Subgroups — C₂×C₃×#65351 #14425075

Order 1920.

1456 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×#4147	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×#4078	C₂	1	2	yes	maximal, complemented
4	C₂×C₃×#3968	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×#65351	C₂	1	8	yes	maximal, direct product factor
6	C₂×C₃×#3937	C₂	1	2	yes	maximal, complemented
7	C₂×#65351	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
10	C₃×#4147	—	2	2	no	—
11	C₃×#4147	—	2	4	no	—
12	C₃×#4147	C₂²	1	4	yes	complemented
13	C₂×C₃×#713	—	2	2	no	—
14	C₂×C₃×Q₈×D₅	—	2	2	no	—
15	C₂×C₃×#709	—	2	2	no	—
16	C₂×C₃×#709	C₂²	1	2	yes	—
17	C₃×C₅×#124	—	2	2	no	—
18	C₃×C₅×#124	C₂²	1	4	yes	complemented
19	C₂×C₃×C₅×C₂²⋊C₄	—	2	2	no	—
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₃×#687	—	2	2	no	—
22	C₃×#4078	—	2	4	no	—
23	C₃×#4078	C₂²	1	8	yes	complemented
24	C₂×C₃×#686	—	2	2	no	—
25	C₂×C₃×#681	C₂²	1	2	yes	—
26	C₃×#3968	C₂²	1	4	yes	complemented
27	C₃×#3937	C₂²	1	8	yes	complemented
28	C₂×C₃×#454	—	5	1	no	maximal, Hall
29	C₂×#4147	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic, complemented
31	C₂×#4078	C₂×C₃	1	2	yes	complemented
32	C₂×#3968	C₂×C₃	1	1	yes	characteristic, complemented
33	#65351	C₂×C₃	1	8	yes	direct product factor
34	C₂×#3937	C₂×C₃	1	2	yes	complemented
35	C₂⁴×C₃×C₅	—	2	1	no	—
36	C₂×C₃×C₅×Q₈	—	2	2	no	—
37	C₂×C₃×C₅×Q₈	—	2	2	no	—
38	C₂×C₃×C₅×Q₈	D₄	1	2	yes	—
39	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
40	C₂×C₃×C₅×D₄	—	2	2	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	—	2	1	no	—
43	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
44	C₂²×C₃×C₄×C₅	—	2	1	no	—
45	C₂²×C₃×C₄×C₅	D₄	1	2	yes	—
46	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₂²⋊D₅	—	2	2	no	—
48	C₃×#713	—	2	8	no	—
49	C₃×#713	—	2	8	no	—
50	C₃×Q₈×D₅	—	2	8	no	—
51	C₃×Q₈×D₅	—	2	8	no	—
52	C₃×#709	—	2	8	no	—
53	C₃×#709	—	2	8	no	—
54	C₃×#709	—	2	2	no	—
55	C₃×#709	—	2	2	no	—
56	C₃×#709	D₄	1	4	yes	—
57	C₃×#709	C₂³	1	4	yes	—
58	C₂×C₃×D₂₀	—	2	2	no	—
59	C₂×C₃×D₂₀	D₄	1	2	yes	—
60	C₂×C₃×C₄×D₅	—	2	4	no	—
61	C₂×C₃×C₄×D₅	—	2	2	no	—
62	C₂×C₃×Dic₁₀	—	2	2	no	—
63	C₂×C₃×Dic₁₀	D₄	1	2	yes	—
