Subgroups — C₂×C₃×C₅×#473 #14276100

Order 1920.

896 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#137	C₂	1	2	yes	maximal
2	C₂²×C₃×C₅×Q₁₆	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#131	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#473	C₂	1	8	yes	maximal, direct product factor
5	C₂×C₃×C₅×#108	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×C₃×C₅×#101	C₂	1	2	yes	maximal, complemented
7	C₂×C₅×#473	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
8	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
9	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
10	C₃×C₅×#137	—	2	4	no	—
11	C₃×C₅×#137	C₂²	1	8	yes	—
12	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
13	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
14	C₂×C₃×C₅×Q₁₆	—	2	1	no	—
15	C₂×C₃×C₅×Q₁₆	—	2	2	no	—
16	C₂×C₃×C₅×Q₁₆	C₂²	1	4	yes	complemented
17	C₂×C₃×C₅×SD₁₆	—	2	2	no	—
18	C₃×C₅×#131	—	2	2	no	—
19	C₃×C₅×#131	C₂²	1	4	yes	—
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×#101	C₂²	1	8	yes	complemented
27	C₂×C₃×#473	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
28	C₂×C₅×#137	C₂×C₃	1	2	yes	—
29	C₂²×C₅×Q₁₆	C₂×C₃	1	1	yes	characteristic, complemented
30	C₂×C₅×#131	C₂×C₃	1	1	yes	characteristic
31	C₅×#473	C₂×C₃	1	8	yes	direct product factor
32	C₂×C₅×#108	C₂×C₃	1	1	yes	characteristic, complemented
33	C₂×C₅×#101	C₂×C₃	1	2	yes	complemented
34	C₃×C₅×#41	—	2	1	no	—
35	C₃×C₅×#41	—	2	1	no	—
36	C₃×C₅×#41	D₄	1	2	yes	—
37	C₃×C₅×#41	C₂³	1	2	yes	—
38	C₂×C₃×C₅×Q₈	—	2	2	no	—
39	C₂×C₃×C₅×Q₈	—	2	2	no	—
40	C₂×C₃×C₅×Q₈	—	2	2	no	—
41	C₂×C₃×C₅×Q₈	—	2	2	no	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	D₄	1	1	yes	characteristic
44	C₂×C₃×C₅×Q₈	C₂³	1	4	yes	—
45	C₂×C₃×C₅×D₄	—	2	1	no	—
46	C₂×C₃×C₅×D₄	D₄	1	1	yes	characteristic
47	C₂²×C₃×C₄×C₅	—	2	1	no	—
48	C₂²×C₃×C₄×C₅	—	2	2	no	—
49	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
50	C₃×C₅×Q₁₆	—	2	8	no	—
51	C₃×C₅×Q₁₆	—	2	4	no	—
52	C₃×C₅×Q₁₆	—	2	4	no	—
53	C₃×C₅×SD₁₆	—	2	8	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×#137	C₂×C₅	1	2	yes	—
67	C₂²×C₃×Q₁₆	C₂×C₅	1	1	yes	characteristic, complemented
68	C₂×C₃×#131	C₂×C₅	1	1	yes	characteristic
69	C₃×#473	C₂×C₅	1	8	yes	direct product factor
70	C₂×C₃×#108	C₂×C₅	1	1	yes	characteristic, complemented
71	C₂×C₃×#101	C₂×C₅	1	2	yes	complemented
72	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
73	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
74	C₅×#137	—	2	4	no	—
75	C₅×#137	C₂²×C₃	1	8	yes	—
76	C₂×C₅×Q₁₆	—	2	2	no	—
77	C₂×C₅×Q₁₆	—	2	1	no	—
