Subgroups — C₂×C₃×C₅×#472 #14276099

Order 1920.

976 conjugacy classes of subgroups.

The subgroup lattice has 436 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	2	yes	maximal, complemented
2	C₂²×C₃×C₅×D₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic, complemented
4	C₃×C₅×#472	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₅×#100	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#472	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
10	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
11	C₃×C₅×AGL(1,ℤ/8)	C₂²	1	8	yes	complemented
12	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
13	C₂×C₃×C₅×D₈	—	2	2	no	—
14	C₂×C₃×C₅×D₈	—	2	1	no	—
15	C₂×C₃×C₅×D₈	—	2	1	no	—
16	C₂×C₃×C₅×D₈	—	2	2	no	—
17	C₂×C₃×C₅×D₈	C₂²	1	4	yes	complemented
18	C₃×C₅×#131	—	2	2	no	—
19	C₃×C₅×#131	C₂²	1	4	yes	complemented
20	C₂×C₃×C₅×M₁₆	—	2	1	no	—
21	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
22	C₂×C₃×C₅×M₁₆	C₂²	1	2	yes	—
23	C₂²×C₃×C₅×C₈	—	2	1	no	—
24	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
25	C₃×C₅×#108	C₂²	1	4	yes	complemented
26	C₃×C₅×#100	C₂²	1	8	yes	complemented
27	C₂×C₃×#472	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	2	yes	complemented
29	C₂²×C₅×D₈	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic, complemented
31	C₅×#472	C₂×C₃	1	8	yes	direct product factor
32	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×#100	C₂×C₃	1	2	yes	complemented
34	C₂⁴×C₃×C₅	—	2	2	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	—	2	1	no	—
37	C₃×C₅×#41	D₄	1	2	yes	—
38	C₃×C₅×#41	C₂³	1	2	yes	—
39	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
40	C₂×C₃×C₅×D₄	—	2	1	no	—
41	C₂×C₃×C₅×D₄	—	2	2	no	—
42	C₂×C₃×C₅×D₄	—	2	2	no	—
43	C₂×C₃×C₅×D₄	—	2	2	no	—
44	C₂×C₃×C₅×D₄	—	2	2	no	—
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
47	C₂×C₃×C₅×D₄	C₂³	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	1	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×SD₁₆	—	2	8	no	—
51	C₃×C₅×D₈	—	2	8	no	—
52	C₃×C₅×D₈	—	2	4	no	—
53	C₃×C₅×D₈	—	2	4	no	—
54	C₃×C₅×M₁₆	—	2	1	no	—
55	C₃×C₅×M₁₆	—	2	2	no	—
56	C₃×C₅×M₁₆	—	2	4	no	—
57	C₃×C₅×M₁₆	C₂³	1	2	yes	—
58	C₃×C₅×M₁₆	C₂³	1	4	yes	—
59	C₂×C₃×C₅×C₈	—	2	1	no	—
60	C₂×C₃×C₅×C₈	—	2	2	no	—
61	C₂×C₃×C₅×C₈	—	2	4	no	—
62	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
63	C₂×C₃×C₅×C₈	D₄	1	1	yes	characteristic
64	C₂×C₃×C₅×C₈	D₄	1	2	yes	—
65	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
66	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	2	yes	complemented
67	C₂²×C₃×D₈	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic, complemented
69	C₃×#472	C₂×C₅	1	8	yes	direct product factor
70	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×#100	C₂×C₅	1	2	yes	complemented
72	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
74	C₅×AGL(1,ℤ/8)	—	2	4	no	—
75	C₅×AGL(1,ℤ/8)	C₂²×C₃	1	8	yes	complemented