64	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
65	C₃×C₄²×C₅	—	2	1	no	—
66	C₃×C₄²×C₅	C₂³	1	2	yes	—
67	C₃×#687	—	2	8	no	—
68	C₃×#686	—	2	8	no	—
69	C₃×#681	—	2	2	no	—
70	C₃×#681	C₂³	1	4	yes	—
71	C₂×C₃×#168	—	2	2	no	—
72	C₂×C₃×2₋¹⁺⁴	—	5	1	no	—
73	C₂×C₃×AGL(1,ℤ/8)	—	5	2	no	—
74	C₂×C₃×#124	D₅	1	1	yes	characteristic, complemented
75	C₃×#454	—	5	8	no	—
76	C₂×C₃×#104	—	5	2	no	—
77	C₂×C₃×#101	—	5	1	no	—
78	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
79	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
80	#4147	—	2	2	no	—
81	#4147	—	2	4	no	—
82	#4147	C₂²×C₃	1	4	yes	complemented
83	C₂×#713	—	2	2	no	—
84	C₂×Q₈×D₅	—	2	2	no	—
85	C₂×#709	—	2	2	no	—
86	C₂×#709	C₂²×C₃	1	2	yes	—
87	C₅×#124	—	2	2	no	—
88	C₅×#124	C₂²×C₃	1	4	yes	complemented
89	C₂×C₅×C₂²⋊C₄	—	2	2	no	—
90	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
91	C₂×#687	—	2	2	no	—
92	#4078	—	2	4	no	—
93	#4078	C₂²×C₃	1	8	yes	complemented
94	C₂×#686	—	2	2	no	—
95	C₂×#681	C₂²×C₃	1	2	yes	—
96	#3968	C₂²×C₃	1	4	yes	complemented
97	#3937	C₂²×C₃	1	8	yes	complemented
98	C₂×#454	—	5	1	no	Sylow
99	C₂³×C₃×C₅	—	2	2	no	—
100	C₂³×C₃×C₅	—	4	4	no	—
101	C₂³×C₃×C₅	—	4	1	no	—
102	C₂³×C₃×C₅	—	4	1	no	—
103	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
104	C₂²×C₃×D₅	—	2	2	no	—
105	C₃×C₅×Q₈	—	2	4	no	—
106	C₃×C₅×Q₈	—	2	4	no	—
107	C₃×C₅×D₄	—	2	4	no	—
108	C₃×C₅×D₄	—	4	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	4	2	no	—
113	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
116	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
117	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
118	C₃×C₂²⋊D₅	—	2	4	no	—
119	C₃×C₂²⋊D₅	—	2	4	no	—
120	C₂×C₃×Dic₅	—	2	2	no	—
121	C₃×D₂₀	—	2	8	no	—
122	C₃×D₂₀	—	2	2	no	—
123	C₃×D₂₀	C₂×D₄	1	4	yes	—
124	C₃×C₄×D₅	—	2	16	no	—
125	C₃×C₄×D₅	—	2	4	no	—
126	C₃×C₄×D₅	—	2	4	no	—
127	C₃×Dic₁₀	—	2	8	no	—
128	C₃×Dic₁₀	—	2	2	no	—
129	C₃×Dic₁₀	C₂×D₄	1	4	yes	—
130	C₃×#168	—	2	4	no	—
131	C₃×2₋¹⁺⁴	—	5	4	no	—
132	C₃×2₋¹⁺⁴	—	10	4	no	—
133	C₃×2₋¹⁺⁴	—	10	2	no	—
134	C₂×C₃×#41	—	5	2	no	—
135	C₂×C₃×#41	—	10	2	no	—
136	C₂×C₃×#41	—	10	2	no	—
137	C₂²×C₃×Q₈	—	10	2	no	—
138	C₂²×C₃×Q₈	C₂×D₅	1	1	yes	characteristic
