Subgroups — C₃×C₅×D₄×C₂²⋊C₄ #14275372

Order 1920.

2504 conjugacy classes of subgroups.

The subgroup lattice has 544 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₃×C₅×D₄	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×D₄	C₂	1	2	yes	maximal, complemented
3	C₂²×C₃×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
4	C₃×C₅×#390	C₂	1	2	yes	maximal, complemented
5	C₃×C₅×#386	C₂	1	4	yes	maximal, complemented
6	C₃×C₅×#380	C₂	1	1	yes	maximal, characteristic, complemented
7	C₃×C₅×#379	C₂	1	2	yes	maximal, complemented
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₅×D₄×C₂²⋊C₄	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
10	C₂⁵×C₃×C₅	C₂²	1	2	yes	—
11	C₂²×C₃×C₅×D₄	—	2	8	no	—
12	C₂²×C₃×C₅×D₄	C₄	1	8	yes	complemented
13	C₂²×C₃×C₅×D₄	C₂²	1	2	yes	—
14	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
15	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
16	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
17	C₂³×C₃×C₄×C₅	C₂²	1	4	yes	complemented
18	C₃×C₄×C₅×D₄	—	2	8	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	complemented
20	C₂×C₃×C₅×C₂²⋊C₄	—	2	8	no	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
23	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
25	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	complemented
27	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
28	C₃×C₅×#95	C₂²	1	2	yes	complemented
29	C₃×C₅×#95	C₂²	1	2	yes	complemented
30	C₃×D₄×C₂²⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
31	C₂³×C₅×D₄	C₂×C₃	1	1	yes	characteristic
32	C₂×C₄×C₅×D₄	C₂×C₃	1	2	yes	complemented
33	C₂²×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	complemented
34	C₅×#390	C₂×C₃	1	2	yes	complemented
35	C₅×#386	C₂×C₃	1	4	yes	complemented
36	C₅×#380	C₂×C₃	1	1	yes	characteristic, complemented
37	C₅×#379	C₂×C₃	1	2	yes	complemented
38	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
39	C₂⁴×C₃×C₅	—	2	4	no	—
40	C₂⁴×C₃×C₅	—	2	8	no	—
41	C₂⁴×C₃×C₅	—	2	4	no	—
42	C₂⁴×C₃×C₅	—	4	4	no	—
43	C₂⁴×C₃×C₅	C₂×C₄	1	8	yes	complemented
44	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
45	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
46	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
47	C₂×C₃×C₅×D₄	—	2	8	no	—
48	C₂×C₃×C₅×D₄	—	2	32	no	—
49	C₂×C₃×C₅×D₄	—	2	4	no	—
50	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
51	C₂×C₃×C₅×D₄	C₂×C₄	1	8	yes	complemented
52	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	complemented
53	C₂×C₃×C₅×D₄	D₄	1	8	yes	—
54	C₂²×C₃×C₄×C₅	—	2	4	no	—
55	C₂²×C₃×C₄×C₅	—	2	8	no	—
56	C₂²×C₃×C₄×C₅	—	2	8	no	—
57	C₂²×C₃×C₄×C₅	—	4	4	no	—
58	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
59	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
60	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
61	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
62	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
63	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
64	C₃×C₅×C₄⋊C₄	—	2	4	no	—
65	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
66	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
