Subgroups — C₃×C₅×#3154 #14276188

Order 1920.

1128 conjugacy classes of subgroups.

The subgroup lattice has 596 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	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₅×#135	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂²×C₃×C₅×SD₁₆	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#536	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#535	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#497	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#496	C₂	1	2	yes	maximal, complemented
9	C₃×C₅×#495	C₂	1	2	yes	maximal, complemented
10	C₃×C₅×#492	C₂	1	2	yes	maximal, complemented
11	C₃×C₅×#405	C₂	1	1	yes	maximal, characteristic, complemented
12	C₅×#3154	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
14	C₂×C₃×C₅×#41	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
16	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
17	C₃×C₅×#137	—	2	4	no	—
18	C₃×C₅×AGL(1,ℤ/8)	—	2	4	no	—
19	C₃×C₅×#135	—	2	4	no	—
20	C₂×C₃×C₅×Q₁₆	C₂²	1	2	yes	complemented
21	C₂×C₃×C₅×Q₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₃×C₅×SD₁₆	—	2	4	no	—
23	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
24	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
25	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	—
26	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₃×C₅×SD₁₆	C₂²	1	2	yes	complemented
28	C₂×C₃×C₅×SD₁₆	C₂²	1	1	yes	characteristic, complemented
29	C₂×C₃×C₅×D₈	C₂²	1	2	yes	—
30	C₂×C₃×C₅×D₈	C₂²	1	1	yes	characteristic, complemented
31	C₂×C₃×C₅×M₁₆	C₂²	1	1	yes	characteristic
32	C₂²×C₃×C₅×C₈	C₂²	1	1	yes	characteristic
33	C₃×C₅×C₄⋊Q₈	C₂²	1	2	yes	complemented
34	C₃×C₅×#127	C₂²	1	2	yes	—
35	C₃×C₅×#124	C₂²	1	2	yes	—
36	C₃×C₅×#124	C₂²	1	2	yes	complemented
37	C₃×C₅×#123	—	2	2	no	—
38	C₃×C₅×C₂²⋊Q₈	—	2	2	no	—
39	C₃×C₅×#121	—	2	2	no	—
40	C₃×C₅×#120	—	2	2	no	—
41	C₃×C₅×#117	C₂²	1	1	yes	characteristic
42	C₃×C₅×#97	C₂²	1	2	yes	complemented
43	C₃×C₄×C₅×C₈	C₂²	1	2	yes	complemented
44	C₃×#3154	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
45	C₂×C₅×#137	C₂×C₃	1	1	yes	characteristic, complemented
46	C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	1	1	yes	characteristic, complemented
47	C₂×C₅×#135	C₂×C₃	1	1	yes	characteristic, complemented
48	C₂²×C₅×SD₁₆	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#536	C₂×C₃	1	1	yes	characteristic, complemented
50	C₅×#535	C₂×C₃	1	1	yes	characteristic, complemented
51	C₅×#497	C₂×C₃	1	2	yes	complemented
52	C₅×#496	C₂×C₃	1	2	yes	complemented
53	C₅×#495	C₂×C₃	1	2	yes	complemented
54	C₅×#492	C₂×C₃	1	2	yes	complemented
55	C₅×#405	C₂×C₃	1	1	yes	characteristic, complemented
56	C₂⁴×C₃×C₅	—	2	1	no	—
57	C₃×C₅×#41	—	2	2	no	—
58	C₃×C₅×#41	—	2	2	no	—
59	C₃×C₅×#41	—	2	2	no	—
60	C₃×C₅×#41	—	2	2	no	—
61	C₂×C₃×C₅×Q₈	—	2	1	no	—
62	C₂×C₃×C₅×Q₈	—	2	2	no	—
63	C₂×C₃×C₅×Q₈	—	2	2	no	—
64	C₂×C₃×C₅×Q₈	C₂³	1	2	yes	—
65	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
66	C₂×C₃×C₅×Q₈	C₂³	1	1	yes	characteristic
67	C₂×C₃×C₅×D₄	—	2	1	no	—
