Subgroups — C₄×C₅×D₃×C₂²⋊C₄ #14319370

Order 1920.

2720 conjugacy classes of subgroups.

The subgroup lattice has 540 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×C₄×C₅×D₃	C₂	1	1	yes	maximal, characteristic
2	C₂×C₅×D₃×C₂²⋊C₄	C₂	1	2	yes	maximal
3	C₂×C₄²×C₅×D₃	C₂	1	2	yes	maximal, complemented
4	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
5	C₄×C₅×#217	C₂	1	1	yes	maximal, characteristic, complemented
6	C₅×Dic₃×C₂²⋊C₄	C₂	1	2	yes	maximal, complemented
7	C₄×C₅×(C₂×D₃)⋊C₄	C₂	1	2	yes	maximal, complemented
8	C₅×#4666	C₂	1	2	yes	maximal, complemented
9	C₅×D₃×#95	C₂	1	2	yes	maximal, complemented
10	C₂×C₄×C₅×C₂²⋊C₄	—	3	1	no	maximal, Hall
11	C₂⁴×C₅×D₃	C₂²	1	1	yes	characteristic
12	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
13	C₂³×C₅×Dic₃	C₂²	1	1	yes	characteristic
14	C₂²×C₄×C₅×D₃	—	2	8	no	—
15	C₂²×C₄×C₅×D₃	C₄	1	8	yes	complemented
16	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
17	C₂²×C₄×C₅×D₃	C₂²	1	4	yes	—
18	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
19	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
20	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	complemented
23	C₂×C₅×#217	C₂²	1	2	yes	—
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	4	yes	—
25	C₂×C₄×C₅×Dic₃	C₂²	1	4	yes	complemented
26	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	complemented
27	C₅×D₃×C₂²⋊C₄	C₄	1	16	yes	direct product factor
28	C₄²×C₅×D₃	—	2	8	no	—
29	C₃×C₅×#95	C₂²	1	2	yes	complemented
30	C₅×C₃⋊#95	C₂²	1	2	yes	complemented
31	C₅×C₃⋊#95	C₂²	1	4	yes	complemented
32	C₄×D₃×C₂²⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
33	C₂⁴×C₄×C₅	—	3	1	no	—
34	C₂²×C₅×C₂²⋊C₄	—	3	2	no	—
35	C₂²×C₄²×C₅	—	3	2	no	—
36	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
37	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
38	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
39	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
40	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, direct product factor
41	C₂×C₅×#95	—	3	2	no	—
42	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
43	C₂³×C₅×D₃	—	2	4	no	—
44	C₂³×C₅×D₃	—	2	4	no	—
45	C₂³×C₅×D₃	C₂×C₄	1	8	yes	—
46	C₂³×C₅×D₃	C₂×C₄	1	4	yes	—
47	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
48	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
49	C₂²×C₃×C₄×C₅	—	2	4	no	—
50	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
51	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
52	C₂²×C₃×C₄×C₅	C₂³	1	4	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
54	C₂²×C₅×Dic₃	—	2	4	no	—
55	C₂²×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
56	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
57	C₂²×C₅×Dic₃	C₂³	1	4	yes	—
58	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
59	C₂×C₄×C₅×D₃	—	2	8	no	—
60	C₂×C₄×C₅×D₃	—	2	4	no	—
61	C₂×C₄×C₅×D₃	—	2	8	no	—
62	C₂×C₄×C₅×D₃	—	2	4	no	—