67	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
68	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
69	C₃×C₅×C₂²⋊C₄	—	4	4	no	—
70	C₃×C₅×C₂²⋊C₄	D₄	1	4	yes	direct product factor
71	C₃×C₄²×C₅	—	2	4	no	—
72	C₂³×C₃×D₄	C₂×C₅	1	1	yes	characteristic
73	C₂×C₃×C₄×D₄	C₂×C₅	1	2	yes	complemented
74	C₂²×C₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
75	C₃×#390	C₂×C₅	1	2	yes	complemented
76	C₃×#386	C₂×C₅	1	4	yes	complemented
77	C₃×#380	C₂×C₅	1	1	yes	characteristic, complemented
78	C₃×#379	C₂×C₅	1	2	yes	complemented
79	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
80	C₂⁵×C₅	C₂²×C₃	1	2	yes	—
81	C₂²×C₅×D₄	—	2	8	no	—
82	C₂²×C₅×D₄	C₃×C₄	1	8	yes	complemented
83	C₂²×C₅×D₄	C₂²×C₃	1	2	yes	—
84	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
85	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
86	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
87	C₂³×C₄×C₅	C₂²×C₃	1	4	yes	complemented
88	C₄×C₅×D₄	—	2	8	no	—
89	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	complemented
90	C₂×C₅×C₂²⋊C₄	—	2	8	no	—
91	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
92	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
93	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
95	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
96	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	complemented
97	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	complemented
98	C₅×#95	C₂²×C₃	1	2	yes	complemented
99	C₅×#95	C₂²×C₃	1	2	yes	complemented
100	D₄×C₂²⋊C₄	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
101	C₂³×C₃×C₅	—	2	2	no	—
102	C₂³×C₃×C₅	—	2	2	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	—	2	4	no	—
105	C₂³×C₃×C₅	—	2	2	no	—
106	C₂³×C₃×C₅	—	2	16	no	—
107	C₂³×C₃×C₅	—	2	16	no	—
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	—	2	4	no	—
110	C₂³×C₃×C₅	—	2	2	no	—
111	C₂³×C₃×C₅	—	2	4	no	—
112	C₂³×C₃×C₅	—	4	8	no	—
113	C₂³×C₃×C₅	—	4	16	no	—
114	C₂³×C₃×C₅	—	4	16	no	—
115	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
116	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
117	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
118	C₂³×C₃×C₅	C₂×D₄	1	8	yes	—
119	C₂³×C₃×C₅	C₂×D₄	1	2	yes	—
120	C₂³×C₃×C₅	#41	1	2	yes	—
121	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
122	C₃×C₅×D₄	—	2	16	no	—
123	C₃×C₅×D₄	—	2	8	no	—
124	C₃×C₅×D₄	C₂²⋊C₄	1	16	yes	direct product factor
125	C₂×C₃×C₄×C₅	—	2	2	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	2	no	—
128	C₂×C₃×C₄×C₅	—	2	8	no	—
129	C₂×C₃×C₄×C₅	—	2	2	no	—
130	C₂×C₃×C₄×C₅	—	2	4	no	—
131	C₂×C₃×C₄×C₅	—	2	4	no	—
132	C₂×C₃×C₄×C₅	—	2	2	no	—
133	C₂×C₃×C₄×C₅	—	2	2	no	—
134	C₂×C₃×C₄×C₅	—	2	4	no	—
135	C₂×C₃×C₄×C₅	—	4	16	no	—
136	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
137	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
138	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
139	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	complemented
140	C₂⁵×C₃	C₂²×C₅	1	2	yes	—
141	C₂²×C₃×D₄	—	2	8	no	—
142	C₂²×C₃×D₄	C₄×C₅	1	8	yes	complemented
143	C₂²×C₃×D₄	C₂²×C₅	1	2	yes	—
144	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