139	C₂²×C₃×D₄	C₂×D₅	1	1	yes	characteristic
140	C₃×AGL(1,ℤ/8)	—	5	8	no	—
141	C₃×AGL(1,ℤ/8)	—	10	4	no	—
142	C₂×C₃×SD₁₆	—	10	2	no	—
143	C₂×C₃×D₈	—	10	2	no	—
144	C₂×C₃×M₁₆	—	5	2	no	—
145	C₃×#124	—	2	2	no	—
146	C₃×#124	C₂×D₅	1	4	yes	complemented
147	C₂×C₃×C₂²⋊C₄	—	2	2	no	—
148	C₂×C₃×C₄²	C₂×D₅	1	1	yes	characteristic
149	C₃×#104	—	5	8	no	—
150	C₃×#101	—	5	4	no	—
151	C₂⁴×C₅	—	2	1	no	—
152	C₂×C₅×Q₈	—	2	2	no	—
153	C₂×C₅×Q₈	—	2	2	no	—
154	C₂×C₅×Q₈	C₃×D₄	1	2	yes	—
155	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
156	C₂×C₅×D₄	—	2	2	no	—
157	C₂×C₅×D₄	—	2	2	no	—
158	C₂×C₅×D₄	—	2	1	no	—
159	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	—	2	1	no	—
161	C₂²×C₄×C₅	C₃×D₄	1	2	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂×C₂²⋊D₅	—	2	2	no	—
164	#713	—	2	8	no	—
165	#713	—	2	8	no	—
166	Q₈×D₅	—	2	8	no	—
167	Q₈×D₅	—	2	8	no	—
168	#709	—	2	8	no	—
169	#709	—	2	8	no	—
170	#709	—	2	2	no	—
171	#709	—	2	2	no	—
172	#709	C₃×D₄	1	4	yes	—
173	#709	C₂³×C₃	1	4	yes	—
174	C₂×D₂₀	—	2	2	no	—
175	C₂×D₂₀	C₃×D₄	1	2	yes	—
176	C₂×C₄×D₅	—	2	4	no	—
177	C₂×C₄×D₅	—	2	2	no	—
178	C₂×Dic₁₀	—	2	2	no	—
179	C₂×Dic₁₀	C₃×D₄	1	2	yes	—
180	C₅×C₂²⋊C₄	—	2	8	no	—
181	C₄²×C₅	—	2	1	no	—
182	C₄²×C₅	C₂³×C₃	1	2	yes	—
183	#687	—	2	8	no	—
184	#686	—	2	8	no	—
185	#681	—	2	2	no	—
186	#681	C₂³×C₃	1	4	yes	—
187	C₂×#168	—	2	2	no	—
188	C₂×2₋¹⁺⁴	—	5	1	no	—
189	C₂×AGL(1,ℤ/8)	—	5	2	no	—
190	C₂×#124	C₃×D₅	1	1	yes	characteristic, complemented
191	#454	—	5	8	no	—
192	C₂×#104	—	5	2	no	—
193	C₂×#101	—	5	1	no	—
194	C₂²×C₃×C₅	—	2	2	no	—
195	C₂²×C₃×C₅	—	4	4	no	—
196	C₂²×C₃×C₅	—	4	2	no	—
197	C₂²×C₃×C₅	—	8	2	no	—
198	C₂²×C₃×C₅	—	8	2	no	—
199	C₂²×C₃×C₅	#120	1	1	yes	characteristic
200	C₂²×C₃×C₅	#120	1	1	yes	characteristic
201	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
202	C₂×C₃×D₅	—	2	4	no	—
203	C₂×C₃×D₅	—	4	4	no	—
204	C₃×C₄×C₅	—	2	4	no	—
205	C₃×C₄×C₅	—	4	2	no	—
206	C₃×C₄×C₅	#120	1	2	yes	—
207	C₃×C₄×C₅	C₂²×D₄	1	2	yes	—
208	C₃×Dic₅	—	2	4	no	—
209	C₂⁴×C₃	—	2	1	no	—
210	C₃×#41	—	5	4	no	—
211	C₃×#41	—	5	4	no	—
212	C₃×#41	—	10	8	no	—
213	C₃×#41	—	10	8	no	—
214	C₃×#41	—	10	8	no	—
215	C₃×#41	—	10	2	no	—
