Subgroups — C₃×C₅×#2360 #14275394

Order 1920.

1240 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×C₃×C₅×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic
2	C₂×C₃×C₄×C₅×Q₈	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×C₃×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
4	C₃×C₅×#391	C₂	1	1	yes	maximal, characteristic, complemented
5	C₃×C₅×#389	C₂	1	1	yes	maximal, characteristic, complemented
6	C₃×C₅×#389	C₂	1	2	yes	maximal, complemented
7	C₃×C₅×#387	C₂	1	2	yes	maximal, complemented
8	C₃×C₅×#385	C₂	1	2	yes	maximal
9	C₃×C₄×C₅×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic, complemented
10	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	2	yes	maximal
11	C₃×C₄×C₅×C₂²⋊C₄	C₂	1	1	yes	maximal, characteristic
12	C₅×#2360	C₃	1	1	yes	maximal, characteristic, direct product factor, Hall
13	C₂²×C₃×C₅×Q₈	C₂²	1	1	yes	characteristic
14	C₂³×C₃×C₄×C₅	C₂²	1	2	yes	—
15	C₂³×C₃×C₄×C₅	C₂²	1	1	yes	characteristic
16	C₃×C₅×C₂²⋊Q₈	C₄	1	8	yes	complemented
17	C₃×C₄×C₅×Q₈	—	2	4	no	—
18	C₂×C₃×C₅×C₄⋊C₄	—	2	4	no	—
19	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
21	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
22	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
23	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
24	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	2	yes	—
25	C₂×C₃×C₅×C₄⋊C₄	C₂²	1	1	yes	characteristic
26	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
27	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	2	yes	—
28	C₂×C₃×C₅×C₂²⋊C₄	C₂²	1	1	yes	characteristic
29	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
30	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
31	C₂×C₃×C₄²×C₅	C₂²	1	1	yes	characteristic
32	C₂×C₃×C₄²×C₅	C₂²	1	2	yes	—
33	C₃×C₅×#95	C₂²	1	1	yes	characteristic
34	C₃×C₅×#95	C₂²	1	2	yes	—
35	C₃×C₅×#95	C₂²	1	1	yes	characteristic
36	C₃×C₅×#95	C₂²	1	2	yes	—
37	C₃×C₅×#95	C₂²	1	2	yes	—
38	C₃×C₅×#95	C₂²	1	2	yes	—
39	C₃×#2360	C₅	1	1	yes	maximal, characteristic, direct product factor, Hall
40	C₂×C₅×C₂²⋊Q₈	C₂×C₃	1	1	yes	characteristic
41	C₂×C₄×C₅×Q₈	C₂×C₃	1	1	yes	characteristic, complemented
42	C₂²×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic
43	C₅×#391	C₂×C₃	1	1	yes	characteristic, complemented
44	C₅×#389	C₂×C₃	1	1	yes	characteristic, complemented
45	C₅×#389	C₂×C₃	1	2	yes	complemented
46	C₅×#387	C₂×C₃	1	2	yes	complemented
47	C₅×#385	C₂×C₃	1	2	yes	—
48	C₄×C₅×C₄⋊C₄	C₂×C₃	1	1	yes	characteristic, complemented
49	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	1	yes	characteristic