145	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
146	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
147	C₂³×C₃×C₄	C₂²×C₅	1	4	yes	complemented
148	C₃×C₄×D₄	—	2	8	no	—
149	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	complemented
150	C₂×C₃×C₂²⋊C₄	—	2	8	no	—
151	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
152	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
153	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
154	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
155	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
156	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	complemented
157	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
158	C₃×#95	C₂²×C₅	1	2	yes	complemented
159	C₃×#95	C₂²×C₅	1	2	yes	complemented
160	C₂⁴×C₅	—	2	4	no	—
161	C₂⁴×C₅	—	2	8	no	—
162	C₂⁴×C₅	—	2	4	no	—
163	C₂⁴×C₅	—	4	4	no	—
164	C₂⁴×C₅	C₂×C₃×C₄	1	8	yes	complemented
165	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
166	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
167	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
168	C₂×C₅×D₄	—	2	8	no	—
169	C₂×C₅×D₄	—	2	32	no	—
170	C₂×C₅×D₄	—	2	4	no	—
171	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
172	C₂×C₅×D₄	C₂×C₃×C₄	1	8	yes	complemented
173	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	complemented
174	C₂×C₅×D₄	C₃×D₄	1	8	yes	—
175	C₂²×C₄×C₅	—	2	4	no	—
176	C₂²×C₄×C₅	—	2	8	no	—
177	C₂²×C₄×C₅	—	2	8	no	—
178	C₂²×C₄×C₅	—	4	4	no	—
179	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	complemented
180	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
181	C₂²×C₄×C₅	C₂³×C₃	1	4	yes	—
182	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
183	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
184	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
185	C₅×C₄⋊C₄	—	2	4	no	—
186	C₅×C₂²⋊C₄	—	2	4	no	—
187	C₅×C₂²⋊C₄	—	2	8	no	—
188	C₅×C₂²⋊C₄	—	2	2	no	—
189	C₅×C₂²⋊C₄	—	2	8	no	—
190	C₅×C₂²⋊C₄	—	4	4	no	—
191	C₅×C₂²⋊C₄	C₃×D₄	1	4	yes	direct product factor
192	C₄²×C₅	—	2	4	no	—
193	C₂³×D₄	C₂×C₃×C₅	1	1	yes	characteristic
194	C₂×C₄×D₄	C₂×C₃×C₅	1	2	yes	complemented
195	C₂²×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	complemented
196	#390	C₂×C₃×C₅	1	2	yes	complemented
197	#386	C₂×C₃×C₅	1	4	yes	complemented
198	#380	C₂×C₃×C₅	1	1	yes	characteristic, complemented
199	#379	C₂×C₃×C₅	1	2	yes	complemented
200	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
201	C₂²×C₃×C₅	—	2	2	no	—
202	C₂²×C₃×C₅	—	2	4	no	—
203	C₂²×C₃×C₅	—	2	2	no	—
204	C₂²×C₃×C₅	—	2	4	no	—
205	C₂²×C₃×C₅	—	2	8	no	—
206	C₂²×C₃×C₅	—	2	4	no	—
207	C₂²×C₃×C₅	—	2	4	no	—
208	C₂²×C₃×C₅	—	2	8	no	—
209	C₂²×C₃×C₅	—	2	4	no	—
210	C₂²×C₃×C₅	—	2	4	no	—
211	C₂²×C₃×C₅	—	2	4	no	—
212	C₂²×C₃×C₅	—	4	32	no	—
213	C₂²×C₃×C₅	—	4	4	no	—
214	C₂²×C₃×C₅	—	4	4	no	—
215	C₂²×C₃×C₅	C₂×C₂²⋊C₄	1	8	yes	complemented
216	C₂²×C₃×C₅	C₄×D₄	1	4	yes	complemented
217	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
218	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
219	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
220	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
