Subgroups — C₃×C₄×C₅×#124 #14275337

Order 1920.

1304 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×#124	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₃×C₄×C₅×D₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#390	C₂	1	1	yes	maximal, characteristic
6	C₃×C₅×#388	C₂	1	4	yes	maximal, complemented
7	C₃×C₅×#382	C₂	1	1	yes	maximal, characteristic, complemented
8	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	4	yes	maximal, complemented
9	C₃×C₄³×C₅	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×C₅×#124	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
11	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
12	C₂²×C₃×C₅×D₄	C₂²	1	1	yes	characteristic
13	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
14	C₃×C₅×#124	C₄	1	8	yes	direct product factor
15	C₃×C₄×C₅×Q₈	—	2	4	no	—
16	C₃×C₄×C₅×D₄	—	2	4	no	—
17	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
21	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
22	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	4	yes	—
23	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
24	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
25	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
26	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
27	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
28	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
29	C₃×C₅×#95	C₂²	1	4	yes	—
30	C₃×C₅×#95	C₂²	1	4	yes	—
31	C₃×C₄×#124	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
32	C₂×C₅×#124	C₂×C₃	1	1	yes	characteristic
33	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
34	C₂×C₄×C₅×D₄	C₂×C₃	1	1	yes	characteristic
35	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
36	C₅×#390	C₂×C₃	1	1	yes	characteristic
37	C₅×#388	C₂×C₃	1	4	yes	complemented
38	C₅×#382	C₂×C₃	1	1	yes	characteristic, complemented
39	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	4	yes	complemented
40	C₄³×C₅	C₂×C₃	1	1	yes	characteristic, complemented
41	C₂⁴×C₃×C₅	C₂³	1	2	yes	—
42	C₂×C₃×C₅×Q₈	—	2	2	no	—
43	C₂×C₃×C₅×Q₈	—	2	2	no	—
44	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
45	C₂×C₃×C₅×D₄	—	2	2	no	—
46	C₂×C₃×C₅×D₄	—	2	2	no	—
47	C₂×C₃×C₅×D₄	C₂×C₄	1	4	yes	—
48	C₂²×C₃×C₄×C₅	—	2	4	no	—
49	C₂²×C₃×C₄×C₅	—	2	8	no	—
50	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
51	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
52	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
53	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
54	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
55	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
56	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
57	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
58	C₃×C₅×C₄⋊C₄	—	2	2	no	—
59	C₃×C₅×C₄⋊C₄	—	2	4	no	—
60	C₃×C₅×C₄⋊C₄	—	2	2	no	—
61	C₃×C₅×C₂²⋊C₄	—	2	4	no	—
62	C₃×C₅×C₂²⋊C₄	—	2	8	no	—
63	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	16	yes	complemented
64	C₃×C₄²×C₅	—	2	4	no	—
65	C₃×C₄²×C₅	—	2	4	no	—
66	C₃×C₄²×C₅	—	2	2	no	—
67	C₃×C₄²×C₅	—	2	4	no	—
68	C₃×C₄²×C₅	C₂×C₄	1	4	yes	complemented
69	C₃×C₄²×C₅	D₄	1	4	yes	—
70	C₂×C₃×#124	C₂×C₅	1	1	yes	characteristic
71	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
72	C₂×C₃×C₄×D₄	C₂×C₅	1	1	yes	characteristic
73	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
74	C₃×#390	C₂×C₅	1	1	yes	characteristic