50	C₄×C₅×C₂²⋊C₄	C₂×C₃	1	2	yes	—
51	C₂⁴×C₃×C₅	C₂³	1	1	yes	characteristic
52	C₂×C₃×C₅×Q₈	—	2	2	no	—
53	C₂×C₃×C₅×Q₈	—	2	2	no	—
54	C₂×C₃×C₅×Q₈	C₂×C₄	1	4	yes	complemented
55	C₂²×C₃×C₄×C₅	—	2	2	no	—
56	C₂²×C₃×C₄×C₅	—	2	2	no	—
57	C₂²×C₃×C₄×C₅	—	2	4	no	—
58	C₂²×C₃×C₄×C₅	—	2	4	no	—
59	C₂²×C₃×C₄×C₅	—	4	2	no	—
60	C₂²×C₃×C₄×C₅	C₂×C₄	1	4	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	2	yes	—
64	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
65	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
66	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
67	C₂²×C₃×C₄×C₅	C₂³	1	2	yes	—
68	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
69	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
70	C₂²×C₃×C₄×C₅	C₂³	1	1	yes	characteristic
71	C₃×C₅×C₄⋊C₄	—	2	4	no	—
72	C₃×C₅×C₄⋊C₄	—	2	2	no	—
73	C₃×C₅×C₄⋊C₄	—	2	4	no	—
74	C₃×C₅×C₄⋊C₄	—	4	2	no	—
75	C₃×C₅×C₄⋊C₄	C₂×C₄	1	4	yes	complemented
76	C₃×C₅×C₄⋊C₄	C₂×C₄	1	8	yes	complemented
77	C₃×C₅×C₄⋊C₄	D₄	1	4	yes	—
78	C₃×C₅×C₂²⋊C₄	—	2	2	no	—
79	C₃×C₅×C₂²⋊C₄	C₂×C₄	1	8	yes	—
80	C₃×C₅×C₂²⋊C₄	Q₈	1	4	yes	complemented
81	C₃×C₄²×C₅	—	2	4	no	—
82	C₃×C₄²×C₅	—	2	2	no	—
83	C₃×C₄²×C₅	—	2	2	no	—
84	C₃×C₄²×C₅	—	4	2	no	—
85	C₂×C₃×C₂²⋊Q₈	C₂×C₅	1	1	yes	characteristic
86	C₂×C₃×C₄×Q₈	C₂×C₅	1	1	yes	characteristic, complemented
87	C₂²×C₃×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic
88	C₃×#391	C₂×C₅	1	1	yes	characteristic, complemented
89	C₃×#389	C₂×C₅	1	1	yes	characteristic, complemented
90	C₃×#389	C₂×C₅	1	2	yes	complemented
91	C₃×#387	C₂×C₅	1	2	yes	complemented
92	C₃×#385	C₂×C₅	1	2	yes	—
93	C₃×C₄×C₄⋊C₄	C₂×C₅	1	1	yes	characteristic, complemented
94	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	1	yes	characteristic
95	C₃×C₄×C₂²⋊C₄	C₂×C₅	1	2	yes	—
96	C₂²×C₅×Q₈	C₂²×C₃	1	1	yes	characteristic
97	C₂³×C₄×C₅	C₂²×C₃	1	2	yes	—
98	C₂³×C₄×C₅	C₂²×C₃	1	1	yes	characteristic
99	C₅×C₂²⋊Q₈	C₃×C₄	1	8	yes	complemented
100	C₄×C₅×Q₈	—	2	4	no	—
101	C₂×C₅×C₄⋊C₄	—	2	4	no	—
102	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
103	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
104	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
105	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
106	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
107	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	2	yes	—
108	C₂×C₅×C₄⋊C₄	C₂²×C₃	1	1	yes	characteristic
109	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
110	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	2	yes	—
111	C₂×C₅×C₂²⋊C₄	C₂²×C₃	1	1	yes	characteristic