216	C₃×#41	—	10	2	no	—
217	C₃×#41	—	10	8	no	—
218	C₂×C₃×Q₈	—	2	2	no	—
219	C₂×C₃×Q₈	—	2	2	no	—
220	C₂×C₃×Q₈	—	5	2	no	—
221	C₂×C₃×Q₈	—	10	2	no	—
222	C₂×C₃×Q₈	—	10	8	no	—
223	C₂×C₃×Q₈	—	10	8	no	—
224	C₂×C₃×Q₈	C₂²⋊D₅	1	2	yes	—
225	C₂×C₃×Q₈	C₂²×D₅	1	2	yes	—
226	C₂×C₃×D₄	—	2	2	no	—
227	C₂×C₃×D₄	—	2	2	no	—
228	C₂×C₃×D₄	—	2	1	no	—
229	C₂×C₃×D₄	—	5	2	no	—
230	C₂×C₃×D₄	—	10	2	no	—
231	C₂×C₃×D₄	—	10	2	no	—
232	C₂×C₃×D₄	C₂²×D₅	1	2	yes	—
233	C₂²×C₃×C₄	—	2	1	no	—
234	C₂²×C₃×C₄	—	10	4	no	—
235	C₂²×C₃×C₄	—	10	2	no	—
236	C₂²×C₃×C₄	C₂²⋊D₅	1	2	yes	—
237	C₂²×C₃×C₄	C₂²×D₅	1	1	yes	characteristic
238	C₃×SD₁₆	—	10	8	no	—
239	C₃×D₈	—	10	8	no	—
240	C₃×M₁₆	—	5	4	no	—
241	C₃×M₁₆	—	10	2	no	—
242	C₂×C₃×C₈	—	10	2	no	—
243	C₃×C₂²⋊C₄	—	2	8	no	—
244	C₃×C₄²	—	2	1	no	—
245	C₃×C₄²	C₂²×D₅	1	2	yes	—
246	C₂³×C₅	—	2	2	no	—
247	C₂³×C₅	—	4	4	no	—
248	C₂³×C₅	—	4	1	no	—
249	C₂³×C₅	—	4	1	no	—
250	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
251	C₂²×D₅	—	2	2	no	—
252	C₅×Q₈	—	2	4	no	—
253	C₅×Q₈	—	2	4	no	—
254	C₅×D₄	—	2	4	no	—
255	C₅×D₄	—	4	2	no	—
256	C₂×C₄×C₅	—	2	2	no	—
257	C₂×C₄×C₅	—	2	2	no	—
258	C₂×C₄×C₅	—	2	2	no	—
259	C₂×C₄×C₅	—	4	2	no	—
260	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
261	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
262	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
263	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
264	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
265	C₂²⋊D₅	—	2	4	no	—
266	C₂²⋊D₅	—	2	4	no	—
267	C₂×Dic₅	—	2	2	no	—
268	D₂₀	—	2	8	no	—
269	D₂₀	—	2	2	no	—
270	D₂₀	C₂×C₃×D₄	1	4	yes	—
271	C₄×D₅	—	2	16	no	—
272	C₄×D₅	—	2	4	no	—
273	C₄×D₅	—	2	4	no	—
274	Dic₁₀	—	2	8	no	—
275	Dic₁₀	—	2	2	no	—
276	Dic₁₀	C₂×C₃×D₄	1	4	yes	—
277	#168	—	2	4	no	—
278	2₋¹⁺⁴	—	5	4	no	—
279	2₋¹⁺⁴	—	10	4	no	—
280	2₋¹⁺⁴	—	10	2	no	—
281	C₂×#41	—	5	2	no	—
282	C₂×#41	—	10	2	no	—
283	C₂×#41	—	10	2	no	—
284	C₂²×Q₈	—	10	2	no	—
285	C₂²×Q₈	C₂×C₃×D₅	1	1	yes	characteristic
286	C₂²×D₄	C₂×C₃×D₅	1	1	yes	characteristic
287	AGL(1,ℤ/8)	—	5	8	no	—
288	AGL(1,ℤ/8)	—	10	4	no	—
289	C₂×SD₁₆	—	10	2	no	—
290	C₂×D₈	—	10	2	no	—
291	C₂×M₁₆	—	5	2	no	—
292	#124	—	2	2	no	—