75	C₃×#388	C₂×C₅	1	4	yes	complemented
76	C₃×#382	C₂×C₅	1	1	yes	characteristic, complemented
77	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	4	yes	complemented
78	C₃×C₄³	C₂×C₅	1	1	yes	characteristic, complemented
79	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
80	C₂²×C₅×D₄	C₂²×C₃	1	1	yes	characteristic
81	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
82	C₅×#124	C₃×C₄	1	8	yes	direct product factor
83	C₄×C₅×Q₈	—	2	4	no	—
84	C₄×C₅×D₄	—	2	4	no	—
85	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
86	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
87	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
88	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
89	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
90	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	4	yes	—
91	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
92	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
93	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
94	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
95	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
96	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
97	C₅×#95	C₂²×C₃	1	4	yes	—
98	C₅×#95	C₂²×C₃	1	4	yes	—
99	C₄×#124	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
100	C₂³×C₃×C₅	—	2	2	no	—
101	C₂³×C₃×C₅	—	2	4	no	—
102	C₂³×C₃×C₅	—	2	4	no	—
103	C₂³×C₃×C₅	—	2	2	no	—
104	C₂³×C₃×C₅	C₂²×C₄	1	4	yes	—
105	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
106	C₃×C₅×Q₈	—	2	8	no	—
107	C₃×C₅×D₄	—	2	8	no	—
108	C₂×C₃×C₄×C₅	—	2	2	no	—
109	C₂×C₃×C₄×C₅	—	2	2	no	—
110	C₂×C₃×C₄×C₅	—	2	2	no	—
111	C₂×C₃×C₄×C₅	—	2	2	no	—
112	C₂×C₃×C₄×C₅	—	2	2	no	—
113	C₂×C₃×C₄×C₅	—	2	2	no	—
114	C₂×C₃×C₄×C₅	—	2	2	no	—
115	C₂×C₃×C₄×C₅	—	2	2	no	—
116	C₂×C₃×C₄×C₅	—	2	2	no	—
117	C₂×C₃×C₄×C₅	—	2	4	no	—
118	C₂×C₃×C₄×C₅	—	2	4	no	—
119	C₂×C₃×C₄×C₅	—	4	8	no	—
120	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
121	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
122	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
123	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
124	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
125	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
126	C₂×C₃×C₄×C₅	#41	1	4	yes	—
127	C₂×C₃×C₄×C₅	#41	1	2	yes	—
128	C₂×C₃×C₄×C₅	#41	1	4	yes	—
129	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
130	C₂²×C₃×D₄	C₂²×C₅	1	1	yes	characteristic
131	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
132	C₃×#124	C₄×C₅	1	8	yes	direct product factor
133	C₃×C₄×Q₈	—	2	4	no	—
134	C₃×C₄×D₄	—	2	4	no	—
135	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
136	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
137	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
138	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
139	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
140	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	4	yes	—
141	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
142	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
143	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
144	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
145	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
146	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
147	C₃×#95	C₂²×C₅	1	4	yes	—
148	C₃×#95	C₂²×C₅	1	4	yes	—
149	C₂⁴×C₅	C₂³×C₃	1	2	yes	—