78	C₂×C₅×Q₁₆	—	2	1	no	—
79	C₂×C₅×Q₁₆	—	2	2	no	—
80	C₂×C₅×Q₁₆	C₂²×C₃	1	4	yes	complemented
81	C₂×C₅×SD₁₆	—	2	2	no	—
82	C₅×#131	—	2	2	no	—
83	C₅×#131	C₂²×C₃	1	4	yes	—
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×#101	C₂²×C₃	1	8	yes	complemented
91	C₂×#473	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
92	C₂³×C₃×C₅	—	2	1	no	—
93	C₂³×C₃×C₅	#41	1	1	yes	characteristic
94	C₃×C₅×Q₈	—	2	1	no	—
95	C₃×C₅×Q₈	—	2	4	no	—
96	C₃×C₅×Q₈	—	2	4	no	—
97	C₃×C₅×Q₈	—	4	2	no	—
98	C₃×C₅×Q₈	—	4	2	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	C₂×D₄	1	2	yes	—
104	C₂×C₃×C₄×C₅	—	2	1	no	—
105	C₂×C₃×C₄×C₅	—	2	2	no	—
106	C₂×C₃×C₄×C₅	—	2	2	no	—
107	C₂×C₃×C₄×C₅	—	2	4	no	—
108	C₂×C₃×C₄×C₅	—	4	2	no	—
109	C₂×C₃×C₄×C₅	—	4	2	no	—
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	C₂×D₄	1	1	yes	characteristic
113	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
114	C₂×C₃×C₄×C₅	#41	1	1	yes	characteristic
115	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
116	C₃×C₅×C₈	—	2	2	no	—
117	C₃×C₅×C₈	—	2	4	no	—
118	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
119	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
120	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
121	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
122	C₃×#137	—	2	4	no	—
123	C₃×#137	C₂²×C₅	1	8	yes	—
124	C₂×C₃×Q₁₆	—	2	2	no	—
125	C₂×C₃×Q₁₆	—	2	1	no	—
126	C₂×C₃×Q₁₆	—	2	1	no	—
127	C₂×C₃×Q₁₆	—	2	2	no	—
128	C₂×C₃×Q₁₆	C₂²×C₅	1	4	yes	complemented
129	C₂×C₃×SD₁₆	—	2	2	no	—
130	C₃×#131	—	2	2	no	—
131	C₃×#131	C₂²×C₅	1	4	yes	—
132	C₂×C₃×M₁₆	—	2	1	no	—
133	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
134	C₂×C₃×M₁₆	C₂²×C₅	1	2	yes	—
135	C₂²×C₃×C₈	—	2	1	no	—
136	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
137	C₃×#108	C₂²×C₅	1	4	yes	complemented
138	C₃×#101	C₂²×C₅	1	8	yes	complemented
139	C₅×#41	—	2	1	no	—
140	C₅×#41	—	2	1	no	—
141	C₅×#41	C₃×D₄	1	2	yes	—
142	C₅×#41	C₂³×C₃	1	2	yes	—
143	C₂×C₅×Q₈	—	2	2	no	—
144	C₂×C₅×Q₈	—	2	2	no	—
145	C₂×C₅×Q₈	—	2	2	no	—
146	C₂×C₅×Q₈	—	2	2	no	—
147	C₂×C₅×Q₈	—	2	2	no	—
148	C₂×C₅×Q₈	C₃×D₄	1	1	yes	characteristic
149	C₂×C₅×Q₈	C₂³×C₃	1	4	yes	—
150	C₂×C₅×D₄	—	2	1	no	—
151	C₂×C₅×D₄	C₃×D₄	1	1	yes	characteristic
152	C₂²×C₄×C₅	—	2	1	no	—
153	C₂²×C₄×C₅	—	2	2	no	—
154	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
155	C₅×Q₁₆	—	2	8	no	—
156	C₅×Q₁₆	—	2	4	no	—
157	C₅×Q₁₆	—	2	4	no	—
158	C₅×SD₁₆	—	2	8	no	—
159	C₅×M₁₆	—	2	1	no	—
160	C₅×M₁₆	—	2	2	no	—
161	C₅×M₁₆	—	2	4	no	—
162	C₅×M₁₆	C₂³×C₃	1	2	yes	—
163	C₅×M₁₆	C₂³×C₃	1	4	yes	—
164	C₂×C₅×C₈	—	2	1	no	—