68	C₂×C₃×C₅×D₄	—	2	1	no	—
69	C₂×C₃×C₅×D₄	—	2	2	no	—
70	C₂×C₃×C₅×D₄	—	2	2	no	—
71	C₂×C₃×C₅×D₄	—	2	1	no	—
72	C₂×C₃×C₅×D₄	—	2	4	no	—
73	C₂×C₃×C₅×D₄	C₂³	1	2	yes	—
74	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
75	C₂×C₃×C₅×D₄	C₂³	1	1	yes	characteristic
76	C₂²×C₃×C₄×C₅	—	2	1	no	—
77	C₂²×C₃×C₄×C₅	—	2	1	no	—
78	C₂²×C₃×C₄×C₅	—	2	1	no	—
79	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
80	C₃×C₅×Q₁₆	—	2	2	no	—
81	C₃×C₅×Q₁₆	—	2	4	no	—
82	C₃×C₅×SD₁₆	—	2	4	no	—
83	C₃×C₅×SD₁₆	—	2	4	no	—
84	C₃×C₅×SD₁₆	—	2	4	no	—
85	C₃×C₅×SD₁₆	—	2	2	no	—
86	C₃×C₅×SD₁₆	—	2	2	no	—
87	C₃×C₅×SD₁₆	—	2	4	no	—
88	C₃×C₅×D₈	—	2	4	no	—
89	C₃×C₅×D₈	—	2	2	no	—
90	C₃×C₅×M₁₆	D₄	1	4	yes	complemented
91	C₂×C₃×C₅×C₈	D₄	1	4	yes	complemented
92	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
93	C₂×C₃×C₅×C₈	C₂³	1	1	yes	characteristic
94	C₂×C₃×C₅×C₈	C₂³	1	2	yes	—
95	C₃×C₅×C₄⋊C₄	—	2	4	no	—
96	C₃×C₅×C₄⋊C₄	D₄	1	2	yes	—
97	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
98	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
99	C₃×C₅×C₂²⋊C₄	D₄	1	2	yes	—
100	C₃×C₄²×C₅	C₂³	1	2	yes	—
101	C₂×C₃×#137	C₂×C₅	1	1	yes	characteristic, complemented
102	C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	1	1	yes	characteristic, complemented
103	C₂×C₃×#135	C₂×C₅	1	1	yes	characteristic, complemented
104	C₂²×C₃×SD₁₆	C₂×C₅	1	1	yes	characteristic, complemented
105	C₃×#536	C₂×C₅	1	1	yes	characteristic, complemented
106	C₃×#535	C₂×C₅	1	1	yes	characteristic, complemented
107	C₃×#497	C₂×C₅	1	2	yes	complemented
108	C₃×#496	C₂×C₅	1	2	yes	complemented
109	C₃×#495	C₂×C₅	1	2	yes	complemented
110	C₃×#492	C₂×C₅	1	2	yes	complemented
111	C₃×#405	C₂×C₅	1	1	yes	characteristic, complemented
112	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×#41	C₂²×C₃	1	1	yes	characteristic
114	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
115	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
116	C₅×#137	—	2	4	no	—
117	C₅×AGL(1,ℤ/8)	—	2	4	no	—
118	C₅×#135	—	2	4	no	—
119	C₂×C₅×Q₁₆	C₂²×C₃	1	2	yes	complemented
120	C₂×C₅×Q₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
121	C₂×C₅×SD₁₆	—	2	4	no	—
122	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
123	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
124	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	—
125	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
126	C₂×C₅×SD₁₆	C₂²×C₃	1	2	yes	complemented
127	C₂×C₅×SD₁₆	C₂²×C₃	1	1	yes	characteristic, complemented
128	C₂×C₅×D₈	C₂²×C₃	1	2	yes	—
129	C₂×C₅×D₈	C₂²×C₃	1	1	yes	characteristic, complemented
130	C₂×C₅×M₁₆	C₂²×C₃	1	1	yes	characteristic
131	C₂²×C₅×C₈	C₂²×C₃	1	1	yes	characteristic
132	C₅×C₄⋊Q₈	C₂²×C₃	1	2	yes	complemented
133	C₅×#127	C₂²×C₃	1	2	yes	—
134	C₅×#124	C₂²×C₃	1	2	yes	—
135	C₅×#124	C₂²×C₃	1	2	yes	complemented
136	C₅×#123	—	2	2	no	—
137	C₅×C₂²⋊Q₈	—	2	2	no	—
138	C₅×#121	—	2	2	no	—
139	C₅×#120	—	2	2	no	—
140	C₅×#117	C₂²×C₃	1	1	yes	characteristic
141	C₅×#97	C₂²×C₃	1	2	yes	complemented
142	C₄×C₅×C₈	C₂²×C₃	1	2	yes	complemented