112	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
113	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
114	C₂×C₄²×C₅	C₂²×C₃	1	1	yes	characteristic
115	C₂×C₄²×C₅	C₂²×C₃	1	2	yes	—
116	C₅×#95	C₂²×C₃	1	1	yes	characteristic
117	C₅×#95	C₂²×C₃	1	2	yes	—
118	C₅×#95	C₂²×C₃	1	1	yes	characteristic
119	C₅×#95	C₂²×C₃	1	2	yes	—
120	C₅×#95	C₂²×C₃	1	2	yes	—
121	C₅×#95	C₂²×C₃	1	2	yes	—
122	#2360	C₃×C₅	1	1	yes	characteristic, direct product factor, Sylow
123	C₂³×C₃×C₅	—	2	1	no	—
124	C₂³×C₃×C₅	—	2	1	no	—
125	C₂³×C₃×C₅	—	2	1	no	—
126	C₂³×C₃×C₅	—	2	1	no	—
127	C₂³×C₃×C₅	C₂²×C₄	1	2	yes	—
128	C₂³×C₃×C₅	C₂×Q₈	1	2	yes	—
129	C₂³×C₃×C₅	#41	1	2	yes	—
130	C₂³×C₃×C₅	C₂⁴	1	1	yes	characteristic
131	C₃×C₅×Q₈	—	2	8	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	1	no	—
136	C₂×C₃×C₄×C₅	—	2	1	no	—
137	C₂×C₃×C₄×C₅	—	2	2	no	—
138	C₂×C₃×C₄×C₅	—	2	2	no	—
139	C₂×C₃×C₄×C₅	—	2	1	no	—
140	C₂×C₃×C₄×C₅	—	2	2	no	—
141	C₂×C₃×C₄×C₅	—	2	2	no	—
142	C₂×C₃×C₄×C₅	—	2	2	no	—
143	C₂×C₃×C₄×C₅	—	2	1	no	—
144	C₂×C₃×C₄×C₅	—	2	8	no	—
145	C₂×C₃×C₄×C₅	—	2	1	no	—
146	C₂×C₃×C₄×C₅	—	2	2	no	—
147	C₂×C₃×C₄×C₅	—	2	1	no	—
148	C₂×C₃×C₄×C₅	—	2	1	no	—
149	C₂×C₃×C₄×C₅	—	2	1	no	—
150	C₂×C₃×C₄×C₅	—	2	2	no	—
151	C₂×C₃×C₄×C₅	—	2	1	no	—
152	C₂×C₃×C₄×C₅	—	2	2	no	—
153	C₂×C₃×C₄×C₅	—	2	1	no	—
154	C₂×C₃×C₄×C₅	—	4	8	no	—
155	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
156	C₂×C₃×C₄×C₅	C₂²×C₄	1	4	yes	—
157	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
158	C₂×C₃×C₄×C₅	C₂²×C₄	1	2	yes	—
159	C₂×C₃×C₄×C₅	C₂×D₄	1	4	yes	—
160	C₂×C₃×C₄×C₅	C₂×D₄	1	2	yes	—
161	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
162	C₂×C₃×C₄×C₅	C₂×Q₈	1	2	yes	—
163	C₂×C₃×C₄×C₅	#41	1	2	yes	—
164	C₂²×C₃×Q₈	C₂²×C₅	1	1	yes	characteristic
165	C₂³×C₃×C₄	C₂²×C₅	1	2	yes	—
166	C₂³×C₃×C₄	C₂²×C₅	1	1	yes	characteristic
167	C₃×C₂²⋊Q₈	C₄×C₅	1	8	yes	complemented
168	C₃×C₄×Q₈	—	2	4	no	—
169	C₂×C₃×C₄⋊C₄	—	2	4	no	—
170	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
171	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
172	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
173	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
174	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
175	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	2	yes	—
176	C₂×C₃×C₄⋊C₄	C₂²×C₅	1	1	yes	characteristic
177	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
178	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	2	yes	—
179	C₂×C₃×C₂²⋊C₄	C₂²×C₅	1	1	yes	characteristic
180	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