150	C₂×C₅×Q₈	—	2	2	no	—
151	C₂×C₅×Q₈	—	2	2	no	—
152	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
153	C₂×C₅×D₄	—	2	2	no	—
154	C₂×C₅×D₄	—	2	2	no	—
155	C₂×C₅×D₄	C₂×C₃×C₄	1	4	yes	—
156	C₂²×C₄×C₅	—	2	4	no	—
157	C₂²×C₄×C₅	—	2	8	no	—
158	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
159	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
160	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
161	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
162	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
163	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
164	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
165	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
166	C₅×C₄⋊C₄	—	2	2	no	—
167	C₅×C₄⋊C₄	—	2	4	no	—
168	C₅×C₄⋊C₄	—	2	2	no	—
169	C₅×C₂²⋊C₄	—	2	4	no	—
170	C₅×C₂²⋊C₄	—	2	8	no	—
171	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	16	yes	complemented
172	C₄²×C₅	—	2	4	no	—
173	C₄²×C₅	—	2	4	no	—
174	C₄²×C₅	—	2	2	no	—
175	C₄²×C₅	—	2	4	no	—
176	C₄²×C₅	C₂×C₃×C₄	1	4	yes	complemented
177	C₄²×C₅	C₃×D₄	1	4	yes	—
178	C₂×#124	C₂×C₃×C₅	1	1	yes	characteristic
179	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
180	C₂×C₄×D₄	C₂×C₃×C₅	1	1	yes	characteristic
181	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
182	#390	C₂×C₃×C₅	1	1	yes	characteristic
183	#388	C₂×C₃×C₅	1	4	yes	complemented
184	#382	C₂×C₃×C₅	1	1	yes	characteristic, complemented
185	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	4	yes	complemented
186	C₄³	C₂×C₃×C₅	1	1	yes	characteristic, complemented
187	C₂²×C₃×C₅	—	2	4	no	—
188	C₂²×C₃×C₅	—	2	8	no	—
189	C₂²×C₃×C₅	—	4	2	no	—
190	C₂²×C₃×C₅	—	4	4	no	—
191	C₂²×C₃×C₅	—	4	2	no	—
192	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
193	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
194	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
195	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
196	C₂²×C₃×C₅	C₂×#41	1	2	yes	—
197	C₃×C₄×C₅	—	2	4	no	—
198	C₃×C₄×C₅	—	2	4	no	—
199	C₃×C₄×C₅	—	2	4	no	—
200	C₃×C₄×C₅	—	2	2	no	—
201	C₃×C₄×C₅	—	4	2	no	—
202	C₃×C₄×C₅	—	4	2	no	—
203	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
204	C₃×C₄×C₅	#124	1	4	yes	direct product factor
205	C₂⁴×C₃	C₂³×C₅	1	2	yes	—
206	C₂×C₃×Q₈	—	2	2	no	—
207	C₂×C₃×Q₈	—	2	2	no	—
208	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
209	C₂×C₃×D₄	—	2	2	no	—
210	C₂×C₃×D₄	—	2	2	no	—
211	C₂×C₃×D₄	C₂×C₄×C₅	1	4	yes	—
212	C₂²×C₃×C₄	—	2	4	no	—
213	C₂²×C₃×C₄	—	2	8	no	—
214	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
215	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
216	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
217	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
218	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
219	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
220	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
221	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
222	C₃×C₄⋊C₄	—	2	2	no	—
223	C₃×C₄⋊C₄	—	2	4	no	—
224	C₃×C₄⋊C₄	—	2	2	no	—
225	C₃×C₂²⋊C₄	—	2	4	no	—
226	C₃×C₂²⋊C₄	—	2	8	no	—
227	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	16	yes	complemented
228	C₃×C₄²	—	2	4	no	—
229	C₃×C₄²	—	2	4	no	—
230	C₃×C₄²	—	2	2	no	—
231	C₃×C₄²	—	2	4	no	—
232	C₃×C₄²	C₂×C₄×C₅	1	4	yes	complemented
233	C₃×C₄²	C₅×D₄	1	4	yes	—
234	C₂³×C₅	—	2	2	no	—
235	C₂³×C₅	—	2	4	no	—