143	#3154	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
144	C₂³×C₃×C₅	—	2	1	no	—
145	C₂³×C₃×C₅	—	2	2	no	—
146	C₂³×C₃×C₅	—	2	1	no	—
147	C₂³×C₃×C₅	—	4	2	no	—
148	C₂³×C₃×C₅	—	8	2	no	—
149	C₂³×C₃×C₅	C₂×D₄	1	1	yes	characteristic
150	C₃×C₅×Q₈	—	2	2	no	—
151	C₃×C₅×Q₈	—	2	1	no	—
152	C₃×C₅×Q₈	—	2	2	no	—
153	C₃×C₅×Q₈	—	2	1	no	—
154	C₃×C₅×Q₈	—	2	1	no	—
155	C₃×C₅×Q₈	—	2	1	no	—
156	C₃×C₅×Q₈	—	4	2	no	—
157	C₃×C₅×D₄	—	2	1	no	—
158	C₃×C₅×D₄	—	2	2	no	—
159	C₃×C₅×D₄	—	2	1	no	—
160	C₃×C₅×D₄	—	2	1	no	—
161	C₃×C₅×D₄	—	2	2	no	—
162	C₃×C₅×D₄	—	2	1	no	—
163	C₃×C₅×D₄	—	4	2	no	—
164	C₃×C₅×D₄	—	4	2	no	—
165	C₃×C₅×D₄	—	4	2	no	—
166	C₃×C₅×D₄	—	8	4	no	—
167	C₂×C₃×C₄×C₅	—	2	1	no	—
168	C₂×C₃×C₄×C₅	—	2	2	no	—
169	C₂×C₃×C₄×C₅	—	2	1	no	—
170	C₂×C₃×C₄×C₅	—	4	2	no	—
171	C₂×C₃×C₄×C₅	—	4	2	no	—
172	C₂×C₃×C₄×C₅	—	4	2	no	—
173	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
174	C₂×C₃×C₄×C₅	C₂×D₄	1	1	yes	characteristic
175	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
176	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
177	C₂×C₃×C₄×C₅	C₂⁴	1	1	yes	characteristic
178	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
179	C₃×C₅×C₈	C₂×D₄	1	2	yes	—
180	C₃×C₅×C₈	C₂×D₄	1	4	yes	—
181	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
182	C₂×C₃×#41	C₂²×C₅	1	1	yes	characteristic
183	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
184	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
185	C₃×#137	—	2	4	no	—
186	C₃×AGL(1,ℤ/8)	—	2	4	no	—
187	C₃×#135	—	2	4	no	—
188	C₂×C₃×Q₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
189	C₂×C₃×Q₁₆	C₂²×C₅	1	2	yes	complemented
190	C₂×C₃×SD₁₆	—	2	4	no	—
191	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
192	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
193	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	—
194	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
195	C₂×C₃×SD₁₆	C₂²×C₅	1	1	yes	characteristic, complemented
196	C₂×C₃×SD₁₆	C₂²×C₅	1	2	yes	complemented
197	C₂×C₃×D₈	C₂²×C₅	1	2	yes	—
198	C₂×C₃×D₈	C₂²×C₅	1	1	yes	characteristic, complemented
199	C₂×C₃×M₁₆	C₂²×C₅	1	1	yes	characteristic
200	C₂²×C₃×C₈	C₂²×C₅	1	1	yes	characteristic
201	C₃×C₄⋊Q₈	C₂²×C₅	1	2	yes	complemented
202	C₃×#127	C₂²×C₅	1	2	yes	—
203	C₃×#124	C₂²×C₅	1	2	yes	—
204	C₃×#124	C₂²×C₅	1	2	yes	complemented
205	C₃×#123	—	2	2	no	—
206	C₃×C₂²⋊Q₈	—	2	2	no	—
207	C₃×#121	—	2	2	no	—
208	C₃×#120	—	2	2	no	—
209	C₃×#117	C₂²×C₅	1	1	yes	characteristic
210	C₃×#97	C₂²×C₅	1	2	yes	complemented
211	C₃×C₄×C₈	C₂²×C₅	1	2	yes	complemented
212	C₂⁴×C₅	—	2	1	no	—
213	C₅×#41	—	2	2	no	—
214	C₅×#41	—	2	2	no	—
215	C₅×#41	—	2	2	no	—
216	C₅×#41	—	2	2	no	—
217	C₂×C₅×Q₈	—	2	1	no	—
218	C₂×C₅×Q₈	—	2	2	no	—
219	C₂×C₅×Q₈	—	2	2	no	—
220	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
221	C₂×C₅×Q₈	C₂³×C₃	1	2	yes	—
222	C₂×C₅×Q₈	C₂³×C₃	1	1	yes	characteristic
223	C₂×C₅×D₄	—	2	1	no	—
224	C₂×C₅×D₄	—	2	1	no	—
225	C₂×C₅×D₄	—	2	2	no	—
226	C₂×C₅×D₄	—	2	2	no	—
227	C₂×C₅×D₄	—	2	1	no	—
228	C₂×C₅×D₄	—	2	4	no	—
229	C₂×C₅×D₄	C₂³×C₃	1	2	yes	—
230	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