76	C₂×C₅×SD₁₆	—	2	2	no	—
77	C₂×C₅×D₈	—	2	2	no	—
78	C₂×C₅×D₈	—	2	1	no	—
79	C₂×C₅×D₈	—	2	1	no	—
80	C₂×C₅×D₈	—	2	2	no	—
81	C₂×C₅×D₈	C₂²×C₃	1	4	yes	complemented
82	C₅×#131	—	2	2	no	—
83	C₅×#131	C₂²×C₃	1	4	yes	complemented
84	C₂×C₅×M₁₆	—	2	1	no	—
85	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×M₁₆	C₂²×C₃	1	2	yes	—
87	C₂²×C₅×C₈	—	2	1	no	—
88	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
89	C₅×#108	C₂²×C₃	1	4	yes	complemented
90	C₅×#100	C₂²×C₃	1	8	yes	complemented
91	C₂×#472	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	—	2	4	no	—
94	C₂³×C₃×C₅	—	4	2	no	—
95	C₂³×C₃×C₅	—	4	2	no	—
96	C₂³×C₃×C₅	—	8	4	no	—
97	C₂³×C₃×C₅	#41	1	1	yes	characteristic
98	C₃×C₅×Q₈	—	2	1	no	—
99	C₃×C₅×Q₈	C₂×D₄	1	2	yes	—
100	C₃×C₅×D₄	—	2	2	no	—
101	C₃×C₅×D₄	—	2	2	no	—
102	C₃×C₅×D₄	—	2	1	no	—
103	C₃×C₅×D₄	—	2	4	no	—
104	C₃×C₅×D₄	—	2	4	no	—
105	C₃×C₅×D₄	—	4	2	no	—
106	C₃×C₅×D₄	—	4	2	no	—
107	C₃×C₅×D₄	C₂×D₄	1	2	yes	—
108	C₂×C₃×C₄×C₅	—	2	1	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
112	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
116	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
117	C₃×C₅×C₈	—	2	2	no	—
118	C₃×C₅×C₈	—	2	4	no	—
119	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
120	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
121	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
122	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
123	C₃×AGL(1,ℤ/8)	—	2	4	no	—
124	C₃×AGL(1,ℤ/8)	C₂²×C₅	1	8	yes	complemented
125	C₂×C₃×SD₁₆	—	2	2	no	—
126	C₂×C₃×D₈	—	2	2	no	—
127	C₂×C₃×D₈	—	2	1	no	—
128	C₂×C₃×D₈	—	2	1	no	—
129	C₂×C₃×D₈	—	2	2	no	—
130	C₂×C₃×D₈	C₂²×C₅	1	4	yes	complemented
131	C₃×#131	—	2	2	no	—
132	C₃×#131	C₂²×C₅	1	4	yes	complemented
133	C₂×C₃×M₁₆	—	2	1	no	—
134	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
135	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
136	C₂²×C₃×C₈	—	2	1	no	—
137	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
138	C₃×#108	C₂²×C₅	1	4	yes	complemented
139	C₃×#100	C₂²×C₅	1	8	yes	complemented
140	C₂⁴×C₅	—	2	2	no	—
141	C₅×#41	—	2	1	no	—
142	C₅×#41	—	2	1	no	—
143	C₅×#41	C₃×D₄	1	2	yes	—
144	C₅×#41	C₂³×C₃	1	2	yes	—
145	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
146	C₂×C₅×D₄	—	2	1	no	—
147	C₂×C₅×D₄	—	2	2	no	—
148	C₂×C₅×D₄	—	2	2	no	—
149	C₂×C₅×D₄	—	2	2	no	—
150	C₂×C₅×D₄	—	2	2	no	—
151	C₂×C₅×D₄	—	2	2	no	—
152	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
153	C₂×C₅×D₄	C₂³×C₃	1	4	yes	—
154	C₂²×C₄×C₅	—	2	1	no	—
155	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
156	C₅×SD₁₆	—	2	8	no	—
157	C₅×D₈	—	2	8	no	—
158	C₅×D₈	—	2	4	no	—
159	C₅×D₈	—	2	4	no	—
160	C₅×M₁₆	—	2	1	no	—
161	C₅×M₁₆	—	2	2	no	—
162	C₅×M₁₆	—	2	4	no	—
163	C₅×M₁₆	C₂³×C₃	1	2	yes	—
164	C₅×M₁₆	C₂³×C₃	1	4	yes	—
165	C₂×C₅×C₈	—	2	1	no	—
166	C₂×C₅×C₈	—	2	2	no	—
167	C₂×C₅×C₈	—	2	4	no	—
168	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
