Subgroups — C₃×C₅×#2451 #14275485

Order 1920.

968 conjugacy classes of subgroups.

The subgroup lattice has 516 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
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic
3	C₃×C₅×#398	C₂	1	2	yes	maximal
4	C₃×C₅×#395	C₂	1	2	yes	maximal
5	C₃×C₅×#391	C₂	1	2	yes	maximal
6	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
7	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic
8	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
9	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic
10	C₃×C₅×#387	C₂	1	2	yes	maximal
11	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2451	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
15	C₃×C₅×C₄⋊Q₈	—	2	4	no	—
16	C₃×C₄×C₅×Q₈	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
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	1	yes	characteristic
26	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
30	C₃×C₅×#95	C₂²	1	1	yes	characteristic
31	C₃×C₅×#95	C₂²	1	1	yes	characteristic
32	C₃×C₅×#95	C₂²	1	2	yes	—
33	C₃×C₅×#95	C₂²	1	2	yes	—
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	2	yes	—
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×#2451	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
39	C₂×C₅×C₄⋊Q₈	C₂×C₃	1	1	yes	characteristic
40	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic
41	C₅×#398	C₂×C₃	1	2	yes	—
42	C₅×#395	C₂×C₃	1	2	yes	—
43	C₅×#391	C₂×C₃	1	1	yes	characteristic
44	C₅×#391	C₂×C₃	1	1	yes	characteristic
45	C₅×#391	C₂×C₃	1	2	yes	—
46	C₅×#389	C₂×C₃	1	1	yes	characteristic
47	C₅×#389	C₂×C₃	1	1	yes	characteristic
48	C₅×#387	C₂×C₃	1	2	yes	—
49	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₂×C₃×C₅×Q₈	—	2	2	no	—
51	C₂×C₃×C₅×Q₈	—	2	4	no	—
52	C₂×C₃×C₅×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	4	no	—
54	C₂×C₃×C₅×Q₈	—	4	2	no	—
55	C₂×C₃×C₅×Q₈	Q₈	1	4	yes	complemented
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₃×C₅×C₄⋊C₄	—	2	4	no	—
68	C₃×C₅×C₄⋊C₄	—	2	4	no	—
69	C₃×C₅×C₄⋊C₄	—	2	2	no	—
70	C₃×C₅×C₄⋊C₄	—	2	2	no	—
71	C₃×C₅×C₄⋊C₄	—	2	2	no	—
72	C₃×C₅×C₄⋊C₄	—	4	2	no	—
73	C₃×C₅×C₄⋊C₄	—	4	2	no	—
74	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
75	C₃×C₅×C₄⋊C₄	Q₈	1	4	yes	complemented
76	C₃×C₄²×C₅	—	2	4	no	—
77	C₃×C₄²×C₅	—	2	2	no	—
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₃×C₄²×C₅	—	2	2	no	—
80	C₂×C₃×C₄⋊Q₈	C₂×C₅	1	1	yes	characteristic
81	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic
82	C₃×#398	C₂×C₅	1	2	yes	—
83	C₃×#395	C₂×C₅	1	2	yes	—
84	C₃×#391	C₂×C₅	1	2	yes	—
85	C₃×#391	C₂×C₅	1	1	yes	characteristic
86	C₃×#391	C₂×C₅	1	1	yes	characteristic
87	C₃×#389	C₂×C₅	1	1	yes	characteristic
88	C₃×#389	C₂×C₅	1	1	yes	characteristic
89	C₃×#387	C₂×C₅	1	2	yes	—
90	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
91	C₂²×C₅×Q₈	C₂²×C₃	1	2	yes	—
92	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
93	C₅×C₄⋊Q₈	—	2	4	no	—
94	C₄×C₅×Q₈	—	2	4	no	—
95	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
97	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
98	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
99	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
100	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
101	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
102	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
104	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
106	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
108	C₅×#95	C₂²×C₃	1	1	yes	characteristic
109	C₅×#95	C₂²×C₃	1	1	yes	characteristic
110	C₅×#95	C₂²×C₃	1	2	yes	—
111	C₅×#95	C₂²×C₃	1	2	yes	—
112	C₅×#95	C₂²×C₃	1	2	yes	—
113	C₅×#95	C₂²×C₃	1	2	yes	—
114	C₅×#95	C₂²×C₃	1	2	yes	—
115	C₅×#95	C₂²×C₃	1	2	yes	—
116	#2451	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
117	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