231	C₂×C₅×D₄	C₂³×C₃	1	1	yes	characteristic
232	C₂²×C₄×C₅	—	2	1	no	—
233	C₂²×C₄×C₅	—	2	1	no	—
234	C₂²×C₄×C₅	—	2	1	no	—
235	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
236	C₅×Q₁₆	—	2	2	no	—
237	C₅×Q₁₆	—	2	4	no	—
238	C₅×SD₁₆	—	2	4	no	—
239	C₅×SD₁₆	—	2	4	no	—
240	C₅×SD₁₆	—	2	4	no	—
241	C₅×SD₁₆	—	2	2	no	—
242	C₅×SD₁₆	—	2	2	no	—
243	C₅×SD₁₆	—	2	4	no	—
244	C₅×D₈	—	2	4	no	—
245	C₅×D₈	—	2	2	no	—
246	C₅×M₁₆	C₃×D₄	1	4	yes	complemented
247	C₂×C₅×C₈	C₃×D₄	1	4	yes	complemented
248	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
249	C₂×C₅×C₈	C₂³×C₃	1	1	yes	characteristic
250	C₂×C₅×C₈	C₂³×C₃	1	2	yes	—
251	C₅×C₄⋊C₄	—	2	4	no	—
252	C₅×C₄⋊C₄	C₃×D₄	1	2	yes	—
253	C₅×C₂²⋊C₄	—	2	4	no	—
254	C₅×C₂²⋊C₄	—	2	4	no	—
255	C₅×C₂²⋊C₄	C₃×D₄	1	2	yes	—
256	C₄²×C₅	C₂³×C₃	1	2	yes	—
257	C₂×#137	C₂×C₃×C₅	1	1	yes	characteristic, complemented
258	C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	1	1	yes	characteristic, complemented
259	C₂×#135	C₂×C₃×C₅	1	1	yes	characteristic, complemented
260	C₂²×SD₁₆	C₂×C₃×C₅	1	1	yes	characteristic, complemented
261	#536	C₂×C₃×C₅	1	1	yes	characteristic, complemented
262	#535	C₂×C₃×C₅	1	1	yes	characteristic, complemented
263	#497	C₂×C₃×C₅	1	2	yes	complemented
264	#496	C₂×C₃×C₅	1	2	yes	complemented
265	#495	C₂×C₃×C₅	1	2	yes	complemented
266	#492	C₂×C₃×C₅	1	2	yes	complemented
267	#405	C₂×C₃×C₅	1	1	yes	characteristic, complemented
268	C₂²×C₃×C₅	—	2	2	no	—
269	C₂²×C₃×C₅	—	4	1	no	—
270	C₂²×C₃×C₅	—	4	1	no	—
271	C₂²×C₃×C₅	—	4	2	no	—
272	C₂²×C₃×C₅	—	4	2	no	—
273	C₂²×C₃×C₅	—	4	4	no	—
274	C₂²×C₃×C₅	—	4	2	no	—
275	C₂²×C₃×C₅	—	8	4	no	—
276	C₂²×C₃×C₅	#127	1	2	yes	—
277	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
278	C₃×C₄×C₅	—	2	4	no	—
279	C₃×C₄×C₅	—	4	1	no	—
280	C₃×C₄×C₅	—	4	1	no	—
281	C₃×C₄×C₅	—	4	2	no	—
282	C₃×C₄×C₅	#127	1	2	yes	—
283	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
284	C₃×C₄×C₅	C₂²×D₄	1	1	yes	characteristic
285	C₂⁴×C₃	—	2	1	no	—
286	C₃×#41	—	2	2	no	—
287	C₃×#41	—	2	2	no	—
288	C₃×#41	—	2	2	no	—
289	C₃×#41	—	2	2	no	—
290	C₂×C₃×Q₈	—	2	1	no	—
291	C₂×C₃×Q₈	—	2	2	no	—
292	C₂×C₃×Q₈	—	2	2	no	—
293	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
294	C₂×C₃×Q₈	C₂³×C₅	1	2	yes	—
295	C₂×C₃×Q₈	C₂³×C₅	1	1	yes	characteristic
296	C₂×C₃×D₄	—	2	1	no	—
297	C₂×C₃×D₄	—	2	1	no	—
298	C₂×C₃×D₄	—	2	2	no	—
299	C₂×C₃×D₄	—	2	2	no	—
300	C₂×C₃×D₄	—	2	1	no	—
301	C₂×C₃×D₄	—	2	4	no	—
302	C₂×C₃×D₄	C₂³×C₅	1	2	yes	—
303	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
304	C₂×C₃×D₄	C₂³×C₅	1	1	yes	characteristic
305	C₂²×C₃×C₄	—	2	1	no	—
306	C₂²×C₃×C₄	—	2	1	no	—
307	C₂²×C₃×C₄	—	2	1	no	—
308	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
309	C₃×Q₁₆	—	2	2	no	—
310	C₃×Q₁₆	—	2	4	no	—
311	C₃×SD₁₆	—	2	4	no	—
312	C₃×SD₁₆	—	2	4	no	—
313	C₃×SD₁₆	—	2	4	no	—
314	C₃×SD₁₆	—	2	2	no	—
315	C₃×SD₁₆	—	2	2	no	—
316	C₃×SD₁₆	—	2	4	no	—
317	C₃×D₈	—	2	4	no	—
318	C₃×D₈	—	2	2	no	—
319	C₃×M₁₆	C₅×D₄	1	4	yes	complemented
320	C₂×C₃×C₈	C₅×D₄	1	4	yes	complemented
321	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
