Subgroups — C₄×C₅×#67⋊C₄ #14319552

Order 1920.

1848 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₄×C₅×#67	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₅×#67⋊C₄	C₂	1	2	yes	maximal
4	C₂×C₄²×C₅×D₃	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₄×C₅×C₂²⋊C₄	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	1	yes	maximal, characteristic, complemented
8	C₄×C₅×Dic₃⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄²×C₅×Dic₃	C₂	1	1	yes	maximal, characteristic, complemented
10	C₅×#4666	C₂	1	2	yes	maximal, complemented
11	C₅×#4649	C₂	1	2	yes	maximal, complemented
12	C₄²×C₅×D₄	—	3	1	no	maximal, Hall
13	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
14	C₂²×C₅×#67	C₂²	1	1	yes	characteristic
15	C₂³×C₅×Dic₃	C₂²	1	2	yes	—
16	C₂²×C₄×C₅×D₃	C₂²	1	2	yes	—
17	C₂²×C₄×C₅×D₃	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
19	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
20	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
21	C₂×C₅×#217	C₂²	1	1	yes	characteristic
22	C₄×C₅×#67	C₄	1	8	yes	complemented
23	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₅×(C₂×D₃)⋊C₄	C₂²	1	2	yes	—
25	C₂×C₅×Dic₃⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₅×Dic₃⋊C₄	C₂²	1	2	yes	—
27	C₂×C₄×C₅×Dic₃	—	2	4	no	—
28	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
29	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
30	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
31	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
32	C₂×C₄×C₅×Dic₃	C₂²	1	2	yes	—
33	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
34	C₂×C₄×C₅×Dic₃	C₂²	1	1	yes	characteristic
35	C₅×#67⋊C₄	C₄	1	16	yes	direct product factor
36	C₄²×C₅×D₃	—	2	4	no	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₅×C₃⋊#95	C₂²	1	2	yes	—
39	C₅×C₃⋊#95	C₂²	1	2	yes	—
40	C₄×#67⋊C₄	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
41	C₂×C₄×C₅×D₄	—	3	1	no	—
42	C₂×C₄×C₅×D₄	—	3	2	no	—
43	C₂²×C₄²×C₅	—	3	1	no	—
44	C₂²×C₄²×C₅	—	3	1	no	—
45	C₄×C₅×C₄⋊C₄	—	3	2	no	—
46	C₄×C₅×C₄⋊C₄	—	3	1	no	—
47	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
48	C₄×C₅×C₂²⋊C₄	—	3	2	no	—
49	C₄×C₅×C₂²⋊C₄	—	3	1	no	—
50	C₄×C₅×C₂²⋊C₄	D₃	1	1	yes	characteristic, complemented
51	C₄³×C₅	—	3	1	no	—
52	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
53	C₂³×C₅×D₃	C₂³	1	1	yes	characteristic
54	C₂²×C₃×C₄×C₅	—	2	2	no	—
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	yes	complemented
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	1	yes	characteristic
61	C₂×C₅×#67	C₂×C₄	1	8	yes	—
62	C₂×C₅×#67	C₂×C₄	1	4	yes	—
63	C₂²×C₅×Dic₃	—	2	4	no	—
64	C₂²×C₅×Dic₃	—	2	4	no	—
65	C₂²×C₅×Dic₃	C₂×C₄	1	8	yes	complemented
66	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
67	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
68	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
69	C₂²×C₅×Dic₃	C₂³	1	1	yes	characteristic
70	C₂²×C₅×Dic₃	C₂³	1	2	yes	—
71	C₂×C₄×C₅×D₃	—	2	2	no	—