181	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
182	C₂×C₃×C₄²	C₂²×C₅	1	1	yes	characteristic
183	C₂×C₃×C₄²	C₂²×C₅	1	2	yes	—
184	C₃×#95	C₂²×C₅	1	1	yes	characteristic
185	C₃×#95	C₂²×C₅	1	2	yes	—
186	C₃×#95	C₂²×C₅	1	1	yes	characteristic
187	C₃×#95	C₂²×C₅	1	2	yes	—
188	C₃×#95	C₂²×C₅	1	2	yes	—
189	C₃×#95	C₂²×C₅	1	2	yes	—
190	C₂⁴×C₅	C₂³×C₃	1	1	yes	characteristic
191	C₂×C₅×Q₈	—	2	2	no	—
192	C₂×C₅×Q₈	—	2	2	no	—
193	C₂×C₅×Q₈	C₂×C₃×C₄	1	4	yes	complemented
194	C₂²×C₄×C₅	—	2	2	no	—
195	C₂²×C₄×C₅	—	2	2	no	—
196	C₂²×C₄×C₅	—	2	4	no	—
197	C₂²×C₄×C₅	—	2	4	no	—
198	C₂²×C₄×C₅	—	4	2	no	—
199	C₂²×C₄×C₅	C₂×C₃×C₄	1	4	yes	—
200	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
201	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
202	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
203	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
204	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
205	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
206	C₂²×C₄×C₅	C₂³×C₃	1	2	yes	—
207	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
208	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
209	C₂²×C₄×C₅	C₂³×C₃	1	1	yes	characteristic
210	C₅×C₄⋊C₄	—	2	4	no	—
211	C₅×C₄⋊C₄	—	2	2	no	—
212	C₅×C₄⋊C₄	—	2	4	no	—
213	C₅×C₄⋊C₄	—	4	2	no	—
214	C₅×C₄⋊C₄	C₂×C₃×C₄	1	4	yes	complemented
215	C₅×C₄⋊C₄	C₂×C₃×C₄	1	8	yes	complemented
216	C₅×C₄⋊C₄	C₃×D₄	1	4	yes	—
217	C₅×C₂²⋊C₄	—	2	2	no	—
218	C₅×C₂²⋊C₄	C₂×C₃×C₄	1	8	yes	—
219	C₅×C₂²⋊C₄	C₃×Q₈	1	4	yes	complemented
220	C₄²×C₅	—	2	4	no	—
221	C₄²×C₅	—	2	2	no	—
222	C₄²×C₅	—	2	2	no	—
223	C₄²×C₅	—	4	2	no	—
224	C₂×C₂²⋊Q₈	C₂×C₃×C₅	1	1	yes	characteristic
225	C₂×C₄×Q₈	C₂×C₃×C₅	1	1	yes	characteristic, complemented
226	C₂²×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
227	#391	C₂×C₃×C₅	1	1	yes	characteristic, complemented
228	#389	C₂×C₃×C₅	1	1	yes	characteristic, complemented
229	#389	C₂×C₃×C₅	1	2	yes	complemented
230	#387	C₂×C₃×C₅	1	2	yes	complemented
231	#385	C₂×C₃×C₅	1	2	yes	—
232	C₄×C₄⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic, complemented
233	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	1	yes	characteristic
234	C₄×C₂²⋊C₄	C₂×C₃×C₅	1	2	yes	—
235	C₂²×C₃×C₅	—	2	2	no	—
236	C₂²×C₃×C₅	—	2	2	no	—
237	C₂²×C₃×C₅	—	2	2	no	—
238	C₂²×C₃×C₅	—	2	2	no	—
239	C₂²×C₃×C₅	—	2	2	no	—
240	C₂²×C₃×C₅	—	2	2	no	—
241	C₂²×C₃×C₅	C₄×Q₈	1	4	yes	complemented
242	C₂²×C₃×C₅	C₂³×C₄	1	1	yes	characteristic
243	C₂²×C₃×C₅	C₂²×D₄	1	1	yes	characteristic
244	C₂²×C₃×C₅	C₂²×Q₈	1	1	yes	characteristic
245	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