165	C₂×C₅×C₈	—	2	2	no	—
166	C₂×C₅×C₈	—	2	4	no	—
167	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
168	C₂×C₅×C₈	C₃×D₄	1	1	yes	characteristic
169	C₂×C₅×C₈	C₃×D₄	1	2	yes	—
170	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
171	C₂×#137	C₂×C₃×C₅	1	2	yes	—
172	C₂²×Q₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
173	C₂×#131	C₂×C₃×C₅	1	1	yes	characteristic
174	#473	C₂×C₃×C₅	1	8	yes	direct product factor
175	C₂×#108	C₂×C₃×C₅	1	1	yes	characteristic, complemented
176	C₂×#101	C₂×C₃×C₅	1	2	yes	complemented
177	C₂²×C₃×C₅	—	2	2	no	—
178	C₂²×C₃×C₅	—	2	2	no	—
179	C₂²×C₃×C₅	—	4	2	no	—
180	C₂²×C₃×C₅	#121	1	1	yes	characteristic
181	C₂²×C₃×C₅	#121	1	1	yes	characteristic
182	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
183	C₃×C₄×C₅	—	2	2	no	—
184	C₃×C₄×C₅	—	4	4	no	—
185	C₃×C₄×C₅	#121	1	1	yes	characteristic
186	C₃×C₄×C₅	#121	1	1	yes	characteristic
187	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
188	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
189	C₃×#41	—	2	1	no	—
190	C₃×#41	—	2	1	no	—
191	C₃×#41	C₅×D₄	1	2	yes	—
192	C₃×#41	C₂³×C₅	1	2	yes	—
193	C₂×C₃×Q₈	—	2	2	no	—
194	C₂×C₃×Q₈	—	2	2	no	—
195	C₂×C₃×Q₈	—	2	2	no	—
196	C₂×C₃×Q₈	—	2	2	no	—
197	C₂×C₃×Q₈	—	2	2	no	—
198	C₂×C₃×Q₈	C₅×D₄	1	1	yes	characteristic
199	C₂×C₃×Q₈	C₂³×C₅	1	4	yes	—
200	C₂×C₃×D₄	—	2	1	no	—
201	C₂×C₃×D₄	C₅×D₄	1	1	yes	characteristic
202	C₂²×C₃×C₄	—	2	1	no	—
203	C₂²×C₃×C₄	—	2	2	no	—
204	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
205	C₃×Q₁₆	—	2	8	no	—
206	C₃×Q₁₆	—	2	4	no	—
207	C₃×Q₁₆	—	2	4	no	—
208	C₃×SD₁₆	—	2	8	no	—
209	C₃×M₁₆	—	2	1	no	—
210	C₃×M₁₆	—	2	2	no	—
211	C₃×M₁₆	—	2	4	no	—
212	C₃×M₁₆	C₂³×C₅	1	2	yes	—
213	C₃×M₁₆	C₂³×C₅	1	4	yes	—
214	C₂×C₃×C₈	—	2	1	no	—
215	C₂×C₃×C₈	—	2	2	no	—
216	C₂×C₃×C₈	—	2	4	no	—
217	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
218	C₂×C₃×C₈	C₅×D₄	1	1	yes	characteristic
219	C₂×C₃×C₈	C₅×D₄	1	2	yes	—
220	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
221	C₂³×C₅	—	2	1	no	—
222	C₂³×C₅	C₃×#41	1	1	yes	characteristic
223	C₅×Q₈	—	2	1	no	—
224	C₅×Q₈	—	2	4	no	—
225	C₅×Q₈	—	2	4	no	—
226	C₅×Q₈	—	4	2	no	—
227	C₅×Q₈	—	4	2	no	—
228	C₅×Q₈	C₂×C₃×D₄	1	2	yes	—
229	C₅×D₄	—	2	2	no	—
230	C₅×D₄	—	2	2	no	—
231	C₅×D₄	—	2	1	no	—
232	C₅×D₄	C₂×C₃×D₄	1	2	yes	—
233	C₂×C₄×C₅	—	2	1	no	—
234	C₂×C₄×C₅	—	2	2	no	—
235	C₂×C₄×C₅	—	2	2	no	—
236	C₂×C₄×C₅	—	2	4	no	—
237	C₂×C₄×C₅	—	4	2	no	—
238	C₂×C₄×C₅	—	4	2	no	—
239	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
240	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