63	C₂×C₄×C₅×D₃	—	2	4	no	—
64	C₂×C₄×C₅×D₃	—	2	32	no	—
65	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
66	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	—
67	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
68	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
69	C₂×C₄×C₅×D₃	C₂×C₄	1	16	yes	complemented
70	C₂×C₄×C₅×D₃	D₄	1	8	yes	—
71	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
72	C₃×C₄²×C₅	—	2	4	no	—
73	C₅×#217	C₂×C₄	1	8	yes	complemented
74	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	16	yes	complemented
75	C₄×C₅×Dic₃	—	2	4	no	—
76	C₄×C₅×Dic₃	—	2	8	no	—
77	C₂³×C₄×D₃	C₂×C₅	1	1	yes	characteristic
78	C₂×D₃×C₂²⋊C₄	C₂×C₅	1	2	yes	—
79	C₂×C₄²×D₃	C₂×C₅	1	2	yes	complemented
80	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
81	C₄×#217	C₂×C₅	1	1	yes	characteristic, complemented
82	Dic₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
83	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	2	yes	complemented
84	#4666	C₂×C₅	1	2	yes	complemented
85	D₃×#95	C₂×C₅	1	2	yes	complemented
86	C₂⁵×C₅	—	3	1	no	—
87	C₂³×C₄×C₅	—	3	1	no	—
88	C₂³×C₄×C₅	—	3	1	no	—
89	C₂³×C₄×C₅	—	3	8	no	—
90	C₂³×C₄×C₅	—	3	1	no	—
91	C₂³×C₄×C₅	—	3	4	no	—
92	C₂³×C₄×C₅	—	3	1	no	—
93	C₂³×C₄×C₅	—	3	1	no	—
94	C₂³×C₄×C₅	—	6	8	no	—
95	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
96	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
97	C₂×C₅×C₂²⋊C₄	—	3	4	no	—
98	C₂×C₅×C₂²⋊C₄	—	3	16	no	—
99	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
100	C₂×C₄²×C₅	—	3	4	no	—
101	C₂×C₄²×C₅	—	3	2	no	—
102	C₂×C₄²×C₅	—	6	8	no	—
103	C₂×C₄²×C₅	C₂×D₃	1	2	yes	complemented
104	C₅×#95	—	3	2	no	—
105	C₅×#95	—	3	4	no	—
106	C₅×#95	C₂×D₃	1	2	yes	complemented
107	C₂×C₄×C₂²⋊C₄	—	3	1	no	Sylow
108	C₂³×C₃×C₅	—	2	2	no	—
109	C₂³×C₃×C₅	—	2	2	no	—
110	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
111	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
112	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
113	C₂²×C₅×D₃	—	2	2	no	—
114	C₂²×C₅×D₃	—	2	2	no	—
115	C₂²×C₅×D₃	—	2	8	no	—
116	C₂²×C₅×D₃	—	2	8	no	—
117	C₂²×C₅×D₃	—	2	32	no	—
118	C₂²×C₅×D₃	C₄²	1	16	yes	complemented
119	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
120	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
121	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
122	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
123	C₂²×C₅×D₃	C₂×D₄	1	4	yes	—
124	C₂²×C₅×D₃	#41	1	4	yes	—
125	C₂×C₃×C₄×C₅	—	2	4	no	—
126	C₂×C₃×C₄×C₅	—	2	2	no	—
127	C₂×C₃×C₄×C₅	—	2	4	no	—
128	C₂×C₃×C₄×C₅	—	2	8	no	—
129	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
130	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
131	C₂×C₃×C₄×C₅	C₂²×C₄	1	8	yes	complemented
132	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
133	C₂×C₅×Dic₃	—	2	4	no	—
134	C₂×C₅×Dic₃	—	2	2	no	—
135	C₂×C₅×Dic₃	—	2	4	no	—
136	C₂×C₅×Dic₃	—	2	8	no	—