72	C₂×C₄×C₅×D₃	—	2	2	no	—
73	C₂×C₄×C₅×D₃	—	2	4	no	—
74	C₂×C₄×C₅×D₃	—	2	4	no	—
75	C₂×C₄×C₅×D₃	C₂×C₄	1	8	yes	complemented
76	C₂×C₄×C₅×D₃	C₂×C₄	1	4	yes	complemented
77	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	complemented
78	C₃×C₄²×C₅	—	2	2	no	—
79	C₃×C₄²×C₅	—	2	2	no	—
80	C₅×#217	C₂×C₄	1	4	yes	complemented
81	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	8	yes	complemented
82	C₅×(C₂×D₃)⋊C₄	C₂×C₄	1	4	yes	complemented
83	C₅×Dic₃⋊C₄	C₂×C₄	1	8	yes	complemented
84	C₅×Dic₃⋊C₄	C₂×C₄	1	4	yes	complemented
85	C₄×C₅×Dic₃	—	2	2	no	—
86	C₄×C₅×Dic₃	—	2	4	no	—
87	C₄×C₅×Dic₃	—	2	4	no	—
88	C₄×C₅×Dic₃	—	2	4	no	—
89	C₄×C₅×Dic₃	C₂×C₄	1	8	yes	complemented
90	C₄×C₅×Dic₃	C₂×C₄	1	4	yes	complemented
91	C₄×C₅×Dic₃	D₄	1	4	yes	complemented
92	C₂×C₄×#67	C₂×C₅	1	1	yes	characteristic
93	C₂²×C₄×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
94	C₂×#67⋊C₄	C₂×C₅	1	2	yes	—
95	C₂×C₄²×D₃	C₂×C₅	1	1	yes	characteristic, complemented
96	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
97	Dic₃×C₂²⋊C₄	C₂×C₅	1	2	yes	complemented
98	C₄×(C₂×D₃)⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
99	C₄×Dic₃⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
100	C₄²×Dic₃	C₂×C₅	1	1	yes	characteristic, complemented
101	#4666	C₂×C₅	1	2	yes	complemented
102	#4649	C₂×C₅	1	2	yes	complemented
103	C₂²×C₅×D₄	—	3	1	no	—
104	C₂³×C₄×C₅	—	3	2	no	—
105	C₂³×C₄×C₅	—	3	2	no	—
106	C₂³×C₄×C₅	—	3	1	no	—
107	C₂³×C₄×C₅	C₂×D₃	1	1	yes	characteristic
108	C₄×C₅×D₄	—	3	8	no	—
109	C₄×C₅×D₄	—	3	16	no	—
110	C₂×C₅×C₄⋊C₄	—	3	1	no	—
111	C₂×C₅×C₄⋊C₄	—	3	2	no	—
112	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
113	C₂×C₅×C₂²⋊C₄	—	3	1	no	—
114	C₂×C₅×C₂²⋊C₄	—	3	2	no	—
115	C₂×C₅×C₂²⋊C₄	C₂×D₃	1	2	yes	—
116	C₂×C₄²×C₅	—	3	2	no	—
117	C₂×C₄²×C₅	—	3	1	no	—
118	C₂×C₄²×C₅	—	3	1	no	—
119	C₂×C₄²×C₅	—	3	2	no	—
120	C₂×C₄²×C₅	—	3	2	no	—
121	C₂×C₄²×C₅	—	3	2	no	—
122	C₂×C₄²×C₅	—	3	1	no	—
123	C₂×C₄²×C₅	—	6	4	no	—
124	C₂×C₄²×C₅	—	6	4	no	—
125	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
126	C₂×C₄²×C₅	C₂×D₃	1	1	yes	characteristic
127	C₅×#95	—	3	2	no	—
128	C₅×#95	—	3	2	no	—
129	C₅×#95	C₂×D₃	1	2	yes	—
130	C₄²×D₄	—	3	1	no	Sylow
131	C₂³×C₃×C₅	—	2	1	no	—
132	C₂³×C₃×C₅	—	2	2	no	—
133	C₂³×C₃×C₅	—	2	1	no	—
134	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
135	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
136	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
137	C₂²×C₅×D₃	—	2	1	no	—
138	C₂²×C₅×D₃	—	2	1	no	—
139	C₂²×C₅×D₃	—	2	2	no	—
140	C₂²×C₅×D₃	C₂²×C₄	1	4	yes	—
141	C₂²×C₅×D₃	C₂²×C₄	1	2	yes	—
142	C₂×C₃×C₄×C₅	—	2	1	no	—
143	C₂×C₃×C₄×C₅	—	2	2	no	—
144	C₂×C₃×C₄×C₅	—	2	2	no	—
145	C₂×C₃×C₄×C₅	—	2	2	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	8	no	—
149	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
150	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
151	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
152	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