221	C₂²×C₃×C₅	H(5,𝔽₂)	1	2	yes	—
222	C₃×C₄×C₅	—	2	2	no	—
223	C₃×C₄×C₅	—	2	4	no	—
224	C₃×C₄×C₅	—	4	4	no	—
225	C₃×C₄×C₅	—	4	2	no	—
226	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	complemented
227	C₂⁴×C₃	—	2	4	no	—
228	C₂⁴×C₃	—	2	8	no	—
229	C₂⁴×C₃	—	2	4	no	—
230	C₂⁴×C₃	—	4	4	no	—
231	C₂⁴×C₃	C₂×C₄×C₅	1	8	yes	complemented
232	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
233	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
234	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
235	C₂×C₃×D₄	—	2	8	no	—
236	C₂×C₃×D₄	—	2	32	no	—
237	C₂×C₃×D₄	—	2	4	no	—
238	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
239	C₂×C₃×D₄	C₂×C₄×C₅	1	8	yes	complemented
240	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	complemented
241	C₂×C₃×D₄	C₅×D₄	1	8	yes	—
242	C₂²×C₃×C₄	—	2	4	no	—
243	C₂²×C₃×C₄	—	2	8	no	—
244	C₂²×C₃×C₄	—	2	8	no	—
245	C₂²×C₃×C₄	—	4	4	no	—
246	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
247	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
248	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
249	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
250	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
251	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
252	C₃×C₄⋊C₄	—	2	4	no	—
253	C₃×C₂²⋊C₄	—	2	4	no	—
254	C₃×C₂²⋊C₄	—	2	8	no	—
255	C₃×C₂²⋊C₄	—	2	2	no	—
256	C₃×C₂²⋊C₄	—	2	8	no	—
257	C₃×C₂²⋊C₄	—	4	4	no	—
258	C₃×C₂²⋊C₄	C₅×D₄	1	4	yes	direct product factor
259	C₃×C₄²	—	2	4	no	—
260	C₂³×C₅	—	2	2	no	—
261	C₂³×C₅	—	2	2	no	—
262	C₂³×C₅	—	2	2	no	—
263	C₂³×C₅	—	2	4	no	—
264	C₂³×C₅	—	2	2	no	—
265	C₂³×C₅	—	2	16	no	—
266	C₂³×C₅	—	2	16	no	—
267	C₂³×C₅	—	2	2	no	—
268	C₂³×C₅	—	2	4	no	—
269	C₂³×C₅	—	2	2	no	—
270	C₂³×C₅	—	2	4	no	—
271	C₂³×C₅	—	4	8	no	—
272	C₂³×C₅	—	4	16	no	—
273	C₂³×C₅	—	4	16	no	—
274	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
275	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
276	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
277	C₂³×C₅	C₂×C₃×D₄	1	8	yes	—
278	C₂³×C₅	C₂×C₃×D₄	1	2	yes	—
279	C₂³×C₅	C₃×#41	1	2	yes	—
280	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
281	C₅×D₄	—	2	16	no	—
282	C₅×D₄	—	2	8	no	—
283	C₅×D₄	C₃×C₂²⋊C₄	1	16	yes	direct product factor
284	C₂×C₄×C₅	—	2	2	no	—
285	C₂×C₄×C₅	—	2	2	no	—
286	C₂×C₄×C₅	—	2	2	no	—
287	C₂×C₄×C₅	—	2	8	no	—
288	C₂×C₄×C₅	—	2	2	no	—
289	C₂×C₄×C₅	—	2	4	no	—
290	C₂×C₄×C₅	—	2	4	no	—
291	C₂×C₄×C₅	—	2	2	no	—
292	C₂×C₄×C₅	—	2	2	no	—
293	C₂×C₄×C₅	—	2	4	no	—
294	C₂×C₄×C₅	—	4	16	no	—
295	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
296	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
297	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
298	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	complemented
299	C₂⁵	C₂²×C₃×C₅	1	2	yes	—
300	C₂²×D₄	—	2	8	no	—
301	C₂²×D₄	C₃×C₄×C₅	1	8	yes	complemented
302	C₂²×D₄	C₂²×C₃×C₅	1	2	yes	—
303	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
304	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
305	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
306	C₂³×C₄	C₂²×C₃×C₅	1	4	yes	complemented
307	C₄×D₄	—	2	8	no	—