322	C₂×C₃×C₈	C₂³×C₅	1	2	yes	—
323	C₂×C₃×C₈	C₂³×C₅	1	1	yes	characteristic
324	C₃×C₄⋊C₄	—	2	4	no	—
325	C₃×C₄⋊C₄	C₅×D₄	1	2	yes	—
326	C₃×C₂²⋊C₄	—	2	4	no	—
327	C₃×C₂²⋊C₄	—	2	4	no	—
328	C₃×C₂²⋊C₄	C₅×D₄	1	2	yes	—
329	C₃×C₄²	C₂³×C₅	1	2	yes	—
330	C₂³×C₅	—	2	1	no	—
331	C₂³×C₅	—	2	2	no	—
332	C₂³×C₅	—	2	1	no	—
333	C₂³×C₅	—	4	2	no	—
334	C₂³×C₅	—	8	2	no	—
335	C₂³×C₅	C₂×C₃×D₄	1	1	yes	characteristic
336	C₅×Q₈	—	2	2	no	—
337	C₅×Q₈	—	2	1	no	—
338	C₅×Q₈	—	2	2	no	—
339	C₅×Q₈	—	2	1	no	—
340	C₅×Q₈	—	2	1	no	—
341	C₅×Q₈	—	2	1	no	—
342	C₅×Q₈	—	4	2	no	—
343	C₅×D₄	—	2	1	no	—
344	C₅×D₄	—	2	2	no	—
345	C₅×D₄	—	2	1	no	—
346	C₅×D₄	—	2	1	no	—
347	C₅×D₄	—	2	2	no	—
348	C₅×D₄	—	2	1	no	—
349	C₅×D₄	—	4	2	no	—
350	C₅×D₄	—	4	2	no	—
351	C₅×D₄	—	4	2	no	—
352	C₅×D₄	—	8	4	no	—
353	C₂×C₄×C₅	—	2	1	no	—
354	C₂×C₄×C₅	—	2	2	no	—
355	C₂×C₄×C₅	—	2	1	no	—
356	C₂×C₄×C₅	—	4	2	no	—
357	C₂×C₄×C₅	—	4	2	no	—
358	C₂×C₄×C₅	—	4	2	no	—
359	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
360	C₂×C₄×C₅	C₂×C₃×D₄	1	1	yes	characteristic
361	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
362	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
363	C₂×C₄×C₅	C₂⁴×C₃	1	1	yes	characteristic
364	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
365	C₅×C₈	C₂×C₃×D₄	1	2	yes	—
366	C₅×C₈	C₂×C₃×D₄	1	4	yes	—
367	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
368	C₂×#41	C₂²×C₃×C₅	1	1	yes	characteristic
369	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
370	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
371	#137	—	2	4	no	—
372	AGL(1,ℤ/8)	—	2	4	no	—
373	#135	—	2	4	no	—
374	C₂×Q₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
375	C₂×Q₁₆	C₂²×C₃×C₅	1	2	yes	complemented
376	C₂×SD₁₆	—	2	4	no	—
377	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
378	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
379	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	—
380	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
381	C₂×SD₁₆	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
382	C₂×SD₁₆	C₂²×C₃×C₅	1	2	yes	complemented
383	C₂×D₈	C₂²×C₃×C₅	1	2	yes	—
384	C₂×D₈	C₂²×C₃×C₅	1	1	yes	characteristic, complemented
385	C₂×M₁₆	C₂²×C₃×C₅	1	1	yes	characteristic
386	C₂²×C₈	C₂²×C₃×C₅	1	1	yes	characteristic
387	C₄⋊Q₈	C₂²×C₃×C₅	1	2	yes	complemented
388	#127	C₂²×C₃×C₅	1	2	yes	—
389	#124	C₂²×C₃×C₅	1	2	yes	—
390	#124	C₂²×C₃×C₅	1	2	yes	complemented
391	#123	—	2	2	no	—
392	C₂²⋊Q₈	—	2	2	no	—
393	#121	—	2	2	no	—
394	#120	—	2	2	no	—
395	#117	C₂²×C₃×C₅	1	1	yes	characteristic
396	#97	C₂²×C₃×C₅	1	2	yes	complemented
397	C₄×C₈	C₂²×C₃×C₅	1	2	yes	complemented
398	C₂×C₃×C₅	—	2	2	no	—
399	C₂×C₃×C₅	—	8	1	no	—
400	C₂×C₃×C₅	—	8	1	no	—
401	C₂×C₃×C₅	—	8	2	no	—
402	C₂×C₃×C₅	C₂×#127	1	1	yes	characteristic
403	C₂×C₃×C₅	#577	1	2	yes	—
404	C₂³×C₃	—	2	1	no	—
405	C₂³×C₃	—	2	2	no	—
406	C₂³×C₃	—	2	1	no	—
407	C₂³×C₃	—	4	2	no	—
408	C₂³×C₃	—	8	2	no	—
409	C₂³×C₃	C₂×C₅×D₄	1	1	yes	characteristic
410	C₃×Q₈	—	2	2	no	—
411	C₃×Q₈	—	2	1	no	—
412	C₃×Q₈	—	2	2	no	—
413	C₃×Q₈	—	2	1	no	—
414	C₃×Q₈	—	2	1	no	—
415	C₃×Q₈	—	2	1	no	—