246	C₂²×C₃×C₅	C₂×#41	1	1	yes	characteristic
247	C₂²×C₃×C₅	H(5,𝔽₂)	1	1	yes	characteristic
248	C₂²×C₃×C₅	2₋¹⁺⁴	1	1	yes	characteristic
249	C₃×C₄×C₅	—	2	2	no	—
250	C₃×C₄×C₅	—	2	4	no	—
251	C₃×C₄×C₅	—	2	4	no	—
252	C₃×C₄×C₅	—	2	4	no	—
253	C₃×C₄×C₅	—	2	2	no	—
254	C₃×C₄×C₅	—	2	2	no	—
255	C₃×C₄×C₅	—	4	1	no	—
256	C₃×C₄×C₅	—	4	2	no	—
257	C₃×C₄×C₅	—	4	1	no	—
258	C₃×C₄×C₅	C₄×D₄	1	4	yes	—
259	C₂⁴×C₃	C₂³×C₅	1	1	yes	characteristic
260	C₂×C₃×Q₈	—	2	2	no	—
261	C₂×C₃×Q₈	—	2	2	no	—
262	C₂×C₃×Q₈	C₂×C₄×C₅	1	4	yes	complemented
263	C₂²×C₃×C₄	—	2	2	no	—
264	C₂²×C₃×C₄	—	2	2	no	—
265	C₂²×C₃×C₄	—	2	4	no	—
266	C₂²×C₃×C₄	—	2	4	no	—
267	C₂²×C₃×C₄	—	4	2	no	—
268	C₂²×C₃×C₄	C₂×C₄×C₅	1	4	yes	—
269	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
270	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
271	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
272	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
273	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
274	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
275	C₂²×C₃×C₄	C₂³×C₅	1	2	yes	—
276	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
277	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
278	C₂²×C₃×C₄	C₂³×C₅	1	1	yes	characteristic
279	C₃×C₄⋊C₄	—	2	4	no	—
280	C₃×C₄⋊C₄	—	2	2	no	—
281	C₃×C₄⋊C₄	—	2	4	no	—
282	C₃×C₄⋊C₄	—	4	2	no	—
283	C₃×C₄⋊C₄	C₂×C₄×C₅	1	4	yes	complemented
284	C₃×C₄⋊C₄	C₂×C₄×C₅	1	8	yes	complemented
285	C₃×C₄⋊C₄	C₅×D₄	1	4	yes	—
286	C₃×C₂²⋊C₄	—	2	2	no	—
287	C₃×C₂²⋊C₄	C₂×C₄×C₅	1	8	yes	—
288	C₃×C₂²⋊C₄	C₅×Q₈	1	4	yes	complemented
289	C₃×C₄²	—	2	4	no	—
290	C₃×C₄²	—	2	2	no	—
291	C₃×C₄²	—	2	2	no	—
292	C₃×C₄²	—	4	2	no	—
293	C₂³×C₅	—	2	1	no	—
294	C₂³×C₅	—	2	1	no	—
295	C₂³×C₅	—	2	1	no	—
296	C₂³×C₅	—	2	1	no	—
297	C₂³×C₅	C₂²×C₃×C₄	1	2	yes	—
298	C₂³×C₅	C₂×C₃×Q₈	1	2	yes	—
299	C₂³×C₅	C₃×#41	1	2	yes	—
300	C₂³×C₅	C₂⁴×C₃	1	1	yes	characteristic
301	C₅×Q₈	—	2	8	no	—
302	C₂×C₄×C₅	—	2	1	no	—
303	C₂×C₄×C₅	—	2	2	no	—
304	C₂×C₄×C₅	—	2	1	no	—
305	C₂×C₄×C₅	—	2	1	no	—
306	C₂×C₄×C₅	—	2	1	no	—
307	C₂×C₄×C₅	—	2	2	no	—
308	C₂×C₄×C₅	—	2	2	no	—
309	C₂×C₄×C₅	—	2	1	no	—
310	C₂×C₄×C₅	—	2	2	no	—
311	C₂×C₄×C₅	—	2	2	no	—
312	C₂×C₄×C₅	—	2	2	no	—
313	C₂×C₄×C₅	—	2	1	no	—
314	C₂×C₄×C₅	—	2	8	no	—
315	C₂×C₄×C₅	—	2	1	no	—
316	C₂×C₄×C₅	—	2	2	no	—
317	C₂×C₄×C₅	—	2	1	no	—
318	C₂×C₄×C₅	—	2	1	no	—
319	C₂×C₄×C₅	—	2	1	no	—
320	C₂×C₄×C₅	—	2	2	no	—
321	C₂×C₄×C₅	—	2	1	no	—
322	C₂×C₄×C₅	—	2	2	no	—
323	C₂×C₄×C₅	—	2	1	no	—
324	C₂×C₄×C₅	—	4	8	no	—
325	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