137	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
138	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
139	C₂×C₅×Dic₃	C₂²×C₄	1	8	yes	complemented
140	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
141	C₄×C₅×D₃	—	2	8	no	—
142	C₄×C₅×D₃	—	2	32	no	—
143	C₄×C₅×D₃	—	2	8	no	—
144	C₄×C₅×D₃	—	2	8	no	—
145	C₄×C₅×D₃	C₂²⋊C₄	1	16	yes	direct product factor
146	C₂⁴×D₃	C₂²×C₅	1	1	yes	characteristic
147	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
148	C₂³×Dic₃	C₂²×C₅	1	1	yes	characteristic
149	C₂²×C₄×D₃	—	2	8	no	—
150	C₂²×C₄×D₃	C₄×C₅	1	8	yes	complemented
151	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
152	C₂²×C₄×D₃	C₂²×C₅	1	4	yes	—
153	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
154	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
155	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
156	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
157	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	complemented
158	C₂×#217	C₂²×C₅	1	2	yes	—
159	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	4	yes	—
160	C₂×C₄×Dic₃	C₂²×C₅	1	4	yes	complemented
161	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	complemented
162	D₃×C₂²⋊C₄	C₄×C₅	1	16	yes	direct product factor
163	C₄²×D₃	—	2	8	no	—
164	C₃×#95	C₂²×C₅	1	2	yes	complemented
165	C₃⋊#95	C₂²×C₅	1	2	yes	complemented
166	C₃⋊#95	C₂²×C₅	1	4	yes	complemented
167	C₂⁴×C₅	—	3	1	no	—
168	C₂⁴×C₅	—	3	8	no	—
169	C₂⁴×C₅	—	3	4	no	—
170	C₂⁴×C₅	—	3	1	no	—
171	C₂⁴×C₅	—	6	4	no	—
172	C₂⁴×C₅	—	6	4	no	—
173	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
174	C₂²×C₄×C₅	—	2	4	no	—
175	C₂²×C₄×C₅	—	3	1	no	—
176	C₂²×C₄×C₅	—	3	4	no	—
177	C₂²×C₄×C₅	—	3	8	no	—
178	C₂²×C₄×C₅	—	3	4	no	—
179	C₂²×C₄×C₅	—	3	4	no	—
180	C₂²×C₄×C₅	—	3	1	no	—
181	C₂²×C₄×C₅	—	3	4	no	—
182	C₂²×C₄×C₅	—	3	4	no	—
183	C₂²×C₄×C₅	—	3	4	no	—
184	C₂²×C₄×C₅	—	3	16	no	—
185	C₂²×C₄×C₅	—	6	4	no	—
186	C₂²×C₄×C₅	—	6	32	no	—
187	C₂²×C₄×C₅	—	6	8	no	—
188	C₂²×C₄×C₅	—	6	4	no	—
189	C₂²×C₄×C₅	—	6	8	no	—
190	C₂²×C₄×C₅	—	6	4	no	—
191	C₂²×C₄×C₅	—	6	4	no	—
192	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
193	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
194	C₂²×C₄×C₅	C₂²×D₃	1	4	yes	—
195	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
196	C₅×C₂²⋊C₄	—	3	8	no	—
197	C₅×C₂²⋊C₄	—	3	16	no	—
198	C₅×C₂²⋊C₄	C₄×D₃	1	8	yes	direct product factor
199	C₄²×C₅	—	2	4	no	—
200	C₄²×C₅	—	6	8	no	—
201	C₄²×C₅	—	6	4	no	—
202	C₂⁴×C₄	—	3	1	no	—
203	C₂²×C₂²⋊C₄	—	3	2	no	—
204	C₂²×C₄²	—	3	2	no	—
205	C₄×C₂²⋊C₄	—	3	1	no	—
206	C₄×C₂²⋊C₄	—	3	2	no	—
207	C₄×C₂²⋊C₄	—	3	2	no	—
208	C₄×C₂²⋊C₄	—	3	2	no	—
209	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, direct product factor
210	C₂×#95	—	3	2	no	—
211	C₂²×C₃×C₅	—	2	2	no	—
212	C₂²×C₃×C₅	—	2	2	no	—
213	C₂²×C₃×C₅	—	2	8	no	—
214	C₂²×C₃×C₅	C₂×C₄²	1	4	yes	complemented
215	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