153	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
154	C₂×C₃×C₄×C₅	#41	1	2	yes	—
155	C₅×#67	C₄²	1	16	yes	complemented
156	C₂×C₅×Dic₃	—	2	1	no	—
157	C₂×C₅×Dic₃	—	2	2	no	—
158	C₂×C₅×Dic₃	—	2	2	no	—
159	C₂×C₅×Dic₃	—	2	1	no	—
160	C₂×C₅×Dic₃	—	2	2	no	—
161	C₂×C₅×Dic₃	—	2	16	no	—
162	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
163	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
164	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
165	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
166	C₂×C₅×Dic₃	C₂²×C₄	1	2	yes	—
167	C₂×C₅×Dic₃	C₂²×C₄	1	4	yes	—
168	C₂×C₅×Dic₃	C₂×D₄	1	4	yes	—
169	C₂×C₅×Dic₃	#41	1	4	yes	—
170	C₄×C₅×D₃	—	2	8	no	—
171	C₄×C₅×D₃	—	2	16	no	—
172	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
173	C₂²×#67	C₂²×C₅	1	1	yes	characteristic
174	C₂³×Dic₃	C₂²×C₅	1	2	yes	—
175	C₂²×C₄×D₃	C₂²×C₅	1	2	yes	—
176	C₂²×C₄×D₃	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
178	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
179	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
180	C₂×#217	C₂²×C₅	1	1	yes	characteristic
181	C₄×#67	C₄×C₅	1	8	yes	complemented
182	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	1	yes	characteristic
183	C₂×(C₂×D₃)⋊C₄	C₂²×C₅	1	2	yes	—
184	C₂×Dic₃⋊C₄	C₂²×C₅	1	1	yes	characteristic
185	C₂×Dic₃⋊C₄	C₂²×C₅	1	2	yes	—
186	C₂×C₄×Dic₃	—	2	4	no	—
187	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
188	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
189	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
190	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
191	C₂×C₄×Dic₃	C₂²×C₅	1	2	yes	—
192	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
193	C₂×C₄×Dic₃	C₂²×C₅	1	1	yes	characteristic
194	#67⋊C₄	C₄×C₅	1	16	yes	direct product factor
195	C₄²×D₃	—	2	4	no	—
196	C₃×#95	C₂²×C₅	1	2	yes	—
197	C₃⋊#95	C₂²×C₅	1	2	yes	—
198	C₃⋊#95	C₂²×C₅	1	2	yes	—
199	C₂⁴×C₅	—	3	1	no	—
200	C₂⁴×C₅	C₂²×D₃	1	1	yes	characteristic
201	C₂×C₅×D₄	—	3	4	no	—
202	C₂×C₅×D₄	—	3	8	no	—
203	C₂²×C₄×C₅	—	2	2	no	—
204	C₂²×C₄×C₅	—	2	2	no	—
205	C₂²×C₄×C₅	—	3	2	no	—
206	C₂²×C₄×C₅	—	3	1	no	—
207	C₂²×C₄×C₅	—	3	8	no	—
208	C₂²×C₄×C₅	—	3	1	no	—
209	C₂²×C₄×C₅	—	3	1	no	—
210	C₂²×C₄×C₅	—	3	2	no	—
211	C₂²×C₄×C₅	—	3	8	no	—
212	C₂²×C₄×C₅	—	3	4	no	—
213	C₂²×C₄×C₅	—	6	4	no	—
214	C₂²×C₄×C₅	—	6	4	no	—
215	C₂²×C₄×C₅	—	6	4	no	—
216	C₂²×C₄×C₅	—	6	4	no	—
217	C₂²×C₄×C₅	—	6	2	no	—
218	C₂²×C₄×C₅	—	6	2	no	—
219	C₂²×C₄×C₅	C₄×D₃	1	4	yes	complemented
220	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
221	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
222	C₂²×C₄×C₅	C₂²×D₃	1	2	yes	—
223	C₂²×C₄×C₅	C₂²×D₃	1	1	yes	characteristic
224	C₅×C₄⋊C₄	—	3	4	no	—
225	C₅×C₄⋊C₄	—	3	8	no	—
226	C₅×C₂²⋊C₄	—	3	4	no	—
227	C₅×C₂²⋊C₄	—	3	4	no	—
228	C₅×C₂²⋊C₄	—	3	8	no	—
229	C₅×C₂²⋊C₄	C₄×D₃	1	8	yes	complemented
230	C₄²×C₅	—	2	2	no	—
231	C₄²×C₅	—	2	2	no	—
232	C₄²×C₅	—	3	8	no	—
233	C₄²×C₅	—	3	4	no	—
234	C₄²×C₅	—	3	4	no	—