169	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
170	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
171	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
172	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	2	yes	complemented
173	C₂²×D₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
174	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic, complemented
175	#472	C₂×C₃×C₅	1	8	yes	direct product factor
176	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
177	C₂×#100	C₂×C₃×C₅	1	2	yes	complemented
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	2	2	no	—
180	C₂²×C₃×C₅	—	4	2	no	—
181	C₂²×C₃×C₅	—	4	4	no	—
182	C₂²×C₃×C₅	—	8	4	no	—
183	C₂²×C₃×C₅	—	8	4	no	—
184	C₂²×C₃×C₅	—	8	4	no	—
185	C₂²×C₃×C₅	#121	1	1	yes	characteristic
186	C₂²×C₃×C₅	#121	1	1	yes	characteristic
187	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
188	C₃×C₄×C₅	—	2	2	no	—
189	C₃×C₄×C₅	#121	1	1	yes	characteristic
190	C₃×C₄×C₅	#121	1	1	yes	characteristic
191	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
192	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
193	C₂⁴×C₃	—	2	2	no	—
194	C₃×#41	—	2	1	no	—
195	C₃×#41	—	2	1	no	—
196	C₃×#41	C₅×D₄	1	2	yes	—
197	C₃×#41	C₂³×C₅	1	2	yes	—
198	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
199	C₂×C₃×D₄	—	2	1	no	—
200	C₂×C₃×D₄	—	2	2	no	—
201	C₂×C₃×D₄	—	2	2	no	—
202	C₂×C₃×D₄	—	2	2	no	—
203	C₂×C₃×D₄	—	2	2	no	—
204	C₂×C₃×D₄	—	2	2	no	—
205	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
206	C₂×C₃×D₄	C₂³×C₅	1	4	yes	—
207	C₂²×C₃×C₄	—	2	1	no	—
208	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
209	C₃×SD₁₆	—	2	8	no	—
210	C₃×D₈	—	2	8	no	—
211	C₃×D₈	—	2	4	no	—
212	C₃×D₈	—	2	4	no	—
213	C₃×M₁₆	—	2	1	no	—
214	C₃×M₁₆	—	2	2	no	—
215	C₃×M₁₆	—	2	4	no	—
216	C₃×M₁₆	C₂³×C₅	1	2	yes	—
217	C₃×M₁₆	C₂³×C₅	1	4	yes	—
218	C₂×C₃×C₈	—	2	1	no	—
219	C₂×C₃×C₈	—	2	2	no	—
220	C₂×C₃×C₈	—	2	4	no	—
221	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
222	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
223	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
224	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
225	C₂³×C₅	—	2	1	no	—
226	C₂³×C₅	—	2	4	no	—
227	C₂³×C₅	—	4	2	no	—
228	C₂³×C₅	—	4	2	no	—
229	C₂³×C₅	—	8	4	no	—
230	C₂³×C₅	C₃×#41	1	1	yes	characteristic
231	C₅×Q₈	—	2	1	no	—
232	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
233	C₅×D₄	—	2	2	no	—
234	C₅×D₄	—	2	2	no	—
235	C₅×D₄	—	2	1	no	—
236	C₅×D₄	—	2	4	no	—
237	C₅×D₄	—	2	4	no	—
238	C₅×D₄	—	4	2	no	—
239	C₅×D₄	—	4	2	no	—
240	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
241	C₂×C₄×C₅	—	2	1	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
245	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
246	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
247	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
248	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