308	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	complemented
309	C₂×C₂²⋊C₄	—	2	8	no	—
310	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
311	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
314	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
315	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	complemented
316	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	complemented
317	#95	C₂²×C₃×C₅	1	2	yes	complemented
318	#95	C₂²×C₃×C₅	1	2	yes	complemented
319	C₂×C₃×C₅	—	2	4	no	—
320	C₂×C₃×C₅	—	2	8	no	—
321	C₂×C₃×C₅	—	4	4	no	—
322	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
323	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
324	C₂×C₃×C₅	#518	1	1	yes	characteristic
325	C₂×C₃×C₅	D₄²	1	2	yes	—
326	C₂×C₃×C₅	#546	1	2	yes	—
327	C₂³×C₃	—	2	2	no	—
328	C₂³×C₃	—	2	2	no	—
329	C₂³×C₃	—	2	2	no	—
330	C₂³×C₃	—	2	4	no	—
331	C₂³×C₃	—	2	2	no	—
332	C₂³×C₃	—	2	16	no	—
333	C₂³×C₃	—	2	16	no	—
334	C₂³×C₃	—	2	2	no	—
335	C₂³×C₃	—	2	4	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	—	2	4	no	—
338	C₂³×C₃	—	4	8	no	—
339	C₂³×C₃	—	4	16	no	—
340	C₂³×C₃	—	4	16	no	—
341	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
342	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
343	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
344	C₂³×C₃	C₂×C₅×D₄	1	8	yes	—
345	C₂³×C₃	C₂×C₅×D₄	1	2	yes	—
346	C₂³×C₃	C₅×#41	1	2	yes	—
347	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
348	C₃×D₄	—	2	16	no	—
349	C₃×D₄	—	2	8	no	—
350	C₃×D₄	C₅×C₂²⋊C₄	1	16	yes	direct product factor
351	C₂×C₃×C₄	—	2	2	no	—
352	C₂×C₃×C₄	—	2	2	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	8	no	—
355	C₂×C₃×C₄	—	2	2	no	—
356	C₂×C₃×C₄	—	2	4	no	—
357	C₂×C₃×C₄	—	2	4	no	—
358	C₂×C₃×C₄	—	2	2	no	—
359	C₂×C₃×C₄	—	2	2	no	—
360	C₂×C₃×C₄	—	2	4	no	—
361	C₂×C₃×C₄	—	4	16	no	—
362	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
363	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
364	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
365	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	complemented
366	C₂²×C₅	—	2	2	no	—
367	C₂²×C₅	—	2	4	no	—
368	C₂²×C₅	—	2	2	no	—
369	C₂²×C₅	—	2	4	no	—
370	C₂²×C₅	—	2	8	no	—
371	C₂²×C₅	—	2	4	no	—
372	C₂²×C₅	—	2	4	no	—
373	C₂²×C₅	—	2	8	no	—
374	C₂²×C₅	—	2	4	no	—
375	C₂²×C₅	—	2	4	no	—
376	C₂²×C₅	—	2	4	no	—
377	C₂²×C₅	—	4	32	no	—
378	C₂²×C₅	—	4	4	no	—
379	C₂²×C₅	—	4	4	no	—
380	C₂²×C₅	C₂×C₃×C₂²⋊C₄	1	8	yes	complemented
381	C₂²×C₅	C₃×C₄×D₄	1	4	yes	complemented
382	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
383	C₂²×C₅	C₂²×C₃×D₄	1	2	yes	—
384	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
385	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
386	C₂²×C₅	C₃×H(5,𝔽₂)	1	2	yes	—
387	C₄×C₅	—	2	2	no	—
388	C₄×C₅	—	2	4	no	—
389	C₄×C₅	—	4	4	no	—
390	C₄×C₅	—	4	2	no	—
391	C₄×C₅	C₂×C₃×C₂²⋊C₄	1	4	yes	complemented
392	C₂⁴	—	2	4	no	—
393	C₂⁴	—	2	8	no	—
394	C₂⁴	—	2	4	no	—
395	C₂⁴	—	4	4	no	—
396	C₂⁴	C₂×C₃×C₄×C₅	1	8	yes	complemented
397	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
398	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