235	C₄²×C₅	—	6	4	no	—
236	C₄²×C₅	—	6	4	no	—
237	C₄²×C₅	—	6	4	no	—
238	C₄²×C₅	—	6	2	no	—
239	C₂×C₄×D₄	—	3	1	no	—
240	C₂×C₄×D₄	—	3	2	no	—
241	C₂²×C₄²	—	3	1	no	—
242	C₂²×C₄²	—	3	1	no	—
243	C₄×C₄⋊C₄	—	3	1	no	—
244	C₄×C₄⋊C₄	—	3	2	no	—
245	C₄×C₂²⋊C₄	—	3	2	no	—
246	C₄×C₂²⋊C₄	—	3	1	no	—
247	C₄×C₂²⋊C₄	—	3	2	no	—
248	C₄×C₂²⋊C₄	C₅×D₃	1	1	yes	characteristic, complemented
249	C₄³	—	3	1	no	—
250	C₂²×C₃×C₅	—	2	4	no	—
251	C₂²×C₃×C₅	—	2	2	no	—
252	C₂²×C₃×C₅	—	2	2	no	—
253	C₂²×C₃×C₅	—	2	4	no	—
254	C₂²×C₃×C₅	C₂×C₄²	1	4	yes	complemented
255	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
256	C₂²×C₃×C₅	C₂³×C₄	1	2	yes	—
257	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
258	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
259	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
260	C₂×C₅×D₃	—	2	2	no	—
261	C₂×C₅×D₃	—	2	4	no	—
262	C₂×C₅×D₃	—	2	2	no	—
263	C₂×C₅×D₃	—	2	4	no	—
264	C₂×C₅×D₃	C₂×C₄²	1	4	yes	complemented
265	C₃×C₄×C₅	—	2	4	no	—
266	C₃×C₄×C₅	—	2	2	no	—
267	C₃×C₄×C₅	—	2	4	no	—
268	C₃×C₄×C₅	C₄×D₄	1	4	yes	complemented
269	C₅×Dic₃	—	2	2	no	—
270	C₅×Dic₃	—	2	4	no	—
271	C₅×Dic₃	—	2	2	no	—
272	C₅×Dic₃	C₂×C₄²	1	4	yes	complemented
273	C₅×Dic₃	C₄×D₄	1	8	yes	complemented
274	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
275	C₂³×D₃	C₂³×C₅	1	1	yes	characteristic
276	C₂²×C₃×C₄	—	2	2	no	—
277	C₂²×C₃×C₄	—	2	2	no	—
278	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	complemented
279	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
280	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
281	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
282	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
283	C₂×#67	C₂×C₄×C₅	1	8	yes	—
284	C₂×#67	C₂×C₄×C₅	1	4	yes	—
285	C₂²×Dic₃	—	2	4	no	—
286	C₂²×Dic₃	—	2	4	no	—
287	C₂²×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
288	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
289	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
290	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
291	C₂²×Dic₃	C₂³×C₅	1	1	yes	characteristic
292	C₂²×Dic₃	C₂³×C₅	1	2	yes	—
293	C₂×C₄×D₃	—	2	2	no	—
294	C₂×C₄×D₃	—	2	2	no	—
295	C₂×C₄×D₃	—	2	4	no	—
296	C₂×C₄×D₃	—	2	4	no	—
297	C₂×C₄×D₃	C₂×C₄×C₅	1	8	yes	complemented
298	C₂×C₄×D₃	C₂×C₄×C₅	1	4	yes	complemented
299	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
300	C₃×C₄²	—	2	2	no	—
301	C₃×C₄²	—	2	2	no	—
302	#217	C₂×C₄×C₅	1	4	yes	complemented
303	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
304	(C₂×D₃)⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
305	Dic₃⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
306	Dic₃⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
307	C₄×Dic₃	—	2	2	no	—
308	C₄×Dic₃	—	2	4	no	—
309	C₄×Dic₃	—	2	4	no	—
310	C₄×Dic₃	—	2	4	no	—
311	C₄×Dic₃	C₂×C₄×C₅	1	8	yes	complemented
312	C₄×Dic₃	C₂×C₄×C₅	1	4	yes	complemented
313	C₄×Dic₃	C₅×D₄	1	4	yes	complemented
314	C₂³×C₅	—	2	1	no	—
315	C₂³×C₅	—	2	1	no	—
