Subgroups — C₃×C₅×#2440 #14275474

Order 1920.

1216 conjugacy classes of subgroups.

The subgroup lattice has 588 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₄⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	2	yes	maximal
3	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#398	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#395	C₂	1	2	yes	maximal, complemented
6	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₅×#385	C₂	1	2	yes	maximal
9	C₃×C₅×#384	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2440	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
17	C₃×C₅×C₂²⋊Q₈	—	2	8	no	—
18	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
26	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
30	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
33	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
34	C₃×C₅×#95	C₂²	1	1	yes	characteristic
35	C₃×C₅×#95	C₂²	1	1	yes	characteristic
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×#2440	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	2	yes	—
42	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
43	C₅×#398	C₂×C₃	1	2	yes	complemented
44	C₅×#395	C₂×C₃	1	2	yes	complemented
45	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
46	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
47	C₅×#385	C₂×C₃	1	2	yes	—
48	C₅×#384	C₂×C₃	1	1	yes	characteristic, complemented
49	C₅×#380	C₂×C₃	1	1	yes	characteristic
50	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
51	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×Q₈	—	2	4	no	—
53	C₂×C₃×C₅×Q₈	—	2	4	no	—
54	C₂×C₃×C₅×Q₈	—	4	2	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	—	2	4	no	—
58	C₂²×C₃×C₄×C₅	—	2	4	no	—
59	C₂²×C₃×C₄×C₅	—	4	2	no	—
60	C₂²×C₃×C₄×C₅	Q₈	1	4	yes	complemented
61	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
67	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	4	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	—	2	4	no	—
74	C₃×C₅×C₄⋊C₄	—	2	4	no	—
75	C₃×C₅×C₄⋊C₄	—	2	4	no	—
76	C₃×C₅×C₄⋊C₄	—	2	4	no	—
77	C₃×C₅×C₄⋊C₄	—	2	2	no	—
78	C₃×C₅×C₄⋊C₄	—	2	2	no	—
79	C₃×C₅×C₄⋊C₄	—	4	2	no	—
80	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
81	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
82	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	—
83	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
84	C₃×C₄²×C₅	—	2	2	no	—
85	C₃×C₄²×C₅	—	2	2	no	—
86	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	2	yes	—
88	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
89	C₃×#398	C₂×C₅	1	2	yes	complemented
90	C₃×#395	C₂×C₅	1	2	yes	complemented
91	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
92	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
93	C₃×#385	C₂×C₅	1	2	yes	—
94	C₃×#384	C₂×C₅	1	1	yes	characteristic, complemented
95	C₃×#380	C₂×C₅	1	1	yes	characteristic
96	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
97	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
98	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
99	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
100	C₅×C₄⋊Q₈	—	2	4	no	—
101	C₅×C₂²⋊Q₈	—	2	8	no	—
102	C₂×C₅×C₄⋊C₄	—	2	4	no	—
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
107	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
109	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
110	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
112	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
114	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
116	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
117	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
118	C₅×#95	C₂²×C₃	1	1	yes	characteristic
119	C₅×#95	C₂²×C₃	1	1	yes	characteristic
120	C₅×#95	C₂²×C₃	1	2	yes	—
121	C₅×#95	C₂²×C₃	1	2	yes	—
122	C₅×#95	C₂²×C₃	1	2	yes	—
123	#2440	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	—	2	1	no	—
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	—	2	1	no	—
128	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
129	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
130	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
131	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
132	C₃×C₅×Q₈	—	4	8	no	—
133	C₂×C₃×C₄×C₅	—	2	1	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	1	no	—
136	C₂×C₃×C₄×C₅	—	2	2	no	—
137	C₂×C₃×C₄×C₅	—	2	1	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	1	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	1	no	—