399	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
400	C₂×D₄	—	2	8	no	—
401	C₂×D₄	—	2	32	no	—
402	C₂×D₄	—	2	4	no	—
403	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
404	C₂×D₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
405	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
406	C₂×D₄	C₃×C₅×D₄	1	8	yes	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	2	8	no	—
410	C₂²×C₄	—	4	4	no	—
411	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
412	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
413	C₂²×C₄	C₂³×C₃×C₅	1	4	yes	—
414	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
415	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
416	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
417	C₄⋊C₄	—	2	4	no	—
418	C₂²⋊C₄	—	2	4	no	—
419	C₂²⋊C₄	—	2	8	no	—
420	C₂²⋊C₄	—	2	2	no	—
421	C₂²⋊C₄	—	2	8	no	—
422	C₂²⋊C₄	—	4	4	no	—
423	C₂²⋊C₄	C₃×C₅×D₄	1	4	yes	direct product factor
424	C₄²	—	2	4	no	—
425	C₃×C₅	D₄×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Hall
426	C₂²×C₃	—	2	2	no	—
427	C₂²×C₃	—	2	4	no	—
428	C₂²×C₃	—	2	2	no	—
429	C₂²×C₃	—	2	4	no	—
430	C₂²×C₃	—	2	8	no	—
431	C₂²×C₃	—	2	4	no	—
432	C₂²×C₃	—	2	4	no	—
433	C₂²×C₃	—	2	8	no	—
434	C₂²×C₃	—	2	4	no	—
435	C₂²×C₃	—	2	4	no	—
436	C₂²×C₃	—	2	4	no	—
437	C₂²×C₃	—	4	32	no	—
438	C₂²×C₃	—	4	4	no	—
439	C₂²×C₃	—	4	4	no	—
440	C₂²×C₃	C₂×C₅×C₂²⋊C₄	1	8	yes	complemented
441	C₂²×C₃	C₄×C₅×D₄	1	4	yes	complemented
442	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
443	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
444	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
445	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
446	C₂²×C₃	C₅×H(5,𝔽₂)	1	2	yes	—
447	C₃×C₄	—	2	2	no	—
448	C₃×C₄	—	2	4	no	—
449	C₃×C₄	—	4	4	no	—
450	C₃×C₄	—	4	2	no	—
451	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
452	C₂×C₅	—	2	4	no	—
453	C₂×C₅	—	2	8	no	—
454	C₂×C₅	—	4	4	no	—
455	C₂×C₅	C₂²×C₃×C₂²⋊C₄	1	1	yes	characteristic
456	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
457	C₂×C₅	C₃×#518	1	1	yes	characteristic
458	C₂×C₅	C₃×D₄²	1	2	yes	—
459	C₂×C₅	C₃×#546	1	2	yes	—
460	C₂³	—	2	2	no	—
461	C₂³	—	2	2	no	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	4	no	—
464	C₂³	—	2	2	no	—
465	C₂³	—	2	16	no	—
466	C₂³	—	2	16	no	—
467	C₂³	—	2	2	no	—
468	C₂³	—	2	4	no	—
469	C₂³	—	2	2	no	—
470	C₂³	—	2	4	no	—
471	C₂³	—	4	8	no	—
472	C₂³	—	4	16	no	—
473	C₂³	—	4	16	no	—
474	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
475	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
476	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
477	C₂³	C₂×C₃×C₅×D₄	1	8	yes	—
478	C₂³	C₂×C₃×C₅×D₄	1	2	yes	—
479	C₂³	C₃×C₅×#41	1	2	yes	—
480	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
481	D₄	—	2	16	no	—
482	D₄	—	2	8	no	—
483	D₄	C₃×C₅×C₂²⋊C₄	1	16	yes	direct product factor
484	C₂×C₄	—	2	2	no	—
485	C₂×C₄	—	2	2	no	—
486	C₂×C₄	—	2	2	no	—
487	C₂×C₄	—	2	8	no	—
488	C₂×C₄	—	2	2	no	—
489	C₂×C₄	—	2	4	no	—
490	C₂×C₄	—	2	4	no	—
491	C₂×C₄	—	2	2	no	—
492	C₂×C₄	—	2	2	no	—
493	C₂×C₄	—	2	4	no	—
494	C₂×C₄	—	4	16	no	—
495	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