118	C₃×C₅×Q₈	—	2	8	no	—
119	C₃×C₅×Q₈	—	4	8	no	—
120	C₂×C₃×C₄×C₅	—	2	1	no	—
121	C₂×C₃×C₄×C₅	—	2	1	no	—
122	C₂×C₃×C₄×C₅	—	2	2	no	—
123	C₂×C₃×C₄×C₅	—	2	1	no	—
124	C₂×C₃×C₄×C₅	—	2	1	no	—
125	C₂×C₃×C₄×C₅	—	2	1	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	2	no	—
129	C₂×C₃×C₄×C₅	—	2	1	no	—
130	C₂×C₃×C₄×C₅	—	2	1	no	—
131	C₂×C₃×C₄×C₅	—	2	1	no	—
132	C₂×C₃×C₄×C₅	—	2	1	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	1	no	—
135	C₂×C₃×C₄×C₅	—	2	2	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	1	no	—
139	C₂×C₃×C₄×C₅	—	2	2	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	2	no	—
144	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
145	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
146	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
147	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
148	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
149	C₂×C₃×C₄×C₅	C₂×Q₈	1	4	yes	—
150	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
151	C₂×C₃×C₄×C₅	#41	1	2	yes	—
152	C₂×C₃×C₄×C₅	#41	1	2	yes	—
153	C₂²×C₃×Q₈	C₂²×C₅	1	2	yes	—
154	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
155	C₃×C₄⋊Q₈	—	2	4	no	—
156	C₃×C₄×Q₈	—	2	4	no	—
157	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
158	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
159	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
160	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
161	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
162	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
163	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
164	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
165	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
166	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
167	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
168	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
169	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
170	C₃×#95	C₂²×C₅	1	1	yes	characteristic
171	C₃×#95	C₂²×C₅	1	1	yes	characteristic
172	C₃×#95	C₂²×C₅	1	2	yes	—
173	C₃×#95	C₂²×C₅	1	2	yes	—
174	C₃×#95	C₂²×C₅	1	2	yes	—
175	C₃×#95	C₂²×C₅	1	2	yes	—
176	C₃×#95	C₂²×C₅	1	2	yes	—
177	C₃×#95	C₂²×C₅	1	2	yes	—
178	C₂×C₅×Q₈	—	2	2	no	—
179	C₂×C₅×Q₈	—	2	4	no	—
180	C₂×C₅×Q₈	—	2	2	no	—
181	C₂×C₅×Q₈	—	2	4	no	—
182	C₂×C₅×Q₈	—	4	2	no	—
183	C₂×C₅×Q₈	C₃×Q₈	1	4	yes	complemented
184	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
186	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
187	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
188	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
189	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
190	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
191	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
192	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
193	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
195	C₅×C₄⋊C₄	—	2	4	no	—
196	C₅×C₄⋊C₄	—	2	4	no	—
197	C₅×C₄⋊C₄	—	2	2	no	—
198	C₅×C₄⋊C₄	—	2	2	no	—
199	C₅×C₄⋊C₄	—	2	2	no	—
200	C₅×C₄⋊C₄	—	4	2	no	—
201	C₅×C₄⋊C₄	—	4	2	no	—
202	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
203	C₅×C₄⋊C₄	C₃×Q₈	1	4	yes	complemented
204	C₄²×C₅	—	2	4	no	—
205	C₄²×C₅	—	2	2	no	—
206	C₄²×C₅	—	2	2	no	—
207	C₄²×C₅	—	2	2	no	—
208	C₂×C₄⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
209	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic
210	#398	C₂×C₃×C₅	1	2	yes	—
211	#395	C₂×C₃×C₅	1	2	yes	—
212	#391	C₂×C₃×C₅	1	2	yes	—
213	#391	C₂×C₃×C₅	1	1	yes	characteristic
214	#391	C₂×C₃×C₅	1	1	yes	characteristic
215	#389	C₂×C₃×C₅	1	1	yes	characteristic
216	#389	C₂×C₃×C₅	1	1	yes	characteristic
217	#387	C₂×C₃×C₅	1	2	yes	—
218	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