316	C₂³×C₅	—	2	2	no	—
317	C₂³×C₅	—	3	2	no	—
318	C₂³×C₅	—	3	4	no	—
319	C₂³×C₅	—	6	1	no	—
320	C₂³×C₅	—	6	1	no	—
321	C₂³×C₅	—	6	2	no	—
322	C₂³×C₅	C₂×C₄×D₃	1	2	yes	—
323	C₂³×C₅	C₂×C₄×D₃	1	4	yes	—
324	C₂³×C₅	C₂³×D₃	1	1	yes	characteristic
325	C₅×D₄	—	3	16	no	—
326	C₂×C₄×C₅	—	2	2	no	—
327	C₂×C₄×C₅	—	2	1	no	—
328	C₂×C₄×C₅	—	2	2	no	—
329	C₂×C₄×C₅	—	2	1	no	—
330	C₂×C₄×C₅	—	2	2	no	—
331	C₂×C₄×C₅	—	2	2	no	—
332	C₂×C₄×C₅	—	2	8	no	—
333	C₂×C₄×C₅	—	3	2	no	—
334	C₂×C₄×C₅	—	3	4	no	—
335	C₂×C₄×C₅	—	3	4	no	—
336	C₂×C₄×C₅	—	3	4	no	—
337	C₂×C₄×C₅	—	3	4	no	—
338	C₂×C₄×C₅	—	3	2	no	—
339	C₂×C₄×C₅	—	3	2	no	—
340	C₂×C₄×C₅	—	3	4	no	—
341	C₂×C₄×C₅	—	6	16	no	—
342	C₂×C₄×C₅	—	6	16	no	—
343	C₂×C₄×C₅	—	6	1	no	—
344	C₂×C₄×C₅	—	6	2	no	—
345	C₂×C₄×C₅	—	6	1	no	—
346	C₂×C₄×C₅	—	6	2	no	—
347	C₂×C₄×C₅	—	6	2	no	—
348	C₂×C₄×C₅	—	6	8	no	—
349	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
350	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
351	C₂×C₄×C₅	C₂×C₄×D₃	1	4	yes	—
352	C₂×C₄×C₅	C₂×C₄×D₃	1	2	yes	—
353	C₂×C₄×C₅	D₃×D₄	1	2	yes	—
354	C₂×C₄×C₅	#237	1	2	yes	—
355	C₂²×D₄	—	3	1	no	—
356	C₂³×C₄	—	3	2	no	—
357	C₂³×C₄	—	3	2	no	—
358	C₂³×C₄	—	3	1	no	—
359	C₂³×C₄	C₂×C₅×D₃	1	1	yes	characteristic
360	C₄×D₄	—	3	8	no	—
361	C₄×D₄	—	3	16	no	—
362	C₂×C₄⋊C₄	—	3	2	no	—
363	C₂×C₄⋊C₄	—	3	1	no	—
364	C₂×C₂²⋊C₄	—	3	1	no	—
365	C₂×C₂²⋊C₄	—	3	1	no	—
366	C₂×C₂²⋊C₄	—	3	2	no	—
367	C₂×C₂²⋊C₄	C₂×C₅×D₃	1	2	yes	—
368	C₂×C₄²	—	3	2	no	—
369	C₂×C₄²	—	3	1	no	—
370	C₂×C₄²	—	3	1	no	—
371	C₂×C₄²	—	3	2	no	—
372	C₂×C₄²	—	3	2	no	—
373	C₂×C₄²	—	3	2	no	—
374	C₂×C₄²	—	3	1	no	—
375	C₂×C₄²	—	6	4	no	—
376	C₂×C₄²	—	6	4	no	—
377	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
378	C₂×C₄²	C₂×C₅×D₃	1	1	yes	characteristic
379	#95	—	3	2	no	—
380	#95	—	3	2	no	—
381	#95	C₂×C₅×D₃	1	2	yes	—
382	C₂×C₃×C₅	—	2	4	no	—
383	C₂×C₃×C₅	C₂²×C₄²	1	1	yes	characteristic
384	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
385	C₂×C₃×C₅	C₂×C₄×D₄	1	2	yes	—
386	C₂×C₃×C₅	C₄×#41	1	1	yes	characteristic
387	C₂×C₃×C₅	C₄×#41	1	2	yes	—
388	C₅×D₃	—	2	4	no	—
389	C₂³×C₃	—	2	1	no	—
390	C₂³×C₃	—	2	2	no	—
391	C₂³×C₃	—	2	1	no	—
392	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
393	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
394	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
395	C₂²×D₃	—	2	1	no	—
396	C₂²×D₃	—	2	1	no	—
397	C₂²×D₃	—	2	2	no	—
398	C₂²×D₃	C₂²×C₄×C₅	1	4	yes	—
399	C₂²×D₃	C₂²×C₄×C₅	1	2	yes	—
400	C₂×C₃×C₄	—	2	1	no	—
401	C₂×C₃×C₄	—	2	2	no	—
402	C₂×C₃×C₄	—	2	2	no	—
403	C₂×C₃×C₄	—	2	2	no	—
404	C₂×C₃×C₄	—	2	2	no	—
405	C₂×C₃×C₄	—	2	1	no	—
406	C₂×C₃×C₄	—	2	8	no	—
407	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
408	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
409	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
410	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
411	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
412	C₂×C₃×C₄	C₅×#41	1	2	yes	—
413	#67	C₄²×C₅	1	16	yes	complemented