241	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
242	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
243	C₂×C₄×C₅	C₃×#41	1	1	yes	characteristic
244	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
245	C₅×C₈	—	2	2	no	—
246	C₅×C₈	—	2	4	no	—
247	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
248	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
249	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
250	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
251	#137	—	2	4	no	—
252	#137	C₂²×C₃×C₅	1	8	yes	—
253	C₂×Q₁₆	—	2	2	no	—
254	C₂×Q₁₆	—	2	1	no	—
255	C₂×Q₁₆	—	2	1	no	—
256	C₂×Q₁₆	—	2	2	no	—
257	C₂×Q₁₆	C₂²×C₃×C₅	1	4	yes	complemented
258	C₂×SD₁₆	—	2	2	no	—
259	#131	—	2	2	no	—
260	#131	C₂²×C₃×C₅	1	4	yes	—
261	C₂×M₁₆	—	2	1	no	—
262	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
263	C₂×M₁₆	C₂²×C₃×C₅	1	2	yes	—
264	C₂²×C₈	—	2	1	no	—
265	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
266	#108	C₂²×C₃×C₅	1	4	yes	complemented
267	#101	C₂²×C₃×C₅	1	8	yes	complemented
268	C₂×C₃×C₅	—	2	1	no	—
269	C₂×C₃×C₅	—	2	1	no	—
270	C₂×C₃×C₅	—	4	2	no	—
271	C₂×C₃×C₅	#473	1	2	yes	direct product factor
272	C₂×C₃×C₅	C₂×#121	1	1	yes	characteristic
273	C₂³×C₃	—	2	1	no	—
274	C₂³×C₃	C₅×#41	1	1	yes	characteristic
275	C₃×Q₈	—	2	1	no	—
276	C₃×Q₈	—	2	4	no	—
277	C₃×Q₈	—	2	4	no	—
278	C₃×Q₈	—	4	2	no	—
279	C₃×Q₈	—	4	2	no	—
280	C₃×Q₈	C₂×C₅×D₄	1	2	yes	—
281	C₃×D₄	—	2	2	no	—
282	C₃×D₄	—	2	2	no	—
283	C₃×D₄	—	2	1	no	—
284	C₃×D₄	C₂×C₅×D₄	1	2	yes	—
285	C₂×C₃×C₄	—	2	1	no	—
286	C₂×C₃×C₄	—	2	2	no	—
287	C₂×C₃×C₄	—	2	2	no	—
288	C₂×C₃×C₄	—	2	4	no	—
289	C₂×C₃×C₄	—	4	2	no	—
290	C₂×C₃×C₄	—	4	2	no	—
291	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
292	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
293	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
294	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
295	C₂×C₃×C₄	C₅×#41	1	1	yes	characteristic
296	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
297	C₃×C₈	—	2	2	no	—
298	C₃×C₈	—	2	4	no	—
299	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
300	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
301	C₂²×C₅	—	2	2	no	—
302	C₂²×C₅	—	2	2	no	—
303	C₂²×C₅	—	4	2	no	—
304	C₂²×C₅	C₃×#121	1	1	yes	characteristic
305	C₂²×C₅	C₃×#121	1	1	yes	characteristic
306	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
307	C₄×C₅	—	2	2	no	—
308	C₄×C₅	—	4	4	no	—
309	C₄×C₅	C₃×#121	1	1	yes	characteristic
310	C₄×C₅	C₃×#121	1	1	yes	characteristic
311	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