416	C₃×Q₈	—	4	2	no	—
417	C₃×D₄	—	2	1	no	—
418	C₃×D₄	—	2	2	no	—
419	C₃×D₄	—	2	1	no	—
420	C₃×D₄	—	2	1	no	—
421	C₃×D₄	—	2	2	no	—
422	C₃×D₄	—	2	1	no	—
423	C₃×D₄	—	4	2	no	—
424	C₃×D₄	—	4	2	no	—
425	C₃×D₄	—	4	2	no	—
426	C₃×D₄	—	8	4	no	—
427	C₂×C₃×C₄	—	2	1	no	—
428	C₂×C₃×C₄	—	2	2	no	—
429	C₂×C₃×C₄	—	2	1	no	—
430	C₂×C₃×C₄	—	4	2	no	—
431	C₂×C₃×C₄	—	4	2	no	—
432	C₂×C₃×C₄	—	4	2	no	—
433	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
434	C₂×C₃×C₄	C₂×C₅×D₄	1	1	yes	characteristic
435	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
436	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
437	C₂×C₃×C₄	C₂⁴×C₅	1	1	yes	characteristic
438	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
439	C₃×C₈	C₂×C₅×D₄	1	2	yes	—
440	C₃×C₈	C₂×C₅×D₄	1	4	yes	—
441	C₂²×C₅	—	2	2	no	—
442	C₂²×C₅	—	4	2	no	—
443	C₂²×C₅	—	4	4	no	—
444	C₂²×C₅	—	4	2	no	—
445	C₂²×C₅	—	4	1	no	—
446	C₂²×C₅	—	4	1	no	—
447	C₂²×C₅	—	4	2	no	—
448	C₂²×C₅	—	8	4	no	—
449	C₂²×C₅	C₃×#127	1	2	yes	—
450	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
451	C₄×C₅	—	2	4	no	—
452	C₄×C₅	—	4	1	no	—
453	C₄×C₅	—	4	1	no	—
454	C₄×C₅	—	4	2	no	—
455	C₄×C₅	C₃×#127	1	2	yes	—
456	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
457	C₄×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
458	C₂⁴	—	2	1	no	—
459	#41	—	2	2	no	—
460	#41	—	2	2	no	—
461	#41	—	2	2	no	—
462	#41	—	2	2	no	—
463	C₂×Q₈	—	2	1	no	—
464	C₂×Q₈	—	2	2	no	—
465	C₂×Q₈	—	2	2	no	—
466	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
467	C₂×Q₈	C₂³×C₃×C₅	1	2	yes	—
468	C₂×Q₈	C₂³×C₃×C₅	1	1	yes	characteristic
469	C₂×D₄	—	2	1	no	—
470	C₂×D₄	—	2	1	no	—
471	C₂×D₄	—	2	2	no	—
472	C₂×D₄	—	2	2	no	—
473	C₂×D₄	—	2	1	no	—
474	C₂×D₄	—	2	4	no	—
475	C₂×D₄	C₂³×C₃×C₅	1	2	yes	—
476	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
477	C₂×D₄	C₂³×C₃×C₅	1	1	yes	characteristic
478	C₂²×C₄	—	2	1	no	—
479	C₂²×C₄	—	2	1	no	—
480	C₂²×C₄	—	2	1	no	—
481	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
482	Q₁₆	—	2	2	no	—
483	Q₁₆	—	2	4	no	—
484	SD₁₆	—	2	4	no	—
485	SD₁₆	—	2	4	no	—
486	SD₁₆	—	2	4	no	—
487	SD₁₆	—	2	2	no	—
488	SD₁₆	—	2	2	no	—
489	SD₁₆	—	2	4	no	—
490	D₈	—	2	4	no	—
491	D₈	—	2	2	no	—
492	M₁₆	C₃×C₅×D₄	1	4	yes	complemented
493	C₂×C₈	C₃×C₅×D₄	1	4	yes	complemented
494	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
495	C₂×C₈	C₂³×C₃×C₅	1	2	yes	—
496	C₂×C₈	C₂³×C₃×C₅	1	1	yes	characteristic
497	C₄⋊C₄	—	2	4	no	—
498	C₄⋊C₄	C₃×C₅×D₄	1	2	yes	—
499	C₂²⋊C₄	—	2	4	no	—
500	C₂²⋊C₄	—	2	4	no	—
501	C₂²⋊C₄	C₃×C₅×D₄	1	2	yes	—
502	C₄²	C₂³×C₃×C₅	1	2	yes	—
503	C₃×C₅	#3154	1	1	yes	characteristic, direct product factor, Hall
504	C₂²×C₃	—	2	2	no	—
505	C₂²×C₃	—	4	1	no	—
506	C₂²×C₃	—	4	1	no	—
507	C₂²×C₃	—	4	2	no	—
508	C₂²×C₃	—	4	2	no	—
509	C₂²×C₃	—	4	4	no	—
510	C₂²×C₃	—	4	2	no	—
511	C₂²×C₃	—	8	4	no	—
512	C₂²×C₃	C₅×#127	1	2	yes	—
513	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
514	C₃×C₄	—	2	4	no	—
515	C₃×C₄	—	4	1	no	—
516	C₃×C₄	—	4	1	no	—
517	C₃×C₄	—	4	2	no	—
518	C₃×C₄	C₅×#127	1	2	yes	—
519	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