216	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
217	C₂²×C₃×C₅	C₂²×D₄	1	2	yes	—
218	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
219	C₂×C₅×D₃	—	2	2	no	—
220	C₂×C₅×D₃	—	2	2	no	—
221	C₂×C₅×D₃	—	2	8	no	—
222	C₂×C₅×D₃	—	2	32	no	—
223	C₂×C₅×D₃	C₂×C₄²	1	4	yes	—
224	C₂×C₅×D₃	C₂×C₄²	1	4	yes	complemented
225	C₂×C₅×D₃	C₂×C₂²⋊C₄	1	4	yes	—
226	C₂×C₅×D₃	#117	1	4	yes	—
227	C₂×C₅×D₃	C₄×D₄	1	16	yes	—
228	C₃×C₄×C₅	—	2	2	no	—
229	C₃×C₄×C₅	—	2	8	no	—
230	C₃×C₄×C₅	C₂×C₂²⋊C₄	1	4	yes	complemented
231	C₅×Dic₃	—	2	2	no	—
232	C₅×Dic₃	—	2	8	no	—
233	C₅×Dic₃	C₂×C₂²⋊C₄	1	4	yes	complemented
234	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
235	C₂³×D₃	—	2	4	no	—
236	C₂³×D₃	—	2	4	no	—
237	C₂³×D₃	C₂×C₄×C₅	1	8	yes	—
238	C₂³×D₃	C₂×C₄×C₅	1	4	yes	—
239	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
240	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
241	C₂²×C₃×C₄	—	2	4	no	—
242	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
243	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
244	C₂²×C₃×C₄	C₂³×C₅	1	4	yes	—
245	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
246	C₂²×Dic₃	—	2	4	no	—
247	C₂²×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
248	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
249	C₂²×Dic₃	C₂³×C₅	1	4	yes	—
250	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
251	C₂×C₄×D₃	—	2	8	no	—
252	C₂×C₄×D₃	—	2	4	no	—
253	C₂×C₄×D₃	—	2	8	no	—
254	C₂×C₄×D₃	—	2	4	no	—
255	C₂×C₄×D₃	—	2	4	no	—
256	C₂×C₄×D₃	—	2	32	no	—
257	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
258	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	—
259	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
260	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
261	C₂×C₄×D₃	C₂×C₄×C₅	1	16	yes	complemented
262	C₂×C₄×D₃	C₅×D₄	1	8	yes	—
263	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
264	C₃×C₄²	—	2	4	no	—
265	#217	C₂×C₄×C₅	1	8	yes	complemented
266	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
267	C₄×Dic₃	—	2	4	no	—
268	C₄×Dic₃	—	2	8	no	—
269	C₂³×C₅	—	2	2	no	—
270	C₂³×C₅	—	2	2	no	—
271	C₂³×C₅	—	3	2	no	—
272	C₂³×C₅	—	3	4	no	—
273	C₂³×C₅	—	3	4	no	—
274	C₂³×C₅	—	3	4	no	—
275	C₂³×C₅	—	3	16	no	—
276	C₂³×C₅	—	3	4	no	—
277	C₂³×C₅	—	3	2	no	—
278	C₂³×C₅	—	6	8	no	—
279	C₂³×C₅	—	6	8	no	—
280	C₂³×C₅	—	6	32	no	—
281	C₂³×C₅	—	6	2	no	—
282	C₂³×C₅	—	6	2	no	—
283	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
284	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
285	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
286	C₂×C₄×C₅	—	2	4	no	—
287	C₂×C₄×C₅	—	2	2	no	—
288	C₂×C₄×C₅	—	2	4	no	—
289	C₂×C₄×C₅	—	2	8	no	—
290	C₂×C₄×C₅	—	3	2	no	—
291	C₂×C₄×C₅	—	3	4	no	—
292	C₂×C₄×C₅	—	3	16	no	—
293	C₂×C₄×C₅	—	3	8	no	—
294	C₂×C₄×C₅	—	3	2	no	—
295	C₂×C₄×C₅	—	6	8	no	—
296	C₂×C₄×C₅	—	6	32	no	—
297	C₂×C₄×C₅	—	6	8	no	—
298	C₂×C₄×C₅	—	6	8	no	—