221	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
222	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
223	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
224	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
225	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
226	C₃×C₄×C₅	—	2	4	no	—
227	C₃×C₄×C₅	—	2	2	no	—
228	C₃×C₄×C₅	—	2	4	no	—
229	C₃×C₄×C₅	—	2	2	no	—
230	C₃×C₄×C₅	—	2	2	no	—
231	C₃×C₄×C₅	—	2	2	no	—
232	C₃×C₄×C₅	—	4	1	no	—
233	C₃×C₄×C₅	—	4	2	no	—
234	C₃×C₄×C₅	—	4	1	no	—
235	C₃×C₄×C₅	—	4	2	no	—
236	C₃×C₄×C₅	C₂²⋊Q₈	1	4	yes	—
237	C₂×C₃×Q₈	—	2	2	no	—
238	C₂×C₃×Q₈	—	2	4	no	—
239	C₂×C₃×Q₈	—	2	2	no	—
240	C₂×C₃×Q₈	—	2	4	no	—
241	C₂×C₃×Q₈	—	4	2	no	—
242	C₂×C₃×Q₈	C₅×Q₈	1	4	yes	complemented
243	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
246	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
247	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
248	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
249	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
250	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
253	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
254	C₃×C₄⋊C₄	—	2	4	no	—
255	C₃×C₄⋊C₄	—	2	4	no	—
256	C₃×C₄⋊C₄	—	2	2	no	—
257	C₃×C₄⋊C₄	—	2	2	no	—
258	C₃×C₄⋊C₄	—	2	2	no	—
259	C₃×C₄⋊C₄	—	4	2	no	—
260	C₃×C₄⋊C₄	—	4	2	no	—
261	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
262	C₃×C₄⋊C₄	C₅×Q₈	1	4	yes	complemented
263	C₃×C₄²	—	2	4	no	—
264	C₃×C₄²	—	2	2	no	—
265	C₃×C₄²	—	2	2	no	—
266	C₃×C₄²	—	2	2	no	—
267	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
268	C₅×Q₈	—	2	8	no	—
269	C₅×Q₈	—	4	8	no	—
270	C₂×C₄×C₅	—	2	1	no	—
271	C₂×C₄×C₅	—	2	1	no	—
272	C₂×C₄×C₅	—	2	2	no	—
273	C₂×C₄×C₅	—	2	1	no	—
274	C₂×C₄×C₅	—	2	1	no	—
275	C₂×C₄×C₅	—	2	1	no	—
276	C₂×C₄×C₅	—	2	2	no	—
277	C₂×C₄×C₅	—	2	2	no	—
278	C₂×C₄×C₅	—	2	2	no	—
279	C₂×C₄×C₅	—	2	1	no	—
280	C₂×C₄×C₅	—	2	1	no	—
281	C₂×C₄×C₅	—	2	1	no	—
282	C₂×C₄×C₅	—	2	1	no	—
283	C₂×C₄×C₅	—	2	2	no	—
284	C₂×C₄×C₅	—	2	1	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	1	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	1	no	—
289	C₂×C₄×C₅	—	2	2	no	—
290	C₂×C₄×C₅	—	2	1	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	1	no	—
293	C₂×C₄×C₅	—	2	2	no	—
294	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
295	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
296	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
297	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
298	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
299	C₂×C₄×C₅	C₂×C₃×Q₈	1	4	yes	—
300	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
301	C₂×C₄×C₅	C₃×#41	1	2	yes	—
302	C₂×C₄×C₅	C₃×#41	1	2	yes	—
303	C₂²×Q₈	C₂²×C₃×C₅	1	2	yes	—
304	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
305	C₄⋊Q₈	—	2	4	no	—
306	C₄×Q₈	—	2	4	no	—
307	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
308	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
309	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
310	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
311	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
313	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
314	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
315	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
316	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
317	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
318	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
319	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
320	#95	C₂²×C₃×C₅	1	1	yes	characteristic
321	#95	C₂²×C₃×C₅	1	1	yes	characteristic
322	#95	C₂²×C₃×C₅	1	2	yes	—
323	#95	C₂²×C₃×C₅	1	2	yes	—
324	#95	C₂²×C₃×C₅	1	2	yes	—
325	#95	C₂²×C₃×C₅	1	2	yes	—
326	#95	C₂²×C₃×C₅	1	2	yes	—
327	#95	C₂²×C₃×C₅	1	2	yes	—
328	C₂×C₃×C₅	C₂×C₂²⋊Q₈	1	1	yes	characteristic