249	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
250	C₅×C₈	—	2	2	no	—
251	C₅×C₈	—	2	4	no	—
252	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
253	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
254	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
255	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
256	AGL(1,ℤ/8)	—	2	4	no	—
257	AGL(1,ℤ/8)	C₂²×C₃×C₅	1	8	yes	complemented
258	C₂×SD₁₆	—	2	2	no	—
259	C₂×D₈	—	2	2	no	—
260	C₂×D₈	—	2	1	no	—
261	C₂×D₈	—	2	1	no	—
262	C₂×D₈	—	2	2	no	—
263	C₂×D₈	C₂²×C₃×C₅	1	4	yes	complemented
264	#131	—	2	2	no	—
265	#131	C₂²×C₃×C₅	1	4	yes	complemented
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
268	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
269	C₂²×C₈	—	2	1	no	—
270	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
271	#108	C₂²×C₃×C₅	1	4	yes	complemented
272	#100	C₂²×C₃×C₅	1	8	yes	complemented
273	C₂×C₃×C₅	—	2	1	no	—
274	C₂×C₃×C₅	—	2	1	no	—
275	C₂×C₃×C₅	—	4	2	no	—
276	C₂×C₃×C₅	—	8	4	no	—
277	C₂×C₃×C₅	#472	1	2	yes	direct product factor
278	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
279	C₂³×C₃	—	2	1	no	—
280	C₂³×C₃	—	2	4	no	—
281	C₂³×C₃	—	4	2	no	—
282	C₂³×C₃	—	4	2	no	—
283	C₂³×C₃	—	8	4	no	—
284	C₂³×C₃	C₅×#41	1	1	yes	characteristic
285	C₃×Q₈	—	2	1	no	—
286	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
287	C₃×D₄	—	2	2	no	—
288	C₃×D₄	—	2	2	no	—
289	C₃×D₄	—	2	1	no	—
290	C₃×D₄	—	2	4	no	—
291	C₃×D₄	—	2	4	no	—
292	C₃×D₄	—	4	2	no	—
293	C₃×D₄	—	4	2	no	—
294	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
295	C₂×C₃×C₄	—	2	1	no	—
296	C₂×C₃×C₄	—	2	2	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
299	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
300	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
301	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
302	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
303	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
304	C₃×C₈	—	2	2	no	—
305	C₃×C₈	—	2	4	no	—
306	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
307	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
308	C₂²×C₅	—	2	2	no	—
309	C₂²×C₅	—	2	2	no	—
310	C₂²×C₅	—	4	2	no	—
311	C₂²×C₅	—	4	4	no	—
312	C₂²×C₅	—	8	4	no	—
313	C₂²×C₅	—	8	4	no	—
314	C₂²×C₅	—	8	4	no	—
315	C₂²×C₅	C₃×#121	1	1	yes	characteristic
316	C₂²×C₅	C₃×#121	1	1	yes	characteristic
317	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
318	C₄×C₅	—	2	2	no	—
319	C₄×C₅	C₃×#121	1	1	yes	characteristic
320	C₄×C₅	C₃×#121	1	1	yes	characteristic
321	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
322	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
323	C₂⁴	—	2	2	no	—
324	#41	—	2	1	no	—
325	#41	—	2	1	no	—
326	#41	C₃×C₅×D₄	1	2	yes	—
327	#41	C₂³×C₃×C₅	1	2	yes	—
328	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
329	C₂×D₄	—	2	1	no	—
330	C₂×D₄	—	2	2	no	—
331	C₂×D₄	—	2	2	no	—