312	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
313	#41	—	2	1	no	—
314	#41	—	2	1	no	—
315	#41	C₃×C₅×D₄	1	2	yes	—
316	#41	C₂³×C₃×C₅	1	2	yes	—
317	C₂×Q₈	—	2	2	no	—
318	C₂×Q₈	—	2	2	no	—
319	C₂×Q₈	—	2	2	no	—
320	C₂×Q₈	—	2	2	no	—
321	C₂×Q₈	—	2	2	no	—
322	C₂×Q₈	C₃×C₅×D₄	1	1	yes	characteristic
323	C₂×Q₈	C₂³×C₃×C₅	1	4	yes	—
324	C₂×D₄	—	2	1	no	—
325	C₂×D₄	C₃×C₅×D₄	1	1	yes	characteristic
326	C₂²×C₄	—	2	1	no	—
327	C₂²×C₄	—	2	2	no	—
328	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
329	Q₁₆	—	2	8	no	—
330	Q₁₆	—	2	4	no	—
331	Q₁₆	—	2	4	no	—
332	SD₁₆	—	2	8	no	—
333	M₁₆	—	2	1	no	—
334	M₁₆	—	2	2	no	—
335	M₁₆	—	2	4	no	—
336	M₁₆	C₂³×C₃×C₅	1	2	yes	—
337	M₁₆	C₂³×C₃×C₅	1	4	yes	—
338	C₂×C₈	—	2	1	no	—
339	C₂×C₈	—	2	2	no	—
340	C₂×C₈	—	2	4	no	—
341	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
342	C₂×C₈	C₃×C₅×D₄	1	1	yes	characteristic
343	C₂×C₈	C₃×C₅×D₄	1	2	yes	—
344	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
345	C₃×C₅	C₂×#473	1	1	yes	characteristic, direct product factor, Hall
346	C₂²×C₃	—	2	2	no	—
347	C₂²×C₃	—	2	2	no	—
348	C₂²×C₃	—	4	2	no	—
349	C₂²×C₃	C₅×#121	1	1	yes	characteristic
350	C₂²×C₃	C₅×#121	1	1	yes	characteristic
351	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
352	C₃×C₄	—	2	2	no	—
353	C₃×C₄	—	4	4	no	—
354	C₃×C₄	C₅×#121	1	1	yes	characteristic
355	C₃×C₄	C₅×#121	1	1	yes	characteristic
356	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
357	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
358	C₂×C₅	—	2	1	no	—
359	C₂×C₅	—	2	1	no	—
360	C₂×C₅	—	4	2	no	—
361	C₂×C₅	C₃×#473	1	2	yes	direct product factor
362	C₂×C₅	C₂×C₃×#121	1	1	yes	characteristic
363	C₂³	—	2	1	no	—
364	C₂³	C₃×C₅×#41	1	1	yes	characteristic
365	Q₈	—	2	1	no	—
366	Q₈	—	2	4	no	—
367	Q₈	—	2	4	no	—
368	Q₈	—	4	2	no	—
369	Q₈	—	4	2	no	—
370	Q₈	C₂×C₃×C₅×D₄	1	2	yes	—
371	D₄	—	2	2	no	—
372	D₄	—	2	2	no	—
373	D₄	—	2	1	no	—
374	D₄	C₂×C₃×C₅×D₄	1	2	yes	—
375	C₂×C₄	—	2	1	no	—
376	C₂×C₄	—	2	2	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	4	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
382	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
383	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
384	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
385	C₂×C₄	C₃×C₅×#41	1	1	yes	characteristic
386	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
387	C₈	—	2	2	no	—
388	C₈	—	2	4	no	—
389	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
390	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
391	C₂×C₃	—	2	1	no	—
392	C₂×C₃	—	2	1	no	—
393	C₂×C₃	—	4	2	no	—