299	C₂×C₄×C₅	—	6	4	no	—
300	C₂×C₄×C₅	—	6	2	no	—
301	C₂×C₄×C₅	—	6	4	no	—
302	C₂×C₄×C₅	—	6	8	no	—
303	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
304	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
305	C₂×C₄×C₅	C₂×C₄×D₃	1	8	yes	complemented
306	C₂×C₄×C₅	D₃×D₄	1	4	yes	—
307	C₂⁵	—	3	1	no	—
308	C₂³×C₄	—	3	1	no	—
309	C₂³×C₄	—	3	1	no	—
310	C₂³×C₄	—	3	8	no	—
311	C₂³×C₄	—	3	4	no	—
312	C₂³×C₄	—	3	1	no	—
313	C₂³×C₄	—	3	1	no	—
314	C₂³×C₄	—	3	1	no	—
315	C₂³×C₄	—	6	8	no	—
316	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
317	C₂×C₂²⋊C₄	—	3	2	no	—
318	C₂×C₂²⋊C₄	—	3	4	no	—
319	C₂×C₂²⋊C₄	—	3	16	no	—
320	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
321	C₂×C₄²	—	3	4	no	—
322	C₂×C₄²	—	3	2	no	—
323	C₂×C₄²	—	6	8	no	—
324	C₂×C₄²	C₂×C₅×D₃	1	2	yes	complemented
325	#95	—	3	4	no	—
326	#95	—	3	2	no	—
327	#95	C₂×C₅×D₃	1	2	yes	complemented
328	C₂×C₃×C₅	—	2	4	no	—
329	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
330	C₂×C₃×C₅	C₂²×C₂²⋊C₄	1	1	yes	characteristic
331	C₂×C₃×C₅	C₂×#117	1	1	yes	characteristic
332	C₂×C₃×C₅	C₂×C₄×D₄	1	4	yes	—
333	C₅×D₃	—	2	4	no	—
334	C₅×D₃	C₄×C₂²⋊C₄	1	8	yes	direct product factor
335	C₂³×C₃	—	2	2	no	—
336	C₂³×C₃	—	2	2	no	—
337	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
338	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
339	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
340	C₂²×D₃	—	2	2	no	—
341	C₂²×D₃	—	2	2	no	—
342	C₂²×D₃	—	2	8	no	—
343	C₂²×D₃	—	2	8	no	—
344	C₂²×D₃	—	2	32	no	—
345	C₂²×D₃	C₄²×C₅	1	16	yes	complemented
346	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
347	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
348	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
349	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
350	C₂²×D₃	C₂×C₅×D₄	1	4	yes	—
351	C₂²×D₃	C₅×#41	1	4	yes	—
352	C₂×C₃×C₄	—	2	4	no	—
353	C₂×C₃×C₄	—	2	2	no	—
354	C₂×C₃×C₄	—	2	4	no	—
355	C₂×C₃×C₄	—	2	8	no	—
356	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
357	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
358	C₂×C₃×C₄	C₂²×C₄×C₅	1	8	yes	complemented
359	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
360	C₂×Dic₃	—	2	4	no	—
361	C₂×Dic₃	—	2	2	no	—
362	C₂×Dic₃	—	2	4	no	—
363	C₂×Dic₃	—	2	8	no	—
364	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
365	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
366	C₂×Dic₃	C₂²×C₄×C₅	1	8	yes	complemented
367	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
368	C₄×D₃	—	2	8	no	—
369	C₄×D₃	—	2	32	no	—
370	C₄×D₃	—	2	8	no	—
371	C₄×D₃	—	2	8	no	—
372	C₄×D₃	C₅×C₂²⋊C₄	1	16	yes	direct product factor
373	C₂²×C₅	—	2	2	no	—
374	C₂²×C₅	—	2	2	no	—
375	C₂²×C₅	—	2	8	no	—
376	C₂²×C₅	—	3	4	no	—
377	C₂²×C₅	—	3	4	no	—
378	C₂²×C₅	—	3	4	no	—
379	C₂²×C₅	—	3	16	no	—
380	C₂²×C₅	—	3	4	no	—
381	C₂²×C₅	—	6	32	no	—
382	C₂²×C₅	—	6	2	no	—
383	C₂²×C₅	—	6	2	no	—
384	C₂²×C₅	—	6	8	no	—