414	C₂×Dic₃	—	2	1	no	—
415	C₂×Dic₃	—	2	2	no	—
416	C₂×Dic₃	—	2	2	no	—
417	C₂×Dic₃	—	2	1	no	—
418	C₂×Dic₃	—	2	2	no	—
419	C₂×Dic₃	—	2	16	no	—
420	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
421	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
422	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
423	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
424	C₂×Dic₃	C₂²×C₄×C₅	1	2	yes	—
425	C₂×Dic₃	C₂²×C₄×C₅	1	4	yes	—
426	C₂×Dic₃	C₂×C₅×D₄	1	4	yes	—
427	C₂×Dic₃	C₅×#41	1	4	yes	—
428	C₄×D₃	—	2	8	no	—
429	C₄×D₃	—	2	16	no	—
430	C₂²×C₅	—	2	2	no	—
431	C₂²×C₅	—	2	2	no	—
432	C₂²×C₅	—	2	4	no	—
433	C₂²×C₅	—	2	4	no	—
434	C₂²×C₅	—	3	4	no	—
435	C₂²×C₅	—	6	2	no	—
436	C₂²×C₅	—	6	2	no	—
437	C₂²×C₅	—	6	4	no	—
438	C₂²×C₅	—	6	4	no	—
439	C₂²×C₅	C₄²×D₃	1	4	yes	complemented
440	C₂²×C₅	C₂²×C₄×D₃	1	1	yes	characteristic
441	C₂²×C₅	C₂²×C₄×D₃	1	2	yes	—
442	C₂²×C₅	C₂×D₃×D₄	1	1	yes	characteristic
443	C₂²×C₅	C₂×#237	1	1	yes	characteristic
444	C₂²×C₅	D₃×#41	1	2	yes	—
445	C₄×C₅	—	2	2	no	—
446	C₄×C₅	—	2	4	no	—
447	C₄×C₅	—	2	4	no	—
448	C₄×C₅	—	3	4	no	—
449	C₄×C₅	—	3	8	no	—
450	C₄×C₅	—	6	2	no	—
451	C₄×C₅	—	6	2	no	—
452	C₄×C₅	—	6	4	no	—
453	C₄×C₅	#67⋊C₄	1	4	yes	direct product factor
454	C₂⁴	—	3	1	no	—
455	C₂⁴	C₂²×C₅×D₃	1	1	yes	characteristic
456	C₂×D₄	—	3	4	no	—
457	C₂×D₄	—	3	8	no	—
458	C₂²×C₄	—	2	2	no	—
459	C₂²×C₄	—	2	2	no	—
460	C₂²×C₄	—	3	2	no	—
461	C₂²×C₄	—	3	1	no	—
462	C₂²×C₄	—	3	8	no	—
463	C₂²×C₄	—	3	1	no	—
464	C₂²×C₄	—	3	1	no	—
465	C₂²×C₄	—	3	2	no	—
466	C₂²×C₄	—	3	8	no	—
467	C₂²×C₄	—	3	4	no	—
468	C₂²×C₄	—	6	4	no	—
469	C₂²×C₄	—	6	4	no	—
470	C₂²×C₄	—	6	4	no	—
471	C₂²×C₄	—	6	4	no	—
472	C₂²×C₄	—	6	2	no	—
473	C₂²×C₄	—	6	2	no	—
474	C₂²×C₄	C₄×C₅×D₃	1	4	yes	complemented
475	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
476	C₂²×C₄	C₂²×C₅×D₃	1	2	yes	—
477	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
478	C₂²×C₄	C₂²×C₅×D₃	1	1	yes	characteristic
479	C₄⋊C₄	—	3	4	no	—
480	C₄⋊C₄	—	3	8	no	—
481	C₂²⋊C₄	—	3	4	no	—
482	C₂²⋊C₄	—	3	4	no	—
483	C₂²⋊C₄	—	3	8	no	—
484	C₂²⋊C₄	C₄×C₅×D₃	1	8	yes	complemented
485	C₄²	—	2	2	no	—
486	C₄²	—	2	2	no	—
487	C₄²	—	3	8	no	—
488	C₄²	—	3	4	no	—
489	C₄²	—	3	4	no	—
490	C₄²	—	6	4	no	—
491	C₄²	—	6	4	no	—
492	C₄²	—	6	4	no	—
493	C₄²	—	6	2	no	—
494	C₃×C₅	C₄²×D₄	1	1	yes	characteristic, complemented, Hall
495	C₂²×C₃	—	2	4	no	—
496	C₂²×C₃	—	2	2	no	—
497	C₂²×C₃	—	2	2	no	—
498	C₂²×C₃	—	2	4	no	—
499	C₂²×C₃	C₂×C₄²×C₅	1	4	yes	complemented
500	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
501	C₂²×C₃	C₂³×C₄×C₅	1	2	yes	—
502	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
503	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
504	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
505	C₂×D₃	—	2	2	no	—
506	C₂×D₃	—	2	4	no	—
507	C₂×D₃	—	2	2	no	—
508	C₂×D₃	—	2	4	no	—
509	C₂×D₃	C₂×C₄²×C₅	1	4	yes	complemented
510	C₃×C₄	—	2	4	no	—
511	C₃×C₄	—	2	2	no	—
512	C₃×C₄	—	2	4	no	—
513	C₃×C₄	C₄×C₅×D₄	1	4	yes	complemented