394	C₂×C₃	C₅×#473	1	2	yes	direct product factor
395	C₂×C₃	C₂×C₅×#121	1	1	yes	characteristic
396	C₅	C₂×C₃×#473	1	1	yes	characteristic, direct product factor, Sylow
397	C₂²	—	2	2	no	—
398	C₂²	—	2	2	no	—
399	C₂²	—	4	2	no	—
400	C₂²	C₃×C₅×#121	1	1	yes	characteristic
401	C₂²	C₃×C₅×#121	1	1	yes	characteristic
402	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
403	C₄	—	2	2	no	—
404	C₄	—	4	4	no	—
405	C₄	C₃×C₅×#121	1	1	yes	characteristic
406	C₄	C₃×C₅×#121	1	1	yes	characteristic
407	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
408	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
409	C₃	C₂×C₅×#473	1	1	yes	characteristic, direct product factor, Sylow
410	C₂	—	2	1	no	—
411	C₂	—	2	1	no	—
412	C₂	—	4	2	no	—
413	C₂	C₃×C₅×#473	1	2	yes	direct product factor
414	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
prime radical	C₂×C₃×C₅×#41	C₂²
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
2. C₂²×C₃×C₅×Q₁₆	C₂	semidirect
4. C₃×C₅×#473	C₂	direct (N × H)
5. C₂×C₃×C₅×#108	C₂	semidirect
6. C₂×C₃×C₅×#101	C₂	semidirect
7. C₂×C₅×#473	C₃	direct (N × H)
16. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
25. C₃×C₅×#108	C₂²	semidirect
26. C₃×C₅×#101	C₂²	semidirect
27. C₂×C₃×#473	C₅	direct (N × H)
29. C₂²×C₅×Q₁₆	C₂×C₃	semidirect
31. C₅×#473	C₂×C₃	direct (N × H)
32. C₂×C₅×#108	C₂×C₃	semidirect
33. C₂×C₅×#101	C₂×C₃	semidirect
67. C₂²×C₃×Q₁₆	C₂×C₅	semidirect
69. C₃×#473	C₂×C₅	direct (N × H)
70. C₂×C₃×#108	C₂×C₅	semidirect
71. C₂×C₃×#101	C₂×C₅	semidirect
80. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
89. C₅×#108	C₂²×C₃	semidirect
90. C₅×#101	C₂²×C₃	semidirect
91. C₂×#473	C₃×C₅	direct (N × H)
128. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
137. C₃×#108	C₂²×C₅	semidirect
138. C₃×#101	C₂²×C₅	semidirect
172. C₂²×Q₁₆	C₂×C₃×C₅	semidirect
174. #473	C₂×C₃×C₅	direct (N × H)
175. C₂×#108	C₂×C₃×C₅	semidirect
176. C₂×#101	C₂×C₃×C₅	semidirect
257. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
266. #108	C₂²×C₃×C₅	semidirect
267. #101	C₂²×C₃×C₅	semidirect
271. C₂×C₃×C₅	#473	direct (N × H)
345. C₃×C₅	C₂×#473	direct (N × H)
361. C₂×C₅	C₃×#473	direct (N × H)
394. C₂×C₃	C₅×#473	direct (N × H)
396. C₅	C₂×C₃×#473	direct (N × H)
409. C₃	C₂×C₅×#473	direct (N × H)
413. C₂	C₃×C₅×#473	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×#137	2
C₂²×C₃×C₅×Q₁₆	2
C₂×C₃×C₅×#131	2
C₃×C₅×#473	2
C₂×C₃×C₅×#108	2
C₂×C₃×C₅×#101	2
C₂×C₅×#473	3
C₂×C₃×#473	5

Subgroups — C2×C3×C5×#473 #14276100

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₃×C₅×#473 #14276100