄	—	10	2	no	—
340	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
341	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
342	Q₁₆	—	10	8	no	—
343	SD₁₆	—	10	8	no	—
344	SD₁₆	—	10	8	no	—
345	D₈	—	10	8	no	—
346	M₁₆	—	5	8	no	—
347	C₂×C₈	—	5	4	no	—
348	C₄⋊C₄	—	10	2	no	—
349	C₂²⋊C₄	—	2	4	no	—
350	C₂²⋊C₄	—	2	4	no	—
351	C₂²⋊C₄	—	10	4	no	—
352	C₄²	C₃×C₂²⋊D₅	1	2	yes	—
353	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
354	C₄²	C₂²×C₃×D₅	1	1	yes	characteristic
355	C₃×C₅	#3153	1	1	yes	characteristic, complemented, Hall
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	4	2	no	—
358	C₂²×C₃	—	4	4	no	—
359	C₂²×C₃	—	8	4	no	—
360	C₂²×C₃	—	20	2	no	—
361	C₂²×C₃	—	20	4	no	—
362	C₂²×C₃	#4086	1	2	yes	—
363	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
364	C₃×C₄	—	2	2	no	—
365	C₃×C₄	—	2	2	no	—
366	C₃×C₄	—	4	2	no	—
367	C₃×C₄	—	20	2	no	—
368	C₃×C₄	#4086	1	2	yes	—
369	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
370	C₂×C₅	—	2	2	no	—
371	C₂×C₅	—	8	2	no	—
372	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
373	C₂×C₅	C₃×#575	1	2	yes	—
374	D₅	—	8	2	no	—
375	C₂³	—	2	2	no	—
376	C₂³	—	4	4	no	—
377	C₂³	—	4	2	no	—
378	C₂³	—	10	2	no	—
379	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
380	Q₈	—	2	4	no	—
381	Q₈	—	4	2	no	—
382	Q₈	—	10	2	no	—
383	Q₈	—	10	2	no	—
384	D₄	—	2	4	no	—
385	D₄	—	4	2	no	—
386	D₄	—	10	2	no	—
387	D₄	—	10	2	no	—
388	D₄	—	20	4	no	—
389	D₄	—	20	4	no	—
390	C₂×C₄	—	2	2	no	—
391	C₂×C₄	—	4	2	no	—
392	C₂×C₄	—	4	2	no	—
393	C₂×C₄	—	10	2	no	—
394	C₂×C₄	—	20	4	no	—
395	C₂×C₄	C₃×D₄×D₅	1	4	yes	—
396	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
397	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	2	yes	—
398	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
399	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
400	C₈	—	5	8	no	—
401	C₂×C₃	—	2	2	no	—
402	C₂×C₃	—	8	2	no	—
403	C₂×C₃	—	40	2	no	—
404	C₂×C₃	C₂×#4086	1	1	yes	characteristic
405	C₂×C₃	#66156	1	2	yes	—
406	C₅	C₃×#3153	1	1	yes	characteristic, complemented, Sylow
407	C₂²	—	2	2	no	—
408	C₂²	—	4	2	no	—
409	C₂²	—	4	4	no	—
410	C₂²	—	8	4	no	—
411	C₂²	—	20	2	no	—
412	C₂²	—	20	4	no	—
413	C₂²	C₃×#4086	1	2	yes	—
414	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
415	C₄	—	2	2	no	—
416	C₄	—	2	2	no	—
417	C₄	—	4	2	no	—
418	C₄	—	20	2	no	—
419	C₄	C₃×#4086	1	2	yes	—
420	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
421	C₃	#10614674	1	1	yes	characteristic, direct product factor, Sylow
422	C₂	—	2	2	no	—
423	C₂	—	8	2	no	—
424	C₂	—	40	2	no	—
425	C₂	C₂×C₃×#4086	1	1	yes	characteristic
426	C₂	C₃×#66156	1	2	yes	—

	subgroup	G/H
center	C₂²×C₃	C₂²×C₂²⋊D₅
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂²×C₃×C₅	C₂²×D₄
hypercenter	C₂×C₃×#124	D₅
hypocenter	C₅	C₃×#3153
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂×C₃×C₄² ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#124	C₂	semidirect
2. C₂×C₃×#4088	C₂	semidirect
3. C₂×C₃×#4078	C₂	semidirect
4. C₃×#65811	C₂	semidirect
5. C₃×#65349	C₂	semidirect
6. C₃×#65348	C₂	semidirect
7. C₃×#65347	C₂	semidirect
8. C₃×C₄×#681	C₂	semidirect
9. #10614674	C₃	direct (N × H)
18. C₂×C₃×#689	C₂²	semidirect
20. C₂×C₃×#688	C₂²	semidirect
26. C₃×#4021	C₂²	semidirect
27. C₃×#4020	C₂²	semidirect
29. C₃×#4015	C₂²	semidirect
30. C₃×#3935	C₂²	semidirect
31. C₃×C₄×#168	C₂²	semidirect
33. C₂×C₅×#124	C₂×C₃	semidirect
34. C₂×#4088	C₂×C₃	semidirect
35. C₂×#4078	C₂×C₃	semidirect
36. #65811	C₂×C₃	semidirect
37. #65349	C₂×C₃	semidirect
38. #65348	C₂×C₃	semidirect
39. #65347	C₂×C₃	semidirect
40. C₄×#681	C₂×C₃	semidirect
69. C₃×#681	D₄	semidirect
74. C₂×C₃×#124	D₅	semidirect
87. C₂×#689	C₂²×C₃	semidirect
89. C₂×#688	C₂²×C₃	semidirect
95. #4021	C₂²×C₃	semidirect
96. #4020	C₂²×C₃	semidirect
98. #4015	C₂²×C₃	semidirect
99. #3935	C₂²×C₃	semidirect
100. C₄×#168	C₂²×C₃	semidirect
178. #681	C₃×D₄	semidirect
183. C₂×#124	C₃×D₅	semidirect
355. C₃×C₅	#3153	semidirect
406. C₅	C₃×#3153	semidirect
421. C₃	#10614674	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×C₅×#124	2
C₂×C₃×#4088	2
C₂×C₃×#4078	2
C₃×#65811	2
C₃×#65349	2
C₃×#65348	2
C₃×#65347	2
C₃×C₄×#681	2
#10614674	3
C₃×#3153	5

Subgroups — C3×#10614674 #14439283

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×#10614674 #14439283