145	C₂×C₃×C₄×C₅	—	2	8	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	2	no	—
148	C₂×C₃×C₄×C₅	—	2	2	no	—
149	C₂×C₃×C₄×C₅	—	2	2	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	2	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	2	no	—
154	C₂×C₃×C₄×C₅	—	2	2	no	—
155	C₂×C₃×C₄×C₅	—	4	8	no	—
156	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
157	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
160	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
163	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
164	C₂×C₃×C₄×C₅	#41	1	2	yes	—
165	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
166	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
167	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
168	C₃×C₄⋊Q₈	—	2	4	no	—
169	C₃×C₂²⋊Q₈	—	2	8	no	—
170	C₂×C₃×C₄⋊C₄	—	2	4	no	—
171	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
172	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
177	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
180	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
182	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
184	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
185	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
186	C₃×#95	C₂²×C₅	1	1	yes	characteristic
187	C₃×#95	C₂²×C₅	1	1	yes	characteristic
188	C₃×#95	C₂²×C₅	1	2	yes	—
189	C₃×#95	C₂²×C₅	1	2	yes	—
190	C₃×#95	C₂²×C₅	1	2	yes	—
191	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₂×C₅×Q₈	—	2	4	no	—
193	C₂×C₅×Q₈	—	2	4	no	—
194	C₂×C₅×Q₈	—	4	2	no	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	—	2	2	no	—
197	C₂²×C₄×C₅	—	2	4	no	—
198	C₂²×C₄×C₅	—	2	4	no	—
199	C₂²×C₄×C₅	—	4	2	no	—
200	C₂²×C₄×C₅	C₃×Q₈	1	4	yes	complemented
201	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
202	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
203	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
204	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
205	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
211	C₅×C₄⋊C₄	—	2	4	no	—
212	C₅×C₄⋊C₄	—	2	2	no	—
213	C₅×C₄⋊C₄	—	2	4	no	—
214	C₅×C₄⋊C₄	—	2	4	no	—
215	C₅×C₄⋊C₄	—	2	4	no	—
216	C₅×C₄⋊C₄	—	2	4	no	—
217	C₅×C₄⋊C₄	—	2	2	no	—
218	C₅×C₄⋊C₄	—	2	2	no	—
219	C₅×C₄⋊C₄	—	4	2	no	—
220	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
221	C₅×C₂²⋊C₄	—	2	4	no	—
222	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	—
223	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
224	C₄²×C₅	—	2	2	no	—
225	C₄²×C₅	—	2	2	no	—
226	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
227	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	2	yes	—
228	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
229	#398	C₂×C₃×C₅	1	2	yes	complemented
230	#395	C₂×C₃×C₅	1	2	yes	complemented
231	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
232	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	#385	C₂×C₃×C₅	1	2	yes	—
234	#384	C₂×C₃×C₅	1	1	yes	characteristic, complemented
235	#380	C₂×C₃×C₅	1	1	yes	characteristic
236	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
237	C₂²×C₃×C₅	—	2	2	no	—
238	C₂²×C₃×C₅	—	2	2	no	—
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	—	2	2	no	—
242	C₂²×C₃×C₅	—	2	2	no	—
243	C₂²×C₃×C₅	C₄⋊Q₈	1	4	yes	complemented
244	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
245	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
246	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
247	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
248	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
249	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
251	C₃×C₄×C₅	—	2	2	no	—
252	C₃×C₄×C₅	—	2	4	no	—
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	2	2	no	—
255	C₃×C₄×C₅	—	2	2	no	—
256	C₃×C₄×C₅	—	2	2	no	—
257	C₃×C₄×C₅	—	4	2	no	—
258	C₃×C₄×C₅	—	4	2	no	—
259	C₃×C₄×C₅	—	4	2	no	—
260	C₃×C₄×C₅	C₂²⋊Q₈	1	4	yes	complemented
261	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
262	C₂×C₃×Q₈	—	2	4	no	—
263	C₂×C₃×Q₈	—	2	4	no	—
264	C₂×C₃×Q₈	—	4	2	no	—
265	C₂²×C₃×C₄	—	2	2	no	—
266	C₂²×C₃×C₄	—	2	2	no	—
267	C₂²×C₃×C₄	—	2	4	no	—
268	C₂²×C₃×C₄	—	2	4	no	—
269	C₂²×C₃×C₄	—	4	2	no	—
270	C₂²×C₃×C₄	C₅×Q₈	1	4	yes	complemented
271	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
274	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
279	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
280	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
281	C₃×C₄⋊C₄	—	2	4	no	—
282	C₃×C₄⋊C₄	—	2	2	no	—