496	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
497	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
498	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	complemented
499	C₂×C₃	—	2	4	no	—
500	C₂×C₃	—	2	8	no	—
501	C₂×C₃	—	4	4	no	—
502	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
503	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
504	C₂×C₃	C₅×#518	1	1	yes	characteristic
505	C₂×C₃	C₅×D₄²	1	2	yes	—
506	C₂×C₃	C₅×#546	1	2	yes	—
507	C₅	C₃×D₄×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	2	4	no	—
510	C₂²	—	2	2	no	—
511	C₂²	—	2	4	no	—
512	C₂²	—	2	8	no	—
513	C₂²	—	2	4	no	—
514	C₂²	—	2	4	no	—
515	C₂²	—	2	8	no	—
516	C₂²	—	2	4	no	—
517	C₂²	—	2	4	no	—
518	C₂²	—	2	4	no	—
519	C₂²	—	4	32	no	—
520	C₂²	—	4	4	no	—
521	C₂²	—	4	4	no	—
522	C₂²	C₂×C₃×C₅×C₂²⋊C₄	1	8	yes	complemented
523	C₂²	C₃×C₄×C₅×D₄	1	4	yes	complemented
524	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
525	C₂²	C₂²×C₃×C₅×D₄	1	2	yes	—
526	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
527	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
528	C₂²	C₃×C₅×H(5,𝔽₂)	1	2	yes	—
529	C₄	—	2	2	no	—
530	C₄	—	2	4	no	—
531	C₄	—	4	4	no	—
532	C₄	—	4	2	no	—
533	C₄	C₂×C₃×C₅×C₂²⋊C₄	1	4	yes	complemented
534	C₃	C₅×D₄×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
535	C₂	—	2	4	no	—
536	C₂	—	2	8	no	—
537	C₂	—	4	4	no	—
538	C₂	C₂²×C₃×C₅×C₂²⋊C₄	1	1	yes	characteristic
539	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
540	C₂	C₃×C₅×#518	1	1	yes	characteristic
541	C₂	C₃×C₅×D₄²	1	2	yes	—
542	C₂	C₃×C₅×#546	1	2	yes	—

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂³×C₃×C₅×D₄	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³×C₃×C₅ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×D₄	C₂	semidirect
3. C₂²×C₃×C₅×C₂²⋊C₄	C₂	semidirect
4. C₃×C₅×#390	C₂	semidirect
5. C₃×C₅×#386	C₂	semidirect
6. C₃×C₅×#380	C₂	semidirect
7. C₃×C₅×#379	C₂	semidirect
8. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
9. C₅×D₄×C₂²⋊C₄	C₃	direct (N × H)
12. C₂²×C₃×C₅×D₄	C₄	semidirect
17. C₂³×C₃×C₄×C₅	C₂²	semidirect
19. C₂×C₃×C₅×C₄⋊C₄	C₂²	semidirect
24. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
25. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
26. C₂×C₃×C₅×C₂²⋊C₄	C₂²	semidirect
27. C₂×C₃×C₄²×C₅	C₂²	semidirect
28. C₃×C₅×#95	C₂²	semidirect
29. C₃×C₅×#95	C₂²	semidirect
30. C₃×D₄×C₂²⋊C₄	C₅	direct (N × H)
32. C₂×C₄×C₅×D₄	C₂×C₃	semidirect
33. C₂²×C₅×C₂²⋊C₄	C₂×C₃	semidirect
34. C₅×#390	C₂×C₃	semidirect
35. C₅×#386	C₂×C₃	semidirect
36. C₅×#380	C₂×C₃	semidirect
37. C₅×#379	C₂×C₃	semidirect
38. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
43. C₂⁴×C₃×C₅	C₂×C₄	semidirect
51. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
52. C₂×C₃×C₅×D₄	C₂×C₄	semidirect
58. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
70. C₃×C₅×C₂²⋊C₄	D₄	direct (N × H)
73. C₂×C₃×C₄×D₄	C₂×C₅	semidirect
74. C₂²×C₃×C₂²⋊C₄	C₂×C₅	semidirect
75. C₃×#390	C₂×C₅	semidirect
76. C₃×#386	C₂×C₅	semidirect
77. C₃×#380	C₂×C₅	semidirect
78. C₃×#379	C₂×C₅	semidirect
79. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
82. C₂²×C₅×D₄	C₃×C₄	semidirect