329	C₂×C₃×C₅	#533	1	1	yes	characteristic
330	C₂×C₃×C₅	#542	1	1	yes	characteristic
331	C₂×C₃×C₅	#546	1	1	yes	characteristic
332	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
333	C₂×C₃×C₅	#557	1	1	yes	characteristic
334	C₂×C₃×C₅	Q₈²	1	1	yes	characteristic
335	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
336	C₃×Q₈	—	2	8	no	—
337	C₃×Q₈	—	4	8	no	—
338	C₂×C₃×C₄	—	2	1	no	—
339	C₂×C₃×C₄	—	2	1	no	—
340	C₂×C₃×C₄	—	2	2	no	—
341	C₂×C₃×C₄	—	2	1	no	—
342	C₂×C₃×C₄	—	2	1	no	—
343	C₂×C₃×C₄	—	2	1	no	—
344	C₂×C₃×C₄	—	2	2	no	—
345	C₂×C₃×C₄	—	2	2	no	—
346	C₂×C₃×C₄	—	2	2	no	—
347	C₂×C₃×C₄	—	2	1	no	—
348	C₂×C₃×C₄	—	2	1	no	—
349	C₂×C₃×C₄	—	2	1	no	—
350	C₂×C₃×C₄	—	2	1	no	—
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	1	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	1	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	1	no	—
357	C₂×C₃×C₄	—	2	2	no	—
358	C₂×C₃×C₄	—	2	1	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	1	no	—
361	C₂×C₃×C₄	—	2	2	no	—
362	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
363	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
365	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
366	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
367	C₂×C₃×C₄	C₂×C₅×Q₈	1	4	yes	—
368	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
369	C₂×C₃×C₄	C₅×#41	1	2	yes	—
370	C₂×C₃×C₄	C₅×#41	1	2	yes	—
371	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
372	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
373	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
374	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
375	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
376	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
377	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
378	C₄×C₅	—	2	4	no	—
379	C₄×C₅	—	2	2	no	—
380	C₄×C₅	—	2	4	no	—
381	C₄×C₅	—	2	2	no	—
382	C₄×C₅	—	2	2	no	—
383	C₄×C₅	—	2	2	no	—
384	C₄×C₅	—	4	1	no	—
385	C₄×C₅	—	4	2	no	—
386	C₄×C₅	—	4	1	no	—
387	C₄×C₅	—	4	2	no	—
388	C₄×C₅	C₃×C₂²⋊Q₈	1	4	yes	—
389	C₂×Q₈	—	2	2	no	—
390	C₂×Q₈	—	2	4	no	—
391	C₂×Q₈	—	2	2	no	—
392	C₂×Q₈	—	2	4	no	—
393	C₂×Q₈	—	4	2	no	—
394	C₂×Q₈	C₃×C₅×Q₈	1	4	yes	complemented
395	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
396	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
397	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
398	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
399	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
400	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
401	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
402	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
403	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
404	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
405	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
406	C₄⋊C₄	—	2	4	no	—
407	C₄⋊C₄	—	2	4	no	—
408	C₄⋊C₄	—	2	2	no	—
409	C₄⋊C₄	—	2	2	no	—
410	C₄⋊C₄	—	2	2	no	—
411	C₄⋊C₄	—	4	2	no	—
412	C₄⋊C₄	—	4	2	no	—
413	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
414	C₄⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
415	C₄²	—	2	4	no	—
416	C₄²	—	2	2	no	—
417	C₄²	—	2	2	no	—
418	C₄²	—	2	2	no	—
419	C₃×C₅	#2451	1	1	yes	characteristic, direct product factor, Hall
420	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
421	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
422	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
423	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
424	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
425	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
426	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
427	C₃×C₄	—	2	4	no	—
428	C₃×C₄	—	2	2	no	—
429	C₃×C₄	—	2	4	no	—
430	C₃×C₄	—	2	2	no	—
431	C₃×C₄	—	2	2	no	—