283	C₃×C₄⋊C₄	—	2	4	no	—
284	C₃×C₄⋊C₄	—	2	4	no	—
285	C₃×C₄⋊C₄	—	2	4	no	—
286	C₃×C₄⋊C₄	—	2	4	no	—
287	C₃×C₄⋊C₄	—	2	2	no	—
288	C₃×C₄⋊C₄	—	2	2	no	—
289	C₃×C₄⋊C₄	—	4	2	no	—
290	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
291	C₃×C₂²⋊C₄	—	2	4	no	—
292	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	—
293	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
294	C₃×C₄²	—	2	2	no	—
295	C₃×C₄²	—	2	2	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	—	2	1	no	—
298	C₂³×C₅	—	2	1	no	—
299	C₂³×C₅	—	2	1	no	—
300	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
301	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
302	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
303	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
304	C₅×Q₈	—	4	8	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	1	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	1	no	—
311	C₂×C₄×C₅	—	2	1	no	—
312	C₂×C₄×C₅	—	2	1	no	—
313	C₂×C₄×C₅	—	2	2	no	—
314	C₂×C₄×C₅	—	2	1	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	1	no	—
317	C₂×C₄×C₅	—	2	8	no	—
318	C₂×C₄×C₅	—	2	2	no	—
319	C₂×C₄×C₅	—	2	2	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	2	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	2	no	—
324	C₂×C₄×C₅	—	2	2	no	—
325	C₂×C₄×C₅	—	2	2	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	4	8	no	—
328	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
329	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
330	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
331	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
332	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
333	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
334	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
335	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
336	C₂×C₄×C₅	C₃×#41	1	2	yes	—
337	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
338	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
339	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
340	C₄⋊Q₈	—	2	4	no	—
341	C₂²⋊Q₈	—	2	8	no	—
342	C₂×C₄⋊C₄	—	2	4	no	—
343	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
344	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
345	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
346	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
347	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
348	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
349	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
350	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
351	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
352	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
353	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
354	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
355	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
356	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
357	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
358	#95	C₂²×C₃×C₅	1	1	yes	characteristic
359	#95	C₂²×C₃×C₅	1	1	yes	characteristic
360	#95	C₂²×C₃×C₅	1	2	yes	—
361	#95	C₂²×C₃×C₅	1	2	yes	—
362	#95	C₂²×C₃×C₅	1	2	yes	—
363	C₂×C₃×C₅	—	2	4	no	—
364	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
365	C₂×C₃×C₅	C₂×C₄⋊Q₈	1	1	yes	characteristic
366	C₂×C₃×C₅	#544	1	1	yes	characteristic
367	C₂×C₃×C₅	D₄²	1	1	yes	characteristic
368	C₂×C₃×C₅	#547	1	1	yes	characteristic
369	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
370	C₂×C₃×C₅	#554	1	1	yes	characteristic
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	—	2	1	no	—
373	C₂³×C₃	—	2	1	no	—
374	C₂³×C₃	—	2	1	no	—
375	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
376	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
377	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
378	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
379	C₃×Q₈	—	4	8	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	1	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	1	no	—
386	C₂×C₃×C₄	—	2	1	no	—
387	C₂×C₃×C₄	—	2	1	no	—
388	C₂×C₃×C₄	—	2	2	no	—
389	C₂×C₃×C₄	—	2	1	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	1	no	—
392	C₂×C₃×C₄	—	2	8	no	—
393	C₂×C₃×C₄	—	2	2	no	—
394	C₂×C₃×C₄	—	2	2	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	2	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	2	no	—
399	C₂×C₃×C₄	—	2	2	no	—
400	C₂×C₃×C₄	—	2	2	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	4	8	no	—