326	C₂×C₄×C₅	C₂²×C₃×C₄	1	4	yes	—
327	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
328	C₂×C₄×C₅	C₂²×C₃×C₄	1	2	yes	—
329	C₂×C₄×C₅	C₂×C₃×D₄	1	4	yes	—
330	C₂×C₄×C₅	C₂×C₃×D₄	1	2	yes	—
331	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
332	C₂×C₄×C₅	C₂×C₃×Q₈	1	2	yes	—
333	C₂×C₄×C₅	C₃×#41	1	2	yes	—
334	C₂²×Q₈	C₂²×C₃×C₅	1	1	yes	characteristic
335	C₂³×C₄	C₂²×C₃×C₅	1	2	yes	—
336	C₂³×C₄	C₂²×C₃×C₅	1	1	yes	characteristic
337	C₂²⋊Q₈	C₃×C₄×C₅	1	8	yes	complemented
338	C₄×Q₈	—	2	4	no	—
339	C₂×C₄⋊C₄	—	2	4	no	—
340	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
341	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
342	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
343	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
344	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
345	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	2	yes	—
346	C₂×C₄⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
347	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
348	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	2	yes	—
349	C₂×C₂²⋊C₄	C₂²×C₃×C₅	1	1	yes	characteristic
350	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
351	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
352	C₂×C₄²	C₂²×C₃×C₅	1	1	yes	characteristic
353	C₂×C₄²	C₂²×C₃×C₅	1	2	yes	—
354	#95	C₂²×C₃×C₅	1	1	yes	characteristic
355	#95	C₂²×C₃×C₅	1	2	yes	—
356	#95	C₂²×C₃×C₅	1	1	yes	characteristic
357	#95	C₂²×C₃×C₅	1	2	yes	—
358	#95	C₂²×C₃×C₅	1	2	yes	—
359	#95	C₂²×C₃×C₅	1	2	yes	—
360	C₂×C₃×C₅	—	2	4	no	—
361	C₂×C₃×C₅	C₂×C₄×D₄	1	1	yes	characteristic
362	C₂×C₃×C₅	C₂×C₄×Q₈	1	1	yes	characteristic
363	C₂×C₃×C₅	#520	1	1	yes	characteristic
364	C₂×C₃×C₅	#546	1	1	yes	characteristic
365	C₂×C₃×C₅	D₄×Q₈	1	1	yes	characteristic
366	C₂×C₃×C₅	#552	1	1	yes	characteristic
367	C₂×C₃×C₅	#554	1	1	yes	characteristic
368	C₂³×C₃	—	2	1	no	—
369	C₂³×C₃	—	2	1	no	—
370	C₂³×C₃	—	2	1	no	—
371	C₂³×C₃	—	2	1	no	—
372	C₂³×C₃	C₂²×C₄×C₅	1	2	yes	—
373	C₂³×C₃	C₂×C₅×Q₈	1	2	yes	—
374	C₂³×C₃	C₅×#41	1	2	yes	—
375	C₂³×C₃	C₂⁴×C₅	1	1	yes	characteristic
376	C₃×Q₈	—	2	8	no	—
377	C₂×C₃×C₄	—	2	1	no	—
378	C₂×C₃×C₄	—	2	2	no	—
379	C₂×C₃×C₄	—	2	1	no	—
380	C₂×C₃×C₄	—	2	1	no	—
381	C₂×C₃×C₄	—	2	1	no	—
382	C₂×C₃×C₄	—	2	2	no	—
383	C₂×C₃×C₄	—	2	2	no	—
384	C₂×C₃×C₄	—	2	1	no	—
385	C₂×C₃×C₄	—	2	2	no	—
386	C₂×C₃×C₄	—	2	2	no	—
387	C₂×C₃×C₄	—	2	2	no	—
388	C₂×C₃×C₄	—	2	1	no	—
389	C₂×C₃×C₄	—	2	8	no	—
390	C₂×C₃×C₄	—	2	1	no	—
391	C₂×C₃×C₄	—	2	2	no	—
392	C₂×C₃×C₄	—	2	1	no	—
393	C₂×C₃×C₄	—	2	1	no	—
394	C₂×C₃×C₄	—	2	1	no	—
395	C₂×C₃×C₄	—	2	2	no	—