293	#124	C₂×C₃×D₅	1	4	yes	complemented
294	C₂×C₂²⋊C₄	—	2	2	no	—
295	C₂×C₄²	C₂×C₃×D₅	1	1	yes	characteristic
296	#104	—	5	8	no	—
297	#101	—	5	4	no	—
298	C₂×C₃×C₅	—	2	1	no	—
299	C₂×C₃×C₅	—	2	1	no	—
300	C₂×C₃×C₅	—	8	2	no	—
301	C₂×C₃×C₅	#454	1	2	yes	complemented
302	C₂×C₃×C₅	C₂×#120	1	1	yes	characteristic
303	C₃×D₅	—	4	4	no	—
304	C₂³×C₃	—	2	2	no	—
305	C₂³×C₃	—	4	4	no	—
306	C₂³×C₃	—	4	1	no	—
307	C₂³×C₃	—	4	1	no	—
308	C₂³×C₃	—	10	2	no	—
309	C₂³×C₃	C₂×C₂²⋊D₅	1	1	yes	characteristic
310	C₃×Q₈	—	2	4	no	—
311	C₃×Q₈	—	2	4	no	—
312	C₃×Q₈	—	5	4	no	—
313	C₃×Q₈	—	10	8	no	—
314	C₃×Q₈	—	10	2	no	—
315	C₃×D₄	—	2	4	no	—
316	C₃×D₄	—	4	2	no	—
317	C₃×D₄	—	5	4	no	—
318	C₃×D₄	—	10	8	no	—
319	C₃×D₄	—	10	4	no	—
320	C₃×D₄	—	10	4	no	—
321	C₃×D₄	—	10	2	no	—
322	C₂×C₃×C₄	—	2	2	no	—
323	C₂×C₃×C₄	—	2	2	no	—
324	C₂×C₃×C₄	—	2	2	no	—
325	C₂×C₃×C₄	—	4	2	no	—
326	C₂×C₃×C₄	—	10	16	no	—
327	C₂×C₃×C₄	—	10	2	no	—
328	C₂×C₃×C₄	—	10	4	no	—
329	C₂×C₃×C₄	—	10	4	no	—
330	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
331	C₂×C₃×C₄	D₄×D₅	1	2	yes	—
332	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	4	yes	—
333	C₂×C₃×C₄	C₂×C₂²⋊D₅	1	1	yes	characteristic
334	C₂×C₃×C₄	C₂³×D₅	1	1	yes	characteristic
335	C₃×C₈	—	10	4	no	—
336	C₂²×C₅	—	2	2	no	—
337	C₂²×C₅	—	4	4	no	—
338	C₂²×C₅	—	4	2	no	—
339	C₂²×C₅	—	8	2	no	—
340	C₂²×C₅	—	8	2	no	—
341	C₂²×C₅	C₃×#120	1	1	yes	characteristic
342	C₂²×C₅	C₃×#120	1	1	yes	characteristic
343	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
344	C₂×D₅	—	2	4	no	—
345	C₂×D₅	—	4	4	no	—
346	C₄×C₅	—	2	4	no	—
347	C₄×C₅	—	4	2	no	—
348	C₄×C₅	C₃×#120	1	2	yes	—
349	C₄×C₅	C₂²×C₃×D₄	1	2	yes	—
350	Dic₅	—	2	4	no	—
351	C₂⁴	—	2	1	no	—
352	#41	—	5	4	no	—
353	#41	—	5	4	no	—
354	#41	—	10	8	no	—
355	#41	—	10	8	no	—
356	#41	—	10	8	no	—
357	#41	—	10	2	no	—
358	#41	—	10	2	no	—
359	#41	—	10	8	no	—
360	C₂×Q₈	—	2	2	no	—
361	C₂×Q₈	—	2	2	no	—
362	C₂×Q₈	—	5	2	no	—
363	C₂×Q₈	—	10	2	no	—
364	C₂×Q₈	—	10	8	no	—
365	C₂×Q₈	—	10	8	no	—
366	C₂×Q₈	C₃×C₂²⋊D₅	1	2	yes	—
367	C₂×Q₈	C₂²×C₃×D₅	1	2	yes	—
368	C₂×D₄	—	2	2	no	—
369	C₂×D₄	—	2	2	no	—
370	C₂×D₄	—	2	1	no	—
371	C₂×D₄	—	5	2	no	—
372	C₂×D₄	—	10	2	no	—
373	C₂×D₄	—	10	2	no	—