520	C₃×C₄	C₂²×C₅×D₄	1	1	yes	characteristic
521	C₂×C₅	—	2	2	no	—
522	C₂×C₅	—	8	2	no	—
523	C₂×C₅	—	8	1	no	—
524	C₂×C₅	—	8	1	no	—
525	C₂×C₅	C₂×C₃×#127	1	1	yes	characteristic
526	C₂×C₅	C₃×#577	1	2	yes	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	1	no	—
530	C₂³	—	4	2	no	—
531	C₂³	—	8	2	no	—
532	C₂³	C₂×C₃×C₅×D₄	1	1	yes	characteristic
533	Q₈	—	2	2	no	—
534	Q₈	—	2	1	no	—
535	Q₈	—	2	2	no	—
536	Q₈	—	2	1	no	—
537	Q₈	—	2	1	no	—
538	Q₈	—	2	1	no	—
539	Q₈	—	4	2	no	—
540	D₄	—	2	1	no	—
541	D₄	—	2	2	no	—
542	D₄	—	2	1	no	—
543	D₄	—	2	1	no	—
544	D₄	—	2	2	no	—
545	D₄	—	2	1	no	—
546	D₄	—	4	2	no	—
547	D₄	—	4	2	no	—
548	D₄	—	4	2	no	—
549	D₄	—	8	4	no	—
550	C₂×C₄	—	2	1	no	—
551	C₂×C₄	—	2	2	no	—
552	C₂×C₄	—	2	1	no	—
553	C₂×C₄	—	4	2	no	—
554	C₂×C₄	—	4	2	no	—
555	C₂×C₄	—	4	2	no	—
556	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
557	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
558	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
559	C₂×C₄	C₂×C₃×C₅×D₄	1	1	yes	characteristic
560	C₂×C₄	C₂⁴×C₃×C₅	1	1	yes	characteristic
561	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
562	C₈	C₂×C₃×C₅×D₄	1	2	yes	—
563	C₈	C₂×C₃×C₅×D₄	1	4	yes	—
564	C₂×C₃	—	2	2	no	—
565	C₂×C₃	—	8	2	no	—
566	C₂×C₃	—	8	1	no	—
567	C₂×C₃	—	8	1	no	—
568	C₂×C₃	C₂×C₅×#127	1	1	yes	characteristic
569	C₂×C₃	C₅×#577	1	2	yes	—
570	C₅	C₃×#3154	1	1	yes	characteristic, direct product factor, Sylow
571	C₂²	—	2	2	no	—
572	C₂²	—	4	1	no	—
573	C₂²	—	4	1	no	—
574	C₂²	—	4	2	no	—
575	C₂²	—	4	2	no	—
576	C₂²	—	4	4	no	—
577	C₂²	—	4	2	no	—
578	C₂²	—	8	4	no	—
579	C₂²	C₃×C₅×#127	1	2	yes	—
580	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
581	C₄	—	2	4	no	—
582	C₄	—	4	1	no	—
583	C₄	—	4	1	no	—
584	C₄	—	4	2	no	—
585	C₄	C₃×C₅×#127	1	2	yes	—
586	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
587	C₄	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
588	C₃	C₅×#3154	1	1	yes	characteristic, direct product factor, Sylow
589	C₂	—	2	2	no	—
590	C₂	—	8	2	no	—
591	C₂	—	8	1	no	—
592	C₂	—	8	1	no	—
593	C₂	C₂×C₃×C₅×#127	1	1	yes	characteristic
594	C₂	C₃×C₅×#577	1	2	yes	—

	subgroup	G/H
center, socle	C₂²×C₃×C₅	C₂²×D₄
commutator, Frattini, cosocle	C₂×C₄	C₂⁴×C₃×C₅
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂²×C₃×C₅ ◁ C₃×C₅×#117 ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×#137	C₂	semidirect
2. C₂×C₃×C₅×AGL(1,ℤ/8)	C₂	semidirect
3. C₂×C₃×C₅×#135	C₂	semidirect
4. C₂²×C₃×C₅×SD₁₆	C₂	semidirect
5. C₃×C₅×#536	C₂	semidirect
6. C₃×C₅×#535	C₂	semidirect
7. C₃×C₅×#497	C₂	semidirect
8. C₃×C₅×#496	C₂	semidirect
9. C₃×C₅×#495	C₂	semidirect
10. C₃×C₅×#492	C₂	semidirect
11. C₃×C₅×#405	C₂	semidirect
12. C₅×#3154	C₃	direct (N × H)
20. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
21. C₂×C₃×C₅×Q₁₆	C₂²	semidirect
26. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
27. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
28. C₂×C₃×C₅×SD₁₆	C₂²	semidirect
30. C₂×C₃×C₅×D₈	C₂²	semidirect
33. C₃×C₅×C₄⋊Q₈	C₂²	semidirect
36. C₃×C₅×#124	C₂²	semidirect
42. C₃×C₅×#97	C₂²	semidirect