403	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
404	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
405	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
406	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
407	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
408	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
409	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
410	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
411	C₂×C₃×C₄	C₅×#41	1	2	yes	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	—	2	2	no	—
416	C₂²×C₅	—	2	2	no	—
417	C₂²×C₅	—	2	2	no	—
418	C₂²×C₅	C₃×C₄⋊Q₈	1	4	yes	complemented
419	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
420	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
421	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
422	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
423	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
424	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
425	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
426	C₄×C₅	—	2	2	no	—
427	C₄×C₅	—	2	4	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	2	2	no	—
430	C₄×C₅	—	2	2	no	—
431	C₄×C₅	—	2	2	no	—
432	C₄×C₅	—	4	2	no	—
433	C₄×C₅	—	4	2	no	—
434	C₄×C₅	—	4	2	no	—
435	C₄×C₅	C₃×C₂²⋊Q₈	1	4	yes	complemented
436	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
437	C₂×Q₈	—	2	4	no	—
438	C₂×Q₈	—	2	4	no	—
439	C₂×Q₈	—	4	2	no	—
440	C₂²×C₄	—	2	2	no	—
441	C₂²×C₄	—	2	2	no	—
442	C₂²×C₄	—	2	4	no	—
443	C₂²×C₄	—	2	4	no	—
444	C₂²×C₄	—	4	2	no	—
445	C₂²×C₄	C₃×C₅×Q₈	1	4	yes	complemented
446	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
447	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
448	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
449	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
450	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
451	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
452	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
453	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
454	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
455	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
456	C₄⋊C₄	—	2	4	no	—
457	C₄⋊C₄	—	2	2	no	—
458	C₄⋊C₄	—	2	4	no	—
459	C₄⋊C₄	—	2	4	no	—
460	C₄⋊C₄	—	2	4	no	—
461	C₄⋊C₄	—	2	4	no	—
462	C₄⋊C₄	—	2	2	no	—
463	C₄⋊C₄	—	2	2	no	—
464	C₄⋊C₄	—	4	2	no	—
465	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
466	C₂²⋊C₄	—	2	4	no	—
467	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	—
468	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
469	C₄²	—	2	2	no	—
470	C₄²	—	2	2	no	—
471	C₃×C₅	#2440	1	1	yes	characteristic, direct product factor, Hall
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	—	2	2	no	—
475	C₂²×C₃	—	2	2	no	—
476	C₂²×C₃	—	2	2	no	—
477	C₂²×C₃	—	2	2	no	—
478	C₂²×C₃	C₅×C₄⋊Q₈	1	4	yes	complemented
479	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
480	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
481	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
482	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
483	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
484	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
485	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
486	C₃×C₄	—	2	2	no	—
487	C₃×C₄	—	2	4	no	—
488	C₃×C₄	—	2	2	no	—
489	C₃×C₄	—	2	2	no	—
490	C₃×C₄	—	2	2	no	—
491	C₃×C₄	—	2	2	no	—
492	C₃×C₄	—	4	2	no	—
493	C₃×C₄	—	4	2	no	—
494	C₃×C₄	—	4	2	no	—
495	C₃×C₄	C₅×C₂²⋊Q₈	1	4	yes	complemented
496	C₂×C₅	—	2	4	no	—
497	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
498	C₂×C₅	C₂×C₃×C₄⋊Q₈	1	1	yes	characteristic
499	C₂×C₅	C₃×#544	1	1	yes	characteristic
500	C₂×C₅	C₃×D₄²	1	1	yes	characteristic
501	C₂×C₅	C₃×#547	1	1	yes	characteristic
502	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
503	C₂×C₅	C₃×#554	1	1	yes	characteristic
504	C₂³	—	2	1	no	—
505	C₂³	—	2	1	no	—
506	C₂³	—	2	1	no	—
507	C₂³	—	2	1	no	—
508	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
509	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
510	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
511	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
512	Q₈	—	4	8	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	1	no	—
515	C₂×C₄	—	2	1	no	—
516	C₂×C₄	—	2	2	no	—
517	C₂×C₄	—	2	1	no	—
518	C₂×C₄	—	2	1	no	—
519	C₂×C₄	—	2	1	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	2	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	1	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	8	no	—