374	C₂×D₄	C₂²×C₃×D₅	1	2	yes	—
375	C₂²×C₄	—	2	1	no	—
376	C₂²×C₄	—	10	4	no	—
377	C₂²×C₄	—	10	2	no	—
378	C₂²×C₄	C₃×C₂²⋊D₅	1	2	yes	—
379	C₂²×C₄	C₂²×C₃×D₅	1	1	yes	characteristic
380	SD₁₆	—	10	8	no	—
381	D₈	—	10	8	no	—
382	M₁₆	—	5	4	no	—
383	M₁₆	—	10	2	no	—
384	C₂×C₈	—	10	2	no	—
385	C₂²⋊C₄	—	2	8	no	—
386	C₄²	—	2	1	no	—
387	C₄²	C₂²×C₃×D₅	1	2	yes	—
388	C₃×C₅	C₂×#454	1	1	yes	characteristic, complemented, Hall
389	C₂²×C₃	—	2	2	no	—
390	C₂²×C₃	—	4	4	no	—
391	C₂²×C₃	—	4	2	no	—
392	C₂²×C₃	—	8	2	no	—
393	C₂²×C₃	—	8	2	no	—
394	C₂²×C₃	—	10	4	no	—
395	C₂²×C₃	—	20	4	no	—
396	C₂²×C₃	#4083	1	1	yes	characteristic
397	C₂²×C₃	#4083	1	1	yes	characteristic
398	C₂²×C₃	C₂²×C₂²⋊D₅	1	1	yes	characteristic
399	C₃×C₄	—	2	4	no	—
400	C₃×C₄	—	4	2	no	—
401	C₃×C₄	—	10	4	no	—
402	C₃×C₄	#4083	1	2	yes	—
403	C₃×C₄	C₂×D₄×D₅	1	2	yes	—
404	C₂×C₅	—	2	1	no	—
405	C₂×C₅	—	2	1	no	—
406	C₂×C₅	—	8	2	no	—
407	C₂×C₅	C₃×#454	1	2	yes	complemented
408	C₂×C₅	C₂×C₃×#120	1	1	yes	characteristic
409	D₅	—	4	4	no	—
410	C₂³	—	2	2	no	—
411	C₂³	—	4	4	no	—
412	C₂³	—	4	1	no	—
413	C₂³	—	4	1	no	—
414	C₂³	—	10	2	no	—
415	C₂³	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
416	Q₈	—	2	4	no	—
417	Q₈	—	2	4	no	—
418	Q₈	—	5	4	no	—
419	Q₈	—	10	8	no	—
420	Q₈	—	10	2	no	—
421	D₄	—	2	4	no	—
422	D₄	—	4	2	no	—
423	D₄	—	5	4	no	—
424	D₄	—	10	8	no	—
425	D₄	—	10	4	no	—
426	D₄	—	10	4	no	—
427	D₄	—	10	2	no	—
428	C₂×C₄	—	2	2	no	—
429	C₂×C₄	—	2	2	no	—
430	C₂×C₄	—	2	2	no	—
431	C₂×C₄	—	4	2	no	—
432	C₂×C₄	—	10	16	no	—
433	C₂×C₄	—	10	2	no	—
434	C₂×C₄	—	10	4	no	—
435	C₂×C₄	—	10	4	no	—
436	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
437	C₂×C₄	C₃×D₄×D₅	1	2	yes	—
438	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	4	yes	—
439	C₂×C₄	C₂×C₃×C₂²⋊D₅	1	1	yes	characteristic
440	C₂×C₄	C₂³×C₃×D₅	1	1	yes	characteristic
441	C₈	—	10	4	no	—
442	C₂×C₃	—	2	1	no	—
443	C₂×C₃	—	2	1	no	—
444	C₂×C₃	—	8	2	no	—
445	C₂×C₃	—	20	4	no	—
446	C₂×C₃	#65351	1	2	yes	direct product factor
447	C₂×C₃	C₂×#4083	1	1	yes	characteristic
448	C₅	C₂×C₃×#454	1	1	yes	characteristic, complemented, Sylow
449	C₂²	—	2	2	no	—
450	C₂²	—	4	4	no	—
451	C₂²	—	4	2	no	—
452	C₂²	—	8	2	no	—