43. C₃×C₄×C₅×C₈	C₂²	semidirect
44. C₃×#3154	C₅	direct (N × H)
45. C₂×C₅×#137	C₂×C₃	semidirect
46. C₂×C₅×AGL(1,ℤ/8)	C₂×C₃	semidirect
47. C₂×C₅×#135	C₂×C₃	semidirect
48. C₂²×C₅×SD₁₆	C₂×C₃	semidirect
49. C₅×#536	C₂×C₃	semidirect
50. C₅×#535	C₂×C₃	semidirect
51. C₅×#497	C₂×C₃	semidirect
52. C₅×#496	C₂×C₃	semidirect
53. C₅×#495	C₂×C₃	semidirect
54. C₅×#492	C₂×C₃	semidirect
55. C₅×#405	C₂×C₃	semidirect
90. C₃×C₅×M₁₆	D₄	semidirect
91. C₂×C₃×C₅×C₈	D₄	semidirect
101. C₂×C₃×#137	C₂×C₅	semidirect
102. C₂×C₃×AGL(1,ℤ/8)	C₂×C₅	semidirect
103. C₂×C₃×#135	C₂×C₅	semidirect
104. C₂²×C₃×SD₁₆	C₂×C₅	semidirect
105. C₃×#536	C₂×C₅	semidirect
106. C₃×#535	C₂×C₅	semidirect
107. C₃×#497	C₂×C₅	semidirect
108. C₃×#496	C₂×C₅	semidirect
109. C₃×#495	C₂×C₅	semidirect
110. C₃×#492	C₂×C₅	semidirect
111. C₃×#405	C₂×C₅	semidirect
119. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
120. C₂×C₅×Q₁₆	C₂²×C₃	semidirect
125. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
126. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
127. C₂×C₅×SD₁₆	C₂²×C₃	semidirect
129. C₂×C₅×D₈	C₂²×C₃	semidirect
132. C₅×C₄⋊Q₈	C₂²×C₃	semidirect
135. C₅×#124	C₂²×C₃	semidirect
141. C₅×#97	C₂²×C₃	semidirect
142. C₄×C₅×C₈	C₂²×C₃	semidirect
143. #3154	C₃×C₅	direct (N × H)
188. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
189. C₂×C₃×Q₁₆	C₂²×C₅	semidirect
194. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
195. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
196. C₂×C₃×SD₁₆	C₂²×C₅	semidirect
198. C₂×C₃×D₈	C₂²×C₅	semidirect
201. C₃×C₄⋊Q₈	C₂²×C₅	semidirect
204. C₃×#124	C₂²×C₅	semidirect
210. C₃×#97	C₂²×C₅	semidirect
211. C₃×C₄×C₈	C₂²×C₅	semidirect
246. C₅×M₁₆	C₃×D₄	semidirect
247. C₂×C₅×C₈	C₃×D₄	semidirect
257. C₂×#137	C₂×C₃×C₅	semidirect
258. C₂×AGL(1,ℤ/8)	C₂×C₃×C₅	semidirect
259. C₂×#135	C₂×C₃×C₅	semidirect
260. C₂²×SD₁₆	C₂×C₃×C₅	semidirect
261. #536	C₂×C₃×C₅	semidirect
262. #535	C₂×C₃×C₅	semidirect
263. #497	C₂×C₃×C₅	semidirect
264. #496	C₂×C₃×C₅	semidirect
265. #495	C₂×C₃×C₅	semidirect
266. #492	C₂×C₃×C₅	semidirect
267. #405	C₂×C₃×C₅	semidirect
319. C₃×M₁₆	C₅×D₄	semidirect
320. C₂×C₃×C₈	C₅×D₄	semidirect
374. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
375. C₂×Q₁₆	C₂²×C₃×C₅	semidirect
380. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
381. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
382. C₂×SD₁₆	C₂²×C₃×C₅	semidirect
384. C₂×D₈	C₂²×C₃×C₅	semidirect
387. C₄⋊Q₈	C₂²×C₃×C₅	semidirect
390. #124	C₂²×C₃×C₅	semidirect
396. #97	C₂²×C₃×C₅	semidirect
397. C₄×C₈	C₂²×C₃×C₅	semidirect
492. M₁₆	C₃×C₅×D₄	semidirect
493. C₂×C₈	C₃×C₅×D₄	semidirect
503. C₃×C₅	#3154	direct (N × H)
570. C₅	C₃×#3154	direct (N × H)
588. C₃	C₅×#3154	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
C₂×C₃×C₅×AGL(1,ℤ/8)	2
C₂×C₃×C₅×#135	2
C₂²×C₃×C₅×SD₁₆	2
C₃×C₅×#536	2
C₃×C₅×#535	2
C₃×C₅×#497	2
C₃×C₅×#496	2
C₃×C₅×#495	2
C₃×C₅×#492	2
C₃×C₅×#405	2
C₅×#3154	3
C₃×#3154	5

Subgroups — C3×C5×#3154 #14276188

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#3154 #14276188