396	C₂×C₃×C₄	—	2	1	no	—
397	C₂×C₃×C₄	—	2	2	no	—
398	C₂×C₃×C₄	—	2	1	no	—
399	C₂×C₃×C₄	—	4	8	no	—
400	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
401	C₂×C₃×C₄	C₂²×C₄×C₅	1	4	yes	—
402	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
403	C₂×C₃×C₄	C₂²×C₄×C₅	1	2	yes	—
404	C₂×C₃×C₄	C₂×C₅×D₄	1	4	yes	—
405	C₂×C₃×C₄	C₂×C₅×D₄	1	2	yes	—
406	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
407	C₂×C₃×C₄	C₂×C₅×Q₈	1	2	yes	—
408	C₂×C₃×C₄	C₅×#41	1	2	yes	—
409	C₂²×C₅	—	2	2	no	—
410	C₂²×C₅	—	2	2	no	—
411	C₂²×C₅	—	2	2	no	—
412	C₂²×C₅	—	2	2	no	—
413	C₂²×C₅	—	2	2	no	—
414	C₂²×C₅	—	2	2	no	—
415	C₂²×C₅	C₃×C₄×Q₈	1	4	yes	complemented
416	C₂²×C₅	C₂³×C₃×C₄	1	1	yes	characteristic
417	C₂²×C₅	C₂²×C₃×D₄	1	1	yes	characteristic
418	C₂²×C₅	C₂²×C₃×Q₈	1	1	yes	characteristic
419	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
420	C₂²×C₅	C₂×C₃×#41	1	1	yes	characteristic
421	C₂²×C₅	C₃×H(5,𝔽₂)	1	1	yes	characteristic
422	C₂²×C₅	C₃×2₋¹⁺⁴	1	1	yes	characteristic
423	C₄×C₅	—	2	2	no	—
424	C₄×C₅	—	2	4	no	—
425	C₄×C₅	—	2	4	no	—
426	C₄×C₅	—	2	4	no	—
427	C₄×C₅	—	2	2	no	—
428	C₄×C₅	—	2	2	no	—
429	C₄×C₅	—	4	1	no	—
430	C₄×C₅	—	4	2	no	—
431	C₄×C₅	—	4	1	no	—
432	C₄×C₅	C₃×C₄×D₄	1	4	yes	—
433	C₂⁴	C₂³×C₃×C₅	1	1	yes	characteristic
434	C₂×Q₈	—	2	2	no	—
435	C₂×Q₈	—	2	2	no	—
436	C₂×Q₈	C₂×C₃×C₄×C₅	1	4	yes	complemented
437	C₂²×C₄	—	2	2	no	—
438	C₂²×C₄	—	2	2	no	—
439	C₂²×C₄	—	2	4	no	—
440	C₂²×C₄	—	2	4	no	—
441	C₂²×C₄	—	4	2	no	—
442	C₂²×C₄	C₂×C₃×C₄×C₅	1	4	yes	—
443	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
444	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
445	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
446	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
447	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
448	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
449	C₂²×C₄	C₂³×C₃×C₅	1	2	yes	—
450	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
451	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
452	C₂²×C₄	C₂³×C₃×C₅	1	1	yes	characteristic
453	C₄⋊C₄	—	2	4	no	—
454	C₄⋊C₄	—	2	2	no	—
455	C₄⋊C₄	—	2	4	no	—
456	C₄⋊C₄	—	4	2	no	—
457	C₄⋊C₄	C₂×C₃×C₄×C₅	1	4	yes	complemented
458	C₄⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	complemented
459	C₄⋊C₄	C₃×C₅×D₄	1	4	yes	—
460	C₂²⋊C₄	—	2	2	no	—
461	C₂²⋊C₄	C₂×C₃×C₄×C₅	1	8	yes	—
462	C₂²⋊C₄	C₃×C₅×Q₈	1	4	yes	complemented
463	C₄²	—	2	4	no	—
464	C₄²	—	2	2	no	—
465	C₄²	—	2	2	no	—
466	C₄²	—	4	2	no	—
467	C₃×C₅	#2360	1	1	yes	characteristic, direct product factor, Hall
468	C₂²×C₃	—	2	2	no	—