332	C₂×D₄	—	2	2	no	—
333	C₂×D₄	—	2	2	no	—
334	C₂×D₄	—	2	2	no	—
335	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
336	C₂×D₄	C₂³×C₃×C₅	1	4	yes	—
337	C₂²×C₄	—	2	1	no	—
338	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
339	SD₁₆	—	2	8	no	—
340	D₈	—	2	8	no	—
341	D₈	—	2	4	no	—
342	D₈	—	2	4	no	—
343	M₁₆	—	2	1	no	—
344	M₁₆	—	2	2	no	—
345	M₁₆	—	2	4	no	—
346	M₁₆	C₂³×C₃×C₅	1	2	yes	—
347	M₁₆	C₂³×C₃×C₅	1	4	yes	—
348	C₂×C₈	—	2	1	no	—
349	C₂×C₈	—	2	2	no	—
350	C₂×C₈	—	2	4	no	—
351	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
352	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
353	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
354	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
355	C₃×C₅	C₂×#472	1	1	yes	characteristic, direct product factor, Hall
356	C₂²×C₃	—	2	2	no	—
357	C₂²×C₃	—	2	2	no	—
358	C₂²×C₃	—	4	2	no	—
359	C₂²×C₃	—	4	4	no	—
360	C₂²×C₃	—	8	4	no	—
361	C₂²×C₃	—	8	4	no	—
362	C₂²×C₃	—	8	4	no	—
363	C₂²×C₃	C₅×#121	1	1	yes	characteristic
364	C₂²×C₃	C₅×#121	1	1	yes	characteristic
365	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
366	C₃×C₄	—	2	2	no	—
367	C₃×C₄	C₅×#121	1	1	yes	characteristic
368	C₃×C₄	C₅×#121	1	1	yes	characteristic
369	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
370	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
371	C₂×C₅	—	2	1	no	—
372	C₂×C₅	—	2	1	no	—
373	C₂×C₅	—	4	2	no	—
374	C₂×C₅	—	8	4	no	—
375	C₂×C₅	C₃×#472	1	2	yes	direct product factor
376	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
377	C₂³	—	2	1	no	—
378	C₂³	—	2	4	no	—
379	C₂³	—	4	2	no	—
380	C₂³	—	4	2	no	—
381	C₂³	—	8	4	no	—
382	C₂³	C₃×C₅×#41	1	1	yes	characteristic
383	Q₈	—	2	1	no	—
384	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
385	D₄	—	2	2	no	—
386	D₄	—	2	2	no	—
387	D₄	—	2	4	no	—
388	D₄	—	2	4	no	—
389	D₄	—	2	1	no	—
390	D₄	—	4	2	no	—
391	D₄	—	4	2	no	—
392	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
393	C₂×C₄	—	2	1	no	—
394	C₂×C₄	—	2	2	no	—
395	C₂×C₄	—	2	2	no	—
396	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
397	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
398	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
399	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
400	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
401	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
402	C₈	—	2	2	no	—
403	C₈	—	2	4	no	—
404	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
405	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
406	C₂×C₃	—	2	1	no	—
407	C₂×C₃	—	2	1	no	—
408	C₂×C₃	—	4	2	no	—
409	C₂×C₃	—	8	4	no	—
410	C₂×C₃	C₅×#472	1	2	yes	direct product factor
411	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
412	C₅	C₂×C₃×#472	1	1	yes	characteristic, direct product factor, Sylow
413	C₂²	—	2	2	no	—
414	C₂²	—	2	2	no	—
415	C₂²	—	4	2	no	—
416	C₂²	—	4	4	no	—
417	C₂²	—	8	4	no	—
418	C₂²	—	8	4	no	—