385	C₂²×C₅	C₄²×D₃	1	4	yes	complemented
386	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
387	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
388	C₂²×C₅	C₂×D₃×D₄	1	2	yes	—
389	C₂²×C₅	D₃×#41	1	2	yes	—
390	C₄×C₅	—	2	2	no	—
391	C₄×C₅	—	2	8	no	—
392	C₄×C₅	—	3	4	no	—
393	C₄×C₅	—	6	2	no	—
394	C₄×C₅	—	6	8	no	—
395	C₄×C₅	D₃×C₂²⋊C₄	1	4	yes	direct product factor
396	C₂⁴	—	3	1	no	—
397	C₂⁴	—	3	8	no	—
398	C₂⁴	—	3	4	no	—
399	C₂⁴	—	3	1	no	—
400	C₂⁴	—	6	4	no	—
401	C₂⁴	—	6	4	no	—
402	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
403	C₂²×C₄	—	2	4	no	—
404	C₂²×C₄	—	3	1	no	—
405	C₂²×C₄	—	3	4	no	—
406	C₂²×C₄	—	3	8	no	—
407	C₂²×C₄	—	3	4	no	—
408	C₂²×C₄	—	3	1	no	—
409	C₂²×C₄	—	3	4	no	—
410	C₂²×C₄	—	3	4	no	—
411	C₂²×C₄	—	3	4	no	—
412	C₂²×C₄	—	3	4	no	—
413	C₂²×C₄	—	3	16	no	—
414	C₂²×C₄	—	6	4	no	—
415	C₂²×C₄	—	6	32	no	—
416	C₂²×C₄	—	6	8	no	—
417	C₂²×C₄	—	6	4	no	—
418	C₂²×C₄	—	6	8	no	—
419	C₂²×C₄	—	6	4	no	—
420	C₂²×C₄	—	6	4	no	—
421	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
422	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
423	C₂²×C₄	C₂²×C₅×D₃	1	4	yes	—
424	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
425	C₂²⋊C₄	—	3	8	no	—
426	C₂²⋊C₄	—	3	16	no	—
427	C₂²⋊C₄	C₄×C₅×D₃	1	8	yes	direct product factor
428	C₄²	—	2	4	no	—
429	C₄²	—	6	8	no	—
430	C₄²	—	6	4	no	—
431	C₃×C₅	C₂×C₄×C₂²⋊C₄	1	1	yes	characteristic, complemented, Hall
432	C₂²×C₃	—	2	2	no	—
433	C₂²×C₃	—	2	2	no	—
434	C₂²×C₃	—	2	8	no	—
435	C₂²×C₃	C₂×C₄²×C₅	1	4	yes	complemented
436	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
437	C₂²×C₃	C₂³×C₄×C₅	1	2	yes	—
438	C₂²×C₃	C₂²×C₅×D₄	1	2	yes	—
439	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
440	C₂×D₃	—	2	2	no	—
441	C₂×D₃	—	2	2	no	—
442	C₂×D₃	—	2	8	no	—
443	C₂×D₃	—	2	32	no	—
444	C₂×D₃	C₂×C₄²×C₅	1	4	yes	—
445	C₂×D₃	C₂×C₄²×C₅	1	4	yes	complemented
446	C₂×D₃	C₂×C₅×C₂²⋊C₄	1	4	yes	—
447	C₂×D₃	C₅×#117	1	4	yes	—
448	C₂×D₃	C₄×C₅×D₄	1	16	yes	—
449	C₃×C₄	—	2	2	no	—
450	C₃×C₄	—	2	8	no	—
451	C₃×C₄	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
452	Dic₃	—	2	2	no	—
453	Dic₃	—	2	8	no	—
454	Dic₃	C₂×C₅×C₂²⋊C₄	1	4	yes	complemented
455	C₂×C₅	—	2	4	no	—
456	C₂×C₅	—	3	8	no	—
457	C₂×C₅	—	6	4	no	—
458	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
459	C₂×C₅	C₂×D₃×C₂²⋊C₄	1	1	yes	characteristic
460	C₂×C₅	D₃×#117	1	1	yes	characteristic
461	C₂×C₅	C₄×D₃×D₄	1	4	yes	—
462	C₂³	—	2	2	no	—
463	C₂³	—	2	2	no	—
464	C₂³	—	3	2	no	—
465	C₂³	—	3	4	no	—
466	C₂³	—	3	4	no	—
467	C₂³	—	3	4	no	—
468	C₂³	—	3	16	no	—
469	C₂³	—	3	4	no	—
470	C₂³	—	3	2	no	—
471	C₂³	—	6	8	no	—
472	C₂³	—	6	8	no	—
473	C₂³	—	6	32	no	—
474	C₂³	—	6	2	no	—
475	C₂³	—	6	2	no	—
476	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
477	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
478	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
479	C₂×C₄	—	2	4	no	—
480	C₂×C₄	—	2	2	no	—