453	C₂²	—	8	2	no	—
454	C₂²	—	10	4	no	—
455	C₂²	—	20	4	no	—
456	C₂²	C₃×#4083	1	1	yes	characteristic
457	C₂²	C₃×#4083	1	1	yes	characteristic
458	C₂²	C₂²×C₃×C₂²⋊D₅	1	1	yes	characteristic
459	C₄	—	2	4	no	—
460	C₄	—	4	2	no	—
461	C₄	—	10	4	no	—
462	C₄	C₃×#4083	1	2	yes	—
463	C₄	C₂×C₃×D₄×D₅	1	2	yes	—
464	C₃	C₂×#65351	1	1	yes	characteristic, direct product factor, Sylow
465	C₂	—	2	1	no	—
466	C₂	—	2	1	no	—
467	C₂	—	8	2	no	—
468	C₂	—	20	4	no	—
469	C₂	C₃×#65351	1	2	yes	direct product factor
470	C₂	C₂×C₃×#4083	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₃	#4083
commutator, cosocle	C₂×C₄×C₅	C₂⁴×C₃
Frattini	C₂×C₄	C₂³×C₃×D₅
Fitting	C₂×C₃×C₅×#124	C₂
socle	C₂²×C₃×C₅	#120
hypercenter	C₂×C₃×#124	D₅
hypocenter	C₅	C₂×C₃×#454
LCS	G ▷ C₂×C₄×C₅ ▷ C₂×C₅ ▷ C₅
UCS	C₁ ◁ C₂²×C₃ ◁ C₂²×C₃×C₄ ◁ C₂×C₃×#124

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×#4147	C₂	semidirect
2. C₂×C₃×C₅×#124	C₂	semidirect
3. C₂×C₃×#4078	C₂	semidirect
4. C₂×C₃×#3968	C₂	semidirect
5. C₃×#65351	C₂	direct (N × H)
6. C₂×C₃×#3937	C₂	semidirect
7. C₂×#65351	C₃	direct (N × H)
12. C₃×#4147	C₂²	semidirect
18. C₃×C₅×#124	C₂²	semidirect
23. C₃×#4078	C₂²	semidirect
26. C₃×#3968	C₂²	semidirect
27. C₃×#3937	C₂²	semidirect
29. C₂×#4147	C₂×C₃	semidirect
30. C₂×C₅×#124	C₂×C₃	semidirect
31. C₂×#4078	C₂×C₃	semidirect
32. C₂×#3968	C₂×C₃	semidirect
33. #65351	C₂×C₃	direct (N × H)
34. C₂×#3937	C₂×C₃	semidirect
74. C₂×C₃×#124	D₅	semidirect
82. #4147	C₂²×C₃	semidirect
88. C₅×#124	C₂²×C₃	semidirect
93. #4078	C₂²×C₃	semidirect
96. #3968	C₂²×C₃	semidirect
97. #3937	C₂²×C₃	semidirect
146. C₃×#124	C₂×D₅	semidirect
190. C₂×#124	C₃×D₅	semidirect
293. #124	C₂×C₃×D₅	semidirect
301. C₂×C₃×C₅	#454	semidirect
388. C₃×C₅	C₂×#454	semidirect
407. C₂×C₅	C₃×#454	semidirect
446. C₂×C₃	#65351	direct (N × H)
448. C₅	C₂×C₃×#454	semidirect
464. C₃	C₂×#65351	direct (N × H)
469. C₂	C₃×#65351	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×#4147	2
C₂×C₃×C₅×#124	2
C₂×C₃×#4078	2
C₂×C₃×#3968	2
C₃×#65351	2
C₂×C₃×#3937	2
C₂×#65351	3
C₂×C₃×#454	5

Subgroups — C2×C3×#65351 #14425075

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×#65351 #14425075