526	C₂×C₄	—	2	2	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	2	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	2	no	—
531	C₂×C₄	—	2	2	no	—
532	C₂×C₄	—	2	2	no	—
533	C₂×C₄	—	2	2	no	—
534	C₂×C₄	—	2	2	no	—
535	C₂×C₄	—	4	8	no	—
536	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
537	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
538	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
539	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
540	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
541	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
542	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
543	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
544	C₂×C₄	C₃×C₅×#41	1	2	yes	—
545	C₂×C₃	—	2	4	no	—
546	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
547	C₂×C₃	C₂×C₅×C₄⋊Q₈	1	1	yes	characteristic
548	C₂×C₃	C₅×#544	1	1	yes	characteristic
549	C₂×C₃	C₅×D₄²	1	1	yes	characteristic
550	C₂×C₃	C₅×#547	1	1	yes	characteristic
551	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
552	C₂×C₃	C₅×#554	1	1	yes	characteristic
553	C₅	C₃×#2440	1	1	yes	characteristic, direct product factor, Sylow
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	—	2	2	no	—
557	C₂²	—	2	2	no	—
558	C₂²	—	2	2	no	—
559	C₂²	—	2	2	no	—
560	C₂²	C₃×C₅×C₄⋊Q₈	1	4	yes	complemented
561	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
562	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
563	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
564	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
565	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
566	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
567	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
568	C₄	—	2	2	no	—
569	C₄	—	2	4	no	—
570	C₄	—	2	2	no	—
571	C₄	—	2	2	no	—
572	C₄	—	2	2	no	—
573	C₄	—	2	2	no	—
574	C₄	—	4	2	no	—
575	C₄	—	4	2	no	—
576	C₄	—	4	2	no	—
577	C₄	C₃×C₅×C₂²⋊Q₈	1	4	yes	complemented
578	C₃	C₅×#2440	1	1	yes	characteristic, direct product factor, Sylow
579	C₂	—	2	4	no	—
580	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
581	C₂	C₂×C₃×C₅×C₄⋊Q₈	1	1	yes	characteristic
582	C₂	C₃×C₅×#544	1	1	yes	characteristic
583	C₂	C₃×C₅×D₄²	1	1	yes	characteristic
584	C₂	C₃×C₅×#547	1	1	yes	characteristic
585	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
586	C₂	C₃×C₅×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
LCS	G ▷ C₂³ ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂×C₃×C₅×C₄⋊Q₈	C₂	semidirect
4. C₃×C₅×#398	C₂	semidirect
5. C₃×C₅×#395	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#389	C₂	semidirect
9. C₃×C₅×#384	C₂	semidirect
12. C₅×#2440	C₃	direct (N × H)
39. C₃×#2440	C₅	direct (N × H)
40. C₂×C₅×C₄⋊Q₈	C₂×C₃	semidirect
43. C₅×#398	C₂×C₃	semidirect
44. C₅×#395	C₂×C₃	semidirect
45. C₅×#389	C₂×C₃	semidirect
46. C₅×#389	C₂×C₃	semidirect
48. C₅×#384	C₂×C₃	semidirect
60. C₂²×C₃×C₄×C₅	Q₈	semidirect
83. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
86. C₂×C₃×C₄⋊Q₈	C₂×C₅	semidirect
89. C₃×#398	C₂×C₅	semidirect
90. C₃×#395	C₂×C₅	semidirect
91. C₃×#389	C₂×C₅	semidirect
92. C₃×#389	C₂×C₅	semidirect
94. C₃×#384	C₂×C₅	semidirect
123. #2440	C₃×C₅	direct (N × H)
200. C₂²×C₄×C₅	C₃×Q₈	semidirect
223. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
226. C₂×C₄⋊Q₈	C₂×C₃×C₅	semidirect
229. #398	C₂×C₃×C₅	semidirect
230. #395	C₂×C₃×C₅	semidirect
231. #389	C₂×C₃×C₅	semidirect
232. #389	C₂×C₃×C₅	semidirect
234. #384	C₂×C₃×C₅	semidirect
243. C₂²×C₃×C₅	C₄⋊Q₈	semidirect
260. C₃×C₄×C₅	C₂²⋊Q₈	semidirect
270. C₂²×C₃×C₄	C₅×Q₈	semidirect
293. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
418. C₂²×C₅	C₃×C₄⋊Q₈	semidirect
435. C₄×C₅	C₃×C₂²⋊Q₈	semidirect
445. C₂²×C₄	C₃×C₅×Q₈	semidirect
468. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
471. C₃×C₅	#2440	direct (N × H)
478. C₂²×C₃	C₅×C₄⋊Q₈	semidirect
495. C₃×C₄	C₅×C₂²⋊Q₈	semidirect
553. C₅	C₃×#2440	direct (N × H)
560. C₂²	C₃×C₅×C₄⋊Q₈	semidirect
577. C₄	C₃×C₅×C₂²⋊Q₈	semidirect
578. C₃	C₅×#2440	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×C₄⋊Q₈	2
C₂×C₃×C₅×C₂²⋊Q₈	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#398	2
C₃×C₅×#395	2
C₃×C₅×#389	2
C₃×C₅×#385	2
C₃×C₅×#384	2
C₃×C₅×#380	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2440	3
C₃×#2440	5

Subgroups — C3×C5×#2440 #14275474

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2440 #14275474