514	Dic₃	—	2	2	no	—
515	Dic₃	—	2	4	no	—
516	Dic₃	—	2	2	no	—
517	Dic₃	C₂×C₄²×C₅	1	4	yes	complemented
518	Dic₃	C₄×C₅×D₄	1	8	yes	complemented
519	C₂×C₅	—	2	4	no	—
520	C₂×C₅	—	6	4	no	—
521	C₂×C₅	C₂×C₄²×D₃	1	1	yes	characteristic
522	C₂×C₅	C₂×#67⋊C₄	1	1	yes	characteristic
523	C₂×C₅	#5522	1	1	yes	characteristic
524	C₂×C₅	C₄×#237	1	2	yes	—
525	C₂×C₅	C₄×D₃×D₄	1	2	yes	—
526	C₂³	—	2	1	no	—
527	C₂³	—	2	1	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	3	2	no	—
530	C₂³	—	3	4	no	—
531	C₂³	—	6	1	no	—
532	C₂³	—	6	1	no	—
533	C₂³	—	6	2	no	—
534	C₂³	C₂×C₄×C₅×D₃	1	2	yes	—
535	C₂³	C₂×C₄×C₅×D₃	1	4	yes	—
536	C₂³	C₂³×C₅×D₃	1	1	yes	characteristic
537	D₄	—	3	16	no	—
538	C₂×C₄	—	2	2	no	—
539	C₂×C₄	—	2	1	no	—
540	C₂×C₄	—	2	2	no	—
541	C₂×C₄	—	2	1	no	—
542	C₂×C₄	—	2	2	no	—
543	C₂×C₄	—	2	2	no	—
544	C₂×C₄	—	2	8	no	—
545	C₂×C₄	—	3	2	no	—
546	C₂×C₄	—	3	4	no	—
547	C₂×C₄	—	3	4	no	—
548	C₂×C₄	—	3	4	no	—
549	C₂×C₄	—	3	4	no	—
550	C₂×C₄	—	3	2	no	—
551	C₂×C₄	—	3	2	no	—
552	C₂×C₄	—	3	4	no	—
553	C₂×C₄	—	6	16	no	—
554	C₂×C₄	—	6	16	no	—
555	C₂×C₄	—	6	1	no	—
556	C₂×C₄	—	6	2	no	—
557	C₂×C₄	—	6	1	no	—
558	C₂×C₄	—	6	2	no	—
559	C₂×C₄	—	6	2	no	—
560	C₂×C₄	—	6	8	no	—
561	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
562	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
563	C₂×C₄	C₂×C₄×C₅×D₃	1	4	yes	—
564	C₂×C₄	C₂×C₄×C₅×D₃	1	2	yes	—
565	C₂×C₄	C₅×D₃×D₄	1	2	yes	—
566	C₂×C₄	C₅×#237	1	2	yes	—
567	C₂×C₃	—	2	4	no	—
568	C₂×C₃	C₂²×C₄²×C₅	1	1	yes	characteristic
569	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
570	C₂×C₃	C₂×C₄×C₅×D₄	1	2	yes	—
571	C₂×C₃	C₄×C₅×#41	1	1	yes	characteristic
572	C₂×C₃	C₄×C₅×#41	1	2	yes	—
573	D₃	—	2	4	no	—
574	C₅	C₄×#67⋊C₄	1	1	yes	characteristic, direct product factor, Sylow
575	C₂²	—	2	2	no	—
576	C₂²	—	2	2	no	—
577	C₂²	—	2	4	no	—
578	C₂²	—	2	4	no	—
579	C₂²	—	3	4	no	—
580	C₂²	—	6	2	no	—
581	C₂²	—	6	2	no	—
582	C₂²	—	6	4	no	—
583	C₂²	—	6	4	no	—
584	C₂²	C₄²×C₅×D₃	1	4	yes	complemented
585	C₂²	C₂²×C₄×C₅×D₃	1	1	yes	characteristic
586	C₂²	C₂²×C₄×C₅×D₃	1	2	yes	—
587	C₂²	C₂×C₅×D₃×D₄	1	1	yes	characteristic
588	C₂²	C₂×C₅×#237	1	1	yes	characteristic
589	C₂²	C₅×D₃×#41	1	2	yes	—
590	C₄	—	2	2	no	—
591	C₄	—	2	4	no	—
592	C₄	—	2	4	no	—
593	C₄	—	3	4	no	—
594	C₄	—	3	8	no	—
595	C₄	—	6	2	no	—
596	C₄	—	6	2	no	—
597	C₄	—	6	4	no	—
598	C₄	C₅×#67⋊C₄	1	4	yes	direct product factor
599	C₃	C₄²×C₅×D₄	1	1	yes	characteristic, complemented, Sylow
600	C₂	—	2	4	no	—
601	C₂	—	6	4	no	—
602	C₂	C₂×C₄²×C₅×D₃	1	1	yes	characteristic
603	C₂	C₂×C₅×#67⋊C₄	1	1	yes	characteristic
604	C₂	C₅×#5522	1	1	yes	characteristic
605	C₂	C₄×C₅×#237	1	2	yes	—
606	C₂	C₄×C₅×D₃×D₄	1	2	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	C₂²×C₅×#67	C₂²
cosocle	C₂³×C₃	C₂⁴×C₅
hypercenter	C₄×C₅×C₂²⋊C₄	D₃
hypocenter	C₃	C₄²×C₅×D₄
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
2. C₂²×C₄×C₅×Dic₃	C₂	semidirect
4. C₂×C₄²×C₅×D₃	C₂	semidirect
5. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