432	C₃×C₄	—	2	2	no	—
433	C₃×C₄	—	4	1	no	—
434	C₃×C₄	—	4	2	no	—
435	C₃×C₄	—	4	1	no	—
436	C₃×C₄	—	4	2	no	—
437	C₃×C₄	C₅×C₂²⋊Q₈	1	4	yes	—
438	C₂×C₅	C₂×C₃×C₂²⋊Q₈	1	1	yes	characteristic
439	C₂×C₅	C₃×#533	1	1	yes	characteristic
440	C₂×C₅	C₃×#542	1	1	yes	characteristic
441	C₂×C₅	C₃×#546	1	1	yes	characteristic
442	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
443	C₂×C₅	C₃×#557	1	1	yes	characteristic
444	C₂×C₅	C₃×Q₈²	1	1	yes	characteristic
445	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
446	Q₈	—	2	8	no	—
447	Q₈	—	4	8	no	—
448	C₂×C₄	—	2	1	no	—
449	C₂×C₄	—	2	1	no	—
450	C₂×C₄	—	2	2	no	—
451	C₂×C₄	—	2	1	no	—
452	C₂×C₄	—	2	1	no	—
453	C₂×C₄	—	2	1	no	—
454	C₂×C₄	—	2	2	no	—
455	C₂×C₄	—	2	2	no	—
456	C₂×C₄	—	2	2	no	—
457	C₂×C₄	—	2	1	no	—
458	C₂×C₄	—	2	1	no	—
459	C₂×C₄	—	2	1	no	—
460	C₂×C₄	—	2	1	no	—
461	C₂×C₄	—	2	2	no	—
462	C₂×C₄	—	2	1	no	—
463	C₂×C₄	—	2	2	no	—
464	C₂×C₄	—	2	1	no	—
465	C₂×C₄	—	2	2	no	—
466	C₂×C₄	—	2	1	no	—
467	C₂×C₄	—	2	2	no	—
468	C₂×C₄	—	2	1	no	—
469	C₂×C₄	—	2	2	no	—
470	C₂×C₄	—	2	1	no	—
471	C₂×C₄	—	2	2	no	—
472	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
473	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
474	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
475	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
476	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
477	C₂×C₄	C₂×C₃×C₅×Q₈	1	4	yes	—
478	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
479	C₂×C₄	C₃×C₅×#41	1	2	yes	—
480	C₂×C₄	C₃×C₅×#41	1	2	yes	—
481	C₂×C₃	C₂×C₅×C₂²⋊Q₈	1	1	yes	characteristic
482	C₂×C₃	C₅×#533	1	1	yes	characteristic
483	C₂×C₃	C₅×#542	1	1	yes	characteristic
484	C₂×C₃	C₅×#546	1	1	yes	characteristic
485	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
486	C₂×C₃	C₅×#557	1	1	yes	characteristic
487	C₂×C₃	C₅×Q₈²	1	1	yes	characteristic
488	C₅	C₃×#2451	1	1	yes	characteristic, direct product factor, Sylow
489	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
490	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
491	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
492	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
493	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
494	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
495	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
496	C₄	—	2	4	no	—
497	C₄	—	2	2	no	—
498	C₄	—	2	4	no	—
499	C₄	—	2	2	no	—
500	C₄	—	2	2	no	—
501	C₄	—	2	2	no	—
502	C₄	—	4	1	no	—
503	C₄	—	4	2	no	—
504	C₄	—	4	2	no	—
505	C₄	—	4	1	no	—
506	C₄	C₃×C₅×C₂²⋊Q₈	1	4	yes	—
507	C₃	C₅×#2451	1	1	yes	characteristic, direct product factor, Sylow
508	C₂	C₂×C₃×C₅×C₂²⋊Q₈	1	1	yes	characteristic
509	C₂	C₃×C₅×#533	1	1	yes	characteristic
510	C₂	C₃×C₅×#542	1	1	yes	characteristic
511	C₂	C₃×C₅×#546	1	1	yes	characteristic
512	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
513	C₂	C₃×C₅×#557	1	1	yes	characteristic
514	C₂	C₃×C₅×Q₈²	1	1	yes	characteristic

	subgroup	G/H
center, socle, prime radical	C₂³×C₃×C₅	C₂⁴
commutator, Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
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
12. C₅×#2451	C₃	direct (N × H)
38. C₃×#2451	C₅	direct (N × H)
55. C₂×C₃×C₅×Q₈	Q₈	semidirect
75. C₃×C₅×C₄⋊C₄	Q₈	semidirect
116. #2451	C₃×C₅	direct (N × H)
183. C₂×C₅×Q₈	C₃×Q₈	semidirect
203. C₅×C₄⋊C₄	C₃×Q₈	semidirect
242. C₂×C₃×Q₈	C₅×Q₈	semidirect
262. C₃×C₄⋊C₄	C₅×Q₈	semidirect
394. C₂×Q₈	C₃×C₅×Q₈	semidirect
414. C₄⋊C₄	C₃×C₅×Q₈	semidirect
419. C₃×C₅	#2451	direct (N × H)
488. C₅	C₃×#2451	direct (N × H)
507. C₃	C₅×#2451	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×C₄×C₅×Q₈	2
C₃×C₅×#398	2
C₃×C₅×#395	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₄×C₅×C₄⋊C₄	2
C₅×#2451	3
C₃×#2451	5

Subgroups — C3×C5×#2451 #14275485

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2451 #14275485