419	C₂²	—	8	4	no	—
420	C₂²	C₃×C₅×#121	1	1	yes	characteristic
421	C₂²	C₃×C₅×#121	1	1	yes	characteristic
422	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
423	C₄	—	2	2	no	—
424	C₄	C₃×C₅×#121	1	1	yes	characteristic
425	C₄	C₃×C₅×#121	1	1	yes	characteristic
426	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
427	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
428	C₃	C₂×C₅×#472	1	1	yes	characteristic, direct product factor, Sylow
429	C₂	—	2	1	no	—
430	C₂	—	2	1	no	—
431	C₂	—	4	2	no	—
432	C₂	—	8	4	no	—
433	C₂	C₃×C₅×#472	1	2	yes	direct product factor
434	C₂	C₂×C₃×C₅×#121	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₃×C₅	#121
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₂²×C₃×C₄×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
2. C₂²×C₃×C₅×D₈	C₂	semidirect
3. C₂×C₃×C₅×#131	C₂	semidirect
4. C₃×C₅×#472	C₂	direct (N × H)
5. C₂×C₃×C₅×#108	C₂	semidirect
6. C₂×C₃×C₅×#100	C₂	semidirect
7. C₂×C₅×#472	C₃	direct (N × H)
11. C₃×C₅×AGL(1,ℤ/8)	C₂²	semidirect
17. C₂×C₃×C₅×D₈	C₂²	semidirect
19. C₃×C₅×#131	C₂²	semidirect
25. C₃×C₅×#108	C₂²	semidirect
26. C₃×C₅×#100	C₂²	semidirect
27. C₂×C₃×#472	C₅	direct (N × H)
28. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
29. C₂²×C₅×D₈	C₂×C₃	semidirect
30. C₂×C₅×#131	C₂×C₃	semidirect
31. C₅×#472	C₂×C₃	direct (N × H)
32. C₂×C₅×#108	C₂×C₃	semidirect
33. C₂×C₅×#100	C₂×C₃	semidirect
66. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
67. C₂²×C₃×D₈	C₂×C₅	semidirect
68. C₂×C₃×#131	C₂×C₅	semidirect
69. C₃×#472	C₂×C₅	direct (N × H)
70. C₂×C₃×#108	C₂×C₅	semidirect
71. C₂×C₃×#100	C₂×C₅	semidirect
75. C₅×AGL(1,ℤ/8)	C₂²×C₃	semidirect
81. C₂×C₅×D₈	C₂²×C₃	semidirect
83. C₅×#131	C₂²×C₃	semidirect
89. C₅×#108	C₂²×C₃	semidirect
90. C₅×#100	C₂²×C₃	semidirect
91. C₂×#472	C₃×C₅	direct (N × H)
124. C₃×AGL(1,ℤ/8)	C₂²×C₅	semidirect
130. C₂×C₃×D₈	C₂²×C₅	semidirect
132. C₃×#131	C₂²×C₅	semidirect
138. C₃×#108	C₂²×C₅	semidirect
139. C₃×#100	C₂²×C₅	semidirect
172. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
173. C₂²×D₈	C₂×C₃×C₅	semidirect
174. C₂×#131	C₂×C₃×C₅	semidirect
175. #472	C₂×C₃×C₅	direct (N × H)
176. C₂×#108	C₂×C₃×C₅	semidirect
177. C₂×#100	C₂×C₃×C₅	semidirect
257. AGL(1,ℤ/8)	C₂²×C₃×C₅	semidirect
263. C₂×D₈	C₂²×C₃×C₅	semidirect
265. #131	C₂²×C₃×C₅	semidirect
271. #108	C₂²×C₃×C₅	semidirect
272. #100	C₂²×C₃×C₅	semidirect
277. C₂×C₃×C₅	#472	direct (N × H)
355. C₃×C₅	C₂×#472	direct (N × H)
375. C₂×C₅	C₃×#472	direct (N × H)
410. C₂×C₃	C₅×#472	direct (N × H)
412. C₅	C₂×C₃×#472	direct (N × H)
428. C₃	C₂×C₅×#472	direct (N × H)
433. C₂	C₃×C₅×#472	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×AGL(1,ℤ/8)	2
C₂²×C₃×C₅×D₈	2
C₂×C₃×C₅×#131	2
C₃×C₅×#472	2
C₂×C₃×C₅×#108	2
C₂×C₃×C₅×#100	2
C₂×C₅×#472	3
C₂×C₃×#472	5

Subgroups — C2×C3×C5×#472 #14276099

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#472 #14276099