6. C₅×Dic₃×C₂²⋊C₄	C₂	semidirect
7. C₄×C₅×(C₂×D₃)⋊C₄	C₂	semidirect
8. C₄×C₅×Dic₃⋊C₄	C₂	semidirect
9. C₄²×C₅×Dic₃	C₂	semidirect
10. C₅×#4666	C₂	semidirect
11. C₅×#4649	C₂	semidirect
22. C₄×C₅×#67	C₄	semidirect
35. C₅×#67⋊C₄	C₄	direct (N × H)
40. C₄×#67⋊C₄	C₅	direct (N × H)
50. C₄×C₅×C₂²⋊C₄	D₃	semidirect
56. C₂²×C₃×C₄×C₅	C₂×C₄	semidirect
65. C₂²×C₅×Dic₃	C₂×C₄	semidirect
75. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
76. C₂×C₄×C₅×D₃	C₂×C₄	semidirect
77. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
80. C₅×#217	C₂×C₄	semidirect
81. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
82. C₅×(C₂×D₃)⋊C₄	C₂×C₄	semidirect
83. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
84. C₅×Dic₃⋊C₄	C₂×C₄	semidirect
89. C₄×C₅×Dic₃	C₂×C₄	semidirect
90. C₄×C₅×Dic₃	C₂×C₄	semidirect
91. C₄×C₅×Dic₃	D₄	semidirect
93. C₂²×C₄×Dic₃	C₂×C₅	semidirect
95. C₂×C₄²×D₃	C₂×C₅	semidirect
96. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
97. Dic₃×C₂²⋊C₄	C₂×C₅	semidirect
98. C₄×(C₂×D₃)⋊C₄	C₂×C₅	semidirect
99. C₄×Dic₃⋊C₄	C₂×C₅	semidirect
100. C₄²×Dic₃	C₂×C₅	semidirect
101. #4666	C₂×C₅	semidirect
102. #4649	C₂×C₅	semidirect
155. C₅×#67	C₄²	semidirect
181. C₄×#67	C₄×C₅	semidirect
194. #67⋊C₄	C₄×C₅	direct (N × H)
219. C₂²×C₄×C₅	C₄×D₃	semidirect
229. C₅×C₂²⋊C₄	C₄×D₃	semidirect
248. C₄×C₂²⋊C₄	C₅×D₃	semidirect
254. C₂²×C₃×C₅	C₂×C₄²	semidirect
264. C₂×C₅×D₃	C₂×C₄²	semidirect
268. C₃×C₄×C₅	C₄×D₄	semidirect
272. C₅×Dic₃	C₂×C₄²	semidirect
273. C₅×Dic₃	C₄×D₄	semidirect
278. C₂²×C₃×C₄	C₂×C₄×C₅	semidirect
287. C₂²×Dic₃	C₂×C₄×C₅	semidirect
297. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
298. C₂×C₄×D₃	C₂×C₄×C₅	semidirect
299. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
302. #217	C₂×C₄×C₅	semidirect
303. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
304. (C₂×D₃)⋊C₄	C₂×C₄×C₅	semidirect
305. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
306. Dic₃⋊C₄	C₂×C₄×C₅	semidirect
311. C₄×Dic₃	C₂×C₄×C₅	semidirect
312. C₄×Dic₃	C₂×C₄×C₅	semidirect
313. C₄×Dic₃	C₅×D₄	semidirect
413. #67	C₄²×C₅	semidirect
439. C₂²×C₅	C₄²×D₃	semidirect
453. C₄×C₅	#67⋊C₄	direct (N × H)
474. C₂²×C₄	C₄×C₅×D₃	semidirect
484. C₂²⋊C₄	C₄×C₅×D₃	semidirect
494. C₃×C₅	C₄²×D₄	semidirect
499. C₂²×C₃	C₂×C₄²×C₅	semidirect
509. C₂×D₃	C₂×C₄²×C₅	semidirect
513. C₃×C₄	C₄×C₅×D₄	semidirect
517. Dic₃	C₂×C₄²×C₅	semidirect
518. Dic₃	C₄×C₅×D₄	semidirect
574. C₅	C₄×#67⋊C₄	direct (N × H)
584. C₂²	C₄²×C₅×D₃	semidirect
598. C₄	C₅×#67⋊C₄	direct (N × H)
599. C₃	C₄²×C₅×D₄	semidirect

Maximal subgroups

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

subgroup	index
C₂×C₄×C₅×#67	2
C₂²×C₄×C₅×Dic₃	2
C₂×C₅×#67⋊C₄	2
C₂×C₄²×C₅×D₃	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×Dic₃×C₂²⋊C₄	2
C₄×C₅×(C₂×D₃)⋊C₄	2
C₄×C₅×Dic₃⋊C₄	2
C₄²×C₅×Dic₃	2
C₅×#4666	2
C₅×#4649	2
C₄²×C₅×D₄	3
C₄×#67⋊C₄	5

Subgroups — C4×C5×#67⋊C4 #14319552

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×C₅×#67⋊C₄ #14319552