236	C₂³×C₅	—	2	4	no	—
237	C₂³×C₅	—	2	2	no	—
238	C₂³×C₅	C₂²×C₃×C₄	1	4	yes	—
239	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
240	C₅×Q₈	—	2	8	no	—
241	C₅×D₄	—	2	8	no	—
242	C₂×C₄×C₅	—	2	2	no	—
243	C₂×C₄×C₅	—	2	2	no	—
244	C₂×C₄×C₅	—	2	2	no	—
245	C₂×C₄×C₅	—	2	2	no	—
246	C₂×C₄×C₅	—	2	2	no	—
247	C₂×C₄×C₅	—	2	2	no	—
248	C₂×C₄×C₅	—	2	2	no	—
249	C₂×C₄×C₅	—	2	2	no	—
250	C₂×C₄×C₅	—	2	2	no	—
251	C₂×C₄×C₅	—	2	4	no	—
252	C₂×C₄×C₅	—	2	4	no	—
253	C₂×C₄×C₅	—	4	8	no	—
254	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
255	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
256	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
257	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
258	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
259	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
260	C₂×C₄×C₅	C₃×#41	1	4	yes	—
261	C₂×C₄×C₅	C₃×#41	1	2	yes	—
262	C₂×C₄×C₅	C₃×#41	1	4	yes	—
263	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
264	C₂²×D₄	C₂²×C₃×C₅	1	1	yes	characteristic
265	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
266	#124	C₃×C₄×C₅	1	8	yes	direct product factor
267	C₄×Q₈	—	2	4	no	—
268	C₄×D₄	—	2	4	no	—
269	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
270	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
271	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
272	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
273	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
274	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	4	yes	—
275	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
276	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
277	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
278	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
279	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
280	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
281	#95	C₂²×C₃×C₅	1	4	yes	—
282	#95	C₂²×C₃×C₅	1	4	yes	—
283	C₂×C₃×C₅	—	4	4	no	—
284	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
285	C₂×C₃×C₅	C₄×#41	1	2	yes	—
286	C₂×C₃×C₅	C₂×#124	1	1	yes	characteristic
287	C₂×C₃×C₅	#529	1	2	yes	—
288	C₂×C₃×C₅	#532	1	1	yes	characteristic
289	C₂³×C₃	—	2	2	no	—
290	C₂³×C₃	—	2	4	no	—
291	C₂³×C₃	—	2	4	no	—
292	C₂³×C₃	—	2	2	no	—
293	C₂³×C₃	C₂²×C₄×C₅	1	4	yes	—
294	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
295	C₃×Q₈	—	2	8	no	—
296	C₃×D₄	—	2	8	no	—
297	C₂×C₃×C₄	—	2	2	no	—
298	C₂×C₃×C₄	—	2	2	no	—
299	C₂×C₃×C₄	—	2	2	no	—
300	C₂×C₃×C₄	—	2	2	no	—
301	C₂×C₃×C₄	—	2	2	no	—
302	C₂×C₃×C₄	—	2	2	no	—
303	C₂×C₃×C₄	—	2	2	no	—
304	C₂×C₃×C₄	—	2	2	no	—
305	C₂×C₃×C₄	—	2	2	no	—
306	C₂×C₃×C₄	—	2	4	no	—
307	C₂×C₃×C₄	—	2	4	no	—
308	C₂×C₃×C₄	—	4	8	no	—
309	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
310	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
311	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
312	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
313	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
314	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
315	C₂×C₃×C₄	C₅×#41	1	4	yes	—
316	C₂×C₃×C₄	C₅×#41	1	2	yes	—
317	C₂×C₃×C₄	C₅×#41	1	4	yes	—
318	C₂²×C₅	—	2	4	no	—
319	C₂²×C₅	—	2	8	no	—
320	C₂²×C₅	—	4	2	no	—
321	C₂²×C₅	—	4	4	no	—
322	C₂²×C₅	—	4	2	no	—
323	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
324	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