481	C₂×C₄	—	2	4	no	—
482	C₂×C₄	—	2	8	no	—
483	C₂×C₄	—	3	2	no	—
484	C₂×C₄	—	3	4	no	—
485	C₂×C₄	—	3	16	no	—
486	C₂×C₄	—	3	8	no	—
487	C₂×C₄	—	3	2	no	—
488	C₂×C₄	—	6	8	no	—
489	C₂×C₄	—	6	8	no	—
490	C₂×C₄	—	6	32	no	—
491	C₂×C₄	—	6	8	no	—
492	C₂×C₄	—	6	4	no	—
493	C₂×C₄	—	6	2	no	—
494	C₂×C₄	—	6	4	no	—
495	C₂×C₄	—	6	8	no	—
496	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
497	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
498	C₂×C₄	C₂×C₄×C₅×D₃	1	8	yes	complemented
499	C₂×C₄	C₅×D₃×D₄	1	4	yes	—
500	C₂×C₃	—	2	4	no	—
501	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
502	C₂×C₃	C₂²×C₅×C₂²⋊C₄	1	1	yes	characteristic
503	C₂×C₃	C₂×C₅×#117	1	1	yes	characteristic
504	C₂×C₃	C₂×C₄×C₅×D₄	1	4	yes	—
505	D₃	—	2	4	no	—
506	D₃	C₄×C₅×C₂²⋊C₄	1	8	yes	direct product factor
507	C₅	C₄×D₃×C₂²⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
508	C₂²	—	2	2	no	—
509	C₂²	—	2	2	no	—
510	C₂²	—	2	8	no	—
511	C₂²	—	3	4	no	—
512	C₂²	—	3	4	no	—
513	C₂²	—	3	4	no	—
514	C₂²	—	3	16	no	—
515	C₂²	—	3	4	no	—
516	C₂²	—	6	32	no	—
517	C₂²	—	6	2	no	—
518	C₂²	—	6	2	no	—
519	C₂²	—	6	8	no	—
520	C₂²	C₄²×C₅×D₃	1	4	yes	complemented
521	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
522	C₂²	C₂²×C₄×C₅×D₃	1	2	yes	—
523	C₂²	C₂×C₅×D₃×D₄	1	2	yes	—
524	C₂²	C₅×D₃×#41	1	2	yes	—
525	C₄	—	2	2	no	—
526	C₄	—	2	8	no	—
527	C₄	—	3	4	no	—
528	C₄	—	6	2	no	—
529	C₄	—	6	8	no	—
530	C₄	C₅×D₃×C₂²⋊C₄	1	4	yes	direct product factor
531	C₃	C₂×C₄×C₅×C₂²⋊C₄	1	1	yes	characteristic, complemented, Sylow
532	C₂	—	2	4	no	—
533	C₂	—	3	8	no	—
534	C₂	—	6	4	no	—
535	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
536	C₂	C₂×C₅×D₃×C₂²⋊C₄	1	1	yes	characteristic
537	C₂	C₅×D₃×#117	1	1	yes	characteristic
538	C₂	C₄×C₅×D₃×D₄	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄×C₅	C₂²×D₃
commutator	C₂×C₃	C₂²×C₄²×C₅
Frattini	C₂³	C₂³×C₅×D₃
Fitting	C₃×C₄×C₅×C₂²⋊C₄	C₂
socle	C₂³×C₃×C₅	C₂⁴
prime radical	C₂⁴×C₅×D₃	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₂×C₄×C₅×C₂²⋊C₄
LCS	G ▷ C₂×C₃ ▷ C₃
UCS	C₁ ◁ C₂²×C₄×C₅ ◁ C₄×C₅×C₂²⋊C₄

Complements

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

N	H ≅ G/N	type
3. C₂×C₄²×C₅×D₃	C₂	semidirect
4. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
5. C₄×C₅×#217	C₂	semidirect
6. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
7. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
8. C₅×#4666	C₂	semidirect
9. C₅×D₃×#95	C₂	semidirect
15. C₂²×C₄×C₅×D₃	C₄	semidirect
22. C₂×C₃×C₄²×C₅	C₂²	semidirect
25. C₂×C₄×C₅×Dic₃	C₂²	semidirect
26. C₂×C₄×C₅×Dic₃	C₂²	semidirect
27. C₅×D₃×C₂²⋊C₄	C₄	direct (N × H)
29. C₃×C₅×#95	C₂²	semidirect
30. C₅×C₃⋊#95	C₂²	semidirect
31. C₅×C₃⋊#95	C₂²	semidirect
32. C₄×D₃×C₂²⋊C₄	C₅	direct (N × H)
40. C₄×C₅×C₂²⋊C₄	D₃	direct (N × H)
50. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
55. C₂²×C₅×Dic₃	C₂×C₄	semidirect
67. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
68. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
69. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
71. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
73. C₅×#217	C₂×C₄	semidirect
74. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
79. C₂×C₄²×D₃	C₂×C₅	semidirect
80. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
81. C₄×#217	C₂×C₅	semidirect
82. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
83. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
84. #4666	C₂×C₅	semidirect
85. D₃×#95	C₂×C₅	semidirect
103. C₂×C₄²×C₅	C₂×D₃	semidirect
106. C₅×#95	C₂×D₃	semidirect
118. C₂²×C₅×D₃	C₄²	semidirect
131. C₂×C₃×C₄×C₅	C₂²×C₄	semidirect
139. C₂×C₅×Dic₃	C₂²×C₄	semidirect
145. C₄×C₅×D₃	C₂²⋊C₄	direct (N × H)
150. C₂²×C₄×D₃	C₄×C₅	semidirect
157. C₂×C₃×C₄²	C₂²×C₅	semidirect
160. C₂×C₄×Dic₃	C₂²×C₅	semidirect
161. C₂×C₄×Dic₃	C₂²×C₅	semidirect
162. D₃×C₂²⋊C₄	C₄×C₅	direct (N × H)
164. C₃×#95	C₂²×C₅	semidirect
165. C₃⋊#95	C₂²×C₅	semidirect
166. C₃⋊#95	C₂²×C₅	semidirect
192. C₂²×C₄×C₅	C₄×D₃	semidirect
198. C₅×C₂²⋊C₄	C₄×D₃	direct (N × H)
209. C₄×C₂²⋊C₄	C₅×D₃	direct (N × H)
214. C₂²×C₃×C₅	C₂×C₄²	semidirect
224. C₂×C₅×D₃	C₂×C₄²	semidirect
230. C₃×C₄×C₅	C₂×C₂²⋊C₄	semidirect
233. C₅×Dic₃	C₂×C₂²⋊C₄	semidirect
242. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
247. C₂²×Dic₃	C₂×C₄×C₅	semidirect
259. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
260. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
261. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
263. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
265. #217	C₂×C₄×C₅	semidirect
266. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
305. C₂×C₄×C₅	C₂×C₄×D₃	semidirect
324. C₂×C₄²	C₂×C₅×D₃	semidirect
327. #95	C₂×C₅×D₃	semidirect
334. C₅×D₃	C₄×C₂²⋊C₄	direct (N × H)
345. C₂²×D₃	C₄²×C₅	semidirect
358. C₂×C₃×C₄	C₂²×C₄×C₅	semidirect
366. C₂×Dic₃	C₂²×C₄×C₅	semidirect
372. C₄×D₃	C₅×C₂²⋊C₄	direct (N × H)
385. C₂²×C₅	C₄²×D₃	semidirect
395. C₄×C₅	D₃×C₂²⋊C₄	direct (N × H)
421. C₂²×C₄	C₄×C₅×D₃	semidirect
427. C₂²⋊C₄	C₄×C₅×D₃	direct (N × H)
431. C₃×C₅	C₂×C₄×C₂²⋊C₄	semidirect
435. C₂²×C₃	C₂×C₄²×C₅	semidirect
445. C₂×D₃	C₂×C₄²×C₅	semidirect
451. C₃×C₄	C₂×C₅×C₂²⋊C₄	semidirect
454. Dic₃	C₂×C₅×C₂²⋊C₄	semidirect
498. C₂×C₄	C₂×C₄×C₅×D₃	semidirect
506. D₃	C₄×C₅×C₂²⋊C₄	direct (N × H)
507. C₅	C₄×D₃×C₂²⋊C₄	direct (N × H)
520. C₂²	C₄²×C₅×D₃	semidirect
530. C₄	C₅×D₃×C₂²⋊C₄	direct (N × H)
531. C₃	C₂×C₄×C₅×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
C₂³×C₄×C₅×D₃	2
C₂×C₅×D₃×C₂²⋊C₄	2
C₂×C₄²×C₅×D₃	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₄×C₅×#217	2
C₅×Dic₃×C₂²⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₅×#4666	2
C₅×D₃×#95	2
C₂×C₄×C₅×C₂²⋊C₄	3
C₄×D₃×C₂²⋊C₄	5

Subgroups — C4×C5×D3×C22⋊C4 #14319370

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×D₃×C₂²⋊C₄ #14319370