87. C₂³×C₄×C₅	C₂²×C₃	semidirect
89. C₂×C₅×C₄⋊C₄	C₂²×C₃	semidirect
94. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
95. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
96. C₂×C₅×C₂²⋊C₄	C₂²×C₃	semidirect
97. C₂×C₄²×C₅	C₂²×C₃	semidirect
98. C₅×#95	C₂²×C₃	semidirect
99. C₅×#95	C₂²×C₃	semidirect
100. D₄×C₂²⋊C₄	C₃×C₅	direct (N × H)
124. C₃×C₅×D₄	C₂²⋊C₄	direct (N × H)
139. C₂×C₃×C₄×C₅	C₂×D₄	semidirect
142. C₂²×C₃×D₄	C₄×C₅	semidirect
147. C₂³×C₃×C₄	C₂²×C₅	semidirect
149. C₂×C₃×C₄⋊C₄	C₂²×C₅	semidirect
154. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
155. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
156. C₂×C₃×C₂²⋊C₄	C₂²×C₅	semidirect
157. C₂×C₃×C₄²	C₂²×C₅	semidirect
158. C₃×#95	C₂²×C₅	semidirect
159. C₃×#95	C₂²×C₅	semidirect
164. C₂⁴×C₅	C₂×C₃×C₄	semidirect
172. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
173. C₂×C₅×D₄	C₂×C₃×C₄	semidirect
179. C₂²×C₄×C₅	C₂×C₃×C₄	semidirect
191. C₅×C₂²⋊C₄	C₃×D₄	direct (N × H)
194. C₂×C₄×D₄	C₂×C₃×C₅	semidirect
195. C₂²×C₂²⋊C₄	C₂×C₃×C₅	semidirect
196. #390	C₂×C₃×C₅	semidirect
197. #386	C₂×C₃×C₅	semidirect
198. #380	C₂×C₃×C₅	semidirect
199. #379	C₂×C₃×C₅	semidirect
200. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
215. C₂²×C₃×C₅	C₂×C₂²⋊C₄	semidirect
216. C₂²×C₃×C₅	C₄×D₄	semidirect
226. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
231. C₂⁴×C₃	C₂×C₄×C₅	semidirect
239. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
240. C₂×C₃×D₄	C₂×C₄×C₅	semidirect
246. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
258. C₃×C₂²⋊C₄	C₅×D₄	direct (N × H)
283. C₅×D₄	C₃×C₂²⋊C₄	direct (N × H)
298. C₂×C₄×C₅	C₂×C₃×D₄	semidirect
301. C₂²×D₄	C₃×C₄×C₅	semidirect
306. C₂³×C₄	C₂²×C₃×C₅	semidirect
308. C₂×C₄⋊C₄	C₂²×C₃×C₅	semidirect
313. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
314. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
315. C₂×C₂²⋊C₄	C₂²×C₃×C₅	semidirect
316. C₂×C₄²	C₂²×C₃×C₅	semidirect
317. #95	C₂²×C₃×C₅	semidirect
318. #95	C₂²×C₃×C₅	semidirect
350. C₃×D₄	C₅×C₂²⋊C₄	direct (N × H)
365. C₂×C₃×C₄	C₂×C₅×D₄	semidirect
380. C₂²×C₅	C₂×C₃×C₂²⋊C₄	semidirect
381. C₂²×C₅	C₃×C₄×D₄	semidirect
391. C₄×C₅	C₂×C₃×C₂²⋊C₄	semidirect
396. C₂⁴	C₂×C₃×C₄×C₅	semidirect
404. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
405. C₂×D₄	C₂×C₃×C₄×C₅	semidirect
411. C₂²×C₄	C₂×C₃×C₄×C₅	semidirect
423. C₂²⋊C₄	C₃×C₅×D₄	direct (N × H)
425. C₃×C₅	D₄×C₂²⋊C₄	direct (N × H)
440. C₂²×C₃	C₂×C₅×C₂²⋊C₄	semidirect
441. C₂²×C₃	C₄×C₅×D₄	semidirect
451. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
483. D₄	C₃×C₅×C₂²⋊C₄	direct (N × H)
498. C₂×C₄	C₂×C₃×C₅×D₄	semidirect
507. C₅	C₃×D₄×C₂²⋊C₄	direct (N × H)
522. C₂²	C₂×C₃×C₅×C₂²⋊C₄	semidirect
523. C₂²	C₃×C₄×C₅×D₄	semidirect
533. C₄	C₂×C₃×C₅×C₂²⋊C₄	semidirect
534. C₃	C₅×D₄×C₂²⋊C₄	direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₂³×C₃×C₅×D₄	2
C₂×C₃×C₄×C₅×D₄	2
C₂²×C₃×C₅×C₂²⋊C₄	2
C₃×C₅×#390	2
C₃×C₅×#386	2
C₃×C₅×#380	2
C₃×C₅×#379	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×D₄×C₂²⋊C₄	3
C₃×D₄×C₂²⋊C₄	5

Subgroups — C3×C5×D4×C22⋊C4 #14275372

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×D₄×C₂²⋊C₄ #14275372