325	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
326	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
327	C₂²×C₅	C₂×C₃×#41	1	2	yes	—
328	C₄×C₅	—	2	4	no	—
329	C₄×C₅	—	2	4	no	—
330	C₄×C₅	—	2	4	no	—
331	C₄×C₅	—	2	2	no	—
332	C₄×C₅	—	4	2	no	—
333	C₄×C₅	—	4	2	no	—
334	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
335	C₄×C₅	C₃×#124	1	4	yes	direct product factor
336	C₂⁴	C₂³×C₃×C₅	1	2	yes	—
337	C₂×Q₈	—	2	2	no	—
338	C₂×Q₈	—	2	2	no	—
339	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
340	C₂×D₄	—	2	2	no	—
341	C₂×D₄	—	2	2	no	—
342	C₂×D₄	C₂×C₃×C₄×C₅	1	4	yes	—
343	C₂²×C₄	—	2	4	no	—
344	C₂²×C₄	—	2	8	no	—
345	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
346	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
347	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
348	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
349	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
350	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
351	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
352	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
353	C₄⋊C₄	—	2	2	no	—
354	C₄⋊C₄	—	2	4	no	—
355	C₄⋊C₄	—	2	2	no	—
356	C₂²⋊C₄	—	2	4	no	—
357	C₂²⋊C₄	—	2	8	no	—
358	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	16	yes	complemented
359	C₄²	—	2	4	no	—
360	C₄²	—	2	4	no	—
361	C₄²	—	2	2	no	—
362	C₄²	—	2	4	no	—
363	C₄²	C₂×C₃×C₄×C₅	1	4	yes	complemented
364	C₄²	C₃×C₅×D₄	1	4	yes	—
365	C₃×C₅	C₄×#124	1	1	yes	characteristic, direct product factor, Hall
366	C₂²×C₃	—	2	4	no	—
367	C₂²×C₃	—	2	8	no	—
368	C₂²×C₃	—	4	2	no	—
369	C₂²×C₃	—	4	4	no	—
370	C₂²×C₃	—	4	2	no	—
371	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
372	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
373	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
374	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
375	C₂²×C₃	C₂×C₅×#41	1	2	yes	—
376	C₃×C₄	—	2	4	no	—
377	C₃×C₄	—	2	4	no	—
378	C₃×C₄	—	2	4	no	—
379	C₃×C₄	—	2	2	no	—
380	C₃×C₄	—	4	2	no	—
381	C₃×C₄	—	4	2	no	—
382	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
383	C₃×C₄	C₅×#124	1	4	yes	direct product factor
384	C₂×C₅	—	4	4	no	—
385	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
386	C₂×C₅	C₃×C₄×#41	1	2	yes	—
387	C₂×C₅	C₂×C₃×#124	1	1	yes	characteristic
388	C₂×C₅	C₃×#529	1	2	yes	—
389	C₂×C₅	C₃×#532	1	1	yes	characteristic
390	C₂³	—	2	2	no	—
391	C₂³	—	2	4	no	—
392	C₂³	—	2	4	no	—
393	C₂³	—	2	2	no	—
394	C₂³	C₂²×C₃×C₄×C₅	1	4	yes	—
395	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
396	Q₈	—	2	8	no	—
397	D₄	—	2	8	no	—
398	C₂×C₄	—	2	2	no	—
399	C₂×C₄	—	2	2	no	—
400	C₂×C₄	—	2	2	no	—
401	C₂×C₄	—	2	2	no	—
402	C₂×C₄	—	2	2	no	—
403	C₂×C₄	—	2	2	no	—
404	C₂×C₄	—	2	2	no	—
405	C₂×C₄	—	2	2	no	—
406	C₂×C₄	—	2	2	no	—
407	C₂×C₄	—	2	4	no	—
408	C₂×C₄	—	2	4	no	—
409	C₂×C₄	—	4	8	no	—
410	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
411	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
412	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
413	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
414	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
415	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
416	C₂×C₄	C₃×C₅×#41	1	4	yes	—
417	C₂×C₄	C₃×C₅×#41	1	2	yes	—
418	C₂×C₄	C₃×C₅×#41	1	4	yes	—
419	C₂×C₃	—	4	4	no	—
420	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
421	C₂×C₃	C₄×C₅×#41	1	2	yes	—
422	C₂×C₃	C₂×C₅×#124	1	1	yes	characteristic
423	C₂×C₃	C₅×#529	1	2	yes	—
424	C₂×C₃	C₅×#532	1	1	yes	characteristic
425	C₅	C₃×C₄×#124	1	1	yes	characteristic, direct product factor, Sylow
426	C₂²	—	2	4	no	—
427	C₂²	—	2	8	no	—
428	C₂²	—	4	2	no	—
429	C₂²	—	4	4	no	—
430	C₂²	—	4	2	no	—
431	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
432	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
433	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
434	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
435	C₂²	C₂×C₃×C₅×#41	1	2	yes	—
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	2	no	—
440	C₄	—	4	2	no	—
441	C₄	—	4	2	no	—
442	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
443	C₄	C₃×C₅×#124	1	4	yes	direct product factor
444	C₃	C₄×C₅×#124	1	1	yes	characteristic, direct product factor, Sylow
445	C₂	—	4	4	no	—
446	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
447	C₂	C₃×C₄×C₅×#41	1	2	yes	—
448	C₂	C₂×C₃×C₅×#124	1	1	yes	characteristic
449	C₂	C₃×C₅×#529	1	2	yes	—
450	C₂	C₃×C₅×#532	1	1	yes	characteristic

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

Complements

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

N	H ≅ G/N	type
2. C₂×C₃×C₄×C₅×Q₈	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
6. C₃×C₅×#388	C₂	semidirect
7. C₃×C₅×#382	C₂	semidirect
8. C₃×C₄×C₅×C₂²⋊C₄	C₂	semidirect
9. C₃×C₄³×C₅	C₂	semidirect
10. C₄×C₅×#124	C₃	direct (N × H)
14. C₃×C₅×#124	C₄	direct (N × H)
31. C₃×C₄×#124	C₅	direct (N × H)
33. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
35. C₅×#391	C₂×C₃	semidirect
37. C₅×#388	C₂×C₃	semidirect
38. C₅×#382	C₂×C₃	semidirect
39. C₄×C₅×C₂²⋊C₄	C₂×C₃	semidirect
40. C₄³×C₅	C₂×C₃	semidirect
44. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
63. C₃×C₅×C₂²⋊C₄	C₂×C₄	semidirect
68. C₃×C₄²×C₅	C₂×C₄	semidirect
71. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
73. C₃×#391	C₂×C₅	semidirect
75. C₃×#388	C₂×C₅	semidirect
76. C₃×#382	C₂×C₅	semidirect
77. C₃×C₄×C₂²⋊C₄	C₂×C₅	semidirect
78. C₃×C₄³	C₂×C₅	semidirect
82. C₅×#124	C₃×C₄	direct (N × H)
99. C₄×#124	C₃×C₅	direct (N × H)
132. C₃×#124	C₄×C₅	direct (N × H)
152. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
171. C₅×C₂²⋊C₄	C₂×C₃×C₄	semidirect
176. C₄²×C₅	C₂×C₃×C₄	semidirect
179. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
181. #391	C₂×C₃×C₅	semidirect
183. #388	C₂×C₃×C₅	semidirect
184. #382	C₂×C₃×C₅	semidirect
185. C₄×C₂²⋊C₄	C₂×C₃×C₅	semidirect
186. C₄³	C₂×C₃×C₅	semidirect
204. C₃×C₄×C₅	#124	direct (N × H)
208. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
227. C₃×C₂²⋊C₄	C₂×C₄×C₅	semidirect
232. C₃×C₄²	C₂×C₄×C₅	semidirect
266. #124	C₃×C₄×C₅	direct (N × H)
335. C₄×C₅	C₃×#124	direct (N × H)
339. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
358. C₂²⋊C₄	C₂×C₃×C₄×C₅	semidirect
363. C₄²	C₂×C₃×C₄×C₅	semidirect
365. C₃×C₅	C₄×#124	direct (N × H)
383. C₃×C₄	C₅×#124	direct (N × H)
425. C₅	C₃×C₄×#124	direct (N × H)
443. C₄	C₃×C₅×#124	direct (N × H)
444. C₃	C₄×C₅×#124	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×#124	2
C₂×C₃×C₄×C₅×Q₈	2
C₂×C₃×C₄×C₅×D₄	2
C₃×C₅×#391	2
C₃×C₅×#390	2
C₃×C₅×#388	2
C₃×C₅×#382	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₃×C₄³×C₅	2
C₄×C₅×#124	3
C₃×C₄×#124	5

Subgroups — C3×C4×C5×#124 #14275337

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₄×C₅×#124 #14275337