469	C₂²×C₃	—	2	2	no	—
470	C₂²×C₃	—	2	2	no	—
471	C₂²×C₃	—	2	2	no	—
472	C₂²×C₃	—	2	2	no	—
473	C₂²×C₃	—	2	2	no	—
474	C₂²×C₃	C₄×C₅×Q₈	1	4	yes	complemented
475	C₂²×C₃	C₂³×C₄×C₅	1	1	yes	characteristic
476	C₂²×C₃	C₂²×C₅×D₄	1	1	yes	characteristic
477	C₂²×C₃	C₂²×C₅×Q₈	1	1	yes	characteristic
478	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
479	C₂²×C₃	C₂×C₅×#41	1	1	yes	characteristic
480	C₂²×C₃	C₅×H(5,𝔽₂)	1	1	yes	characteristic
481	C₂²×C₃	C₅×2₋¹⁺⁴	1	1	yes	characteristic
482	C₃×C₄	—	2	2	no	—
483	C₃×C₄	—	2	4	no	—
484	C₃×C₄	—	2	4	no	—
485	C₃×C₄	—	2	4	no	—
486	C₃×C₄	—	2	2	no	—
487	C₃×C₄	—	2	2	no	—
488	C₃×C₄	—	4	1	no	—
489	C₃×C₄	—	4	2	no	—
490	C₃×C₄	—	4	1	no	—
491	C₃×C₄	C₄×C₅×D₄	1	4	yes	—
492	C₂×C₅	—	2	4	no	—
493	C₂×C₅	C₂×C₃×C₄×D₄	1	1	yes	characteristic
494	C₂×C₅	C₂×C₃×C₄×Q₈	1	1	yes	characteristic
495	C₂×C₅	C₃×#520	1	1	yes	characteristic
496	C₂×C₅	C₃×#546	1	1	yes	characteristic
497	C₂×C₅	C₃×D₄×Q₈	1	1	yes	characteristic
498	C₂×C₅	C₃×#552	1	1	yes	characteristic
499	C₂×C₅	C₃×#554	1	1	yes	characteristic
500	C₂³	—	2	1	no	—
501	C₂³	—	2	1	no	—
502	C₂³	—	2	1	no	—
503	C₂³	—	2	1	no	—
504	C₂³	C₂²×C₃×C₄×C₅	1	2	yes	—
505	C₂³	C₂×C₃×C₅×Q₈	1	2	yes	—
506	C₂³	C₃×C₅×#41	1	2	yes	—
507	C₂³	C₂⁴×C₃×C₅	1	1	yes	characteristic
508	Q₈	—	2	8	no	—
509	C₂×C₄	—	2	1	no	—
510	C₂×C₄	—	2	2	no	—
511	C₂×C₄	—	2	1	no	—
512	C₂×C₄	—	2	1	no	—
513	C₂×C₄	—	2	1	no	—
514	C₂×C₄	—	2	2	no	—
515	C₂×C₄	—	2	2	no	—
516	C₂×C₄	—	2	1	no	—
517	C₂×C₄	—	2	2	no	—
518	C₂×C₄	—	2	2	no	—
519	C₂×C₄	—	2	2	no	—
520	C₂×C₄	—	2	1	no	—
521	C₂×C₄	—	2	8	no	—
522	C₂×C₄	—	2	1	no	—
523	C₂×C₄	—	2	2	no	—
524	C₂×C₄	—	2	1	no	—
525	C₂×C₄	—	2	1	no	—
526	C₂×C₄	—	2	1	no	—
527	C₂×C₄	—	2	2	no	—
528	C₂×C₄	—	2	1	no	—
529	C₂×C₄	—	2	2	no	—
530	C₂×C₄	—	2	1	no	—
531	C₂×C₄	—	4	8	no	—
532	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
533	C₂×C₄	C₂²×C₃×C₄×C₅	1	4	yes	—
534	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
535	C₂×C₄	C₂²×C₃×C₄×C₅	1	2	yes	—
536	C₂×C₄	C₂×C₃×C₅×D₄	1	4	yes	—
537	C₂×C₄	C₂×C₃×C₅×D₄	1	2	yes	—
538	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
539	C₂×C₄	C₂×C₃×C₅×Q₈	1	2	yes	—
540	C₂×C₄	C₃×C₅×#41	1	2	yes	—
541	C₂×C₃	—	2	4	no	—
542	C₂×C₃	C₂×C₄×C₅×D₄	1	1	yes	characteristic
543	C₂×C₃	C₂×C₄×C₅×Q₈	1	1	yes	characteristic
544	C₂×C₃	C₅×#520	1	1	yes	characteristic
545	C₂×C₃	C₅×#546	1	1	yes	characteristic
546	C₂×C₃	C₅×D₄×Q₈	1	1	yes	characteristic
547	C₂×C₃	C₅×#552	1	1	yes	characteristic
548	C₂×C₃	C₅×#554	1	1	yes	characteristic
549	C₅	C₃×#2360	1	1	yes	characteristic, direct product factor, Sylow
550	C₂²	—	2	2	no	—
551	C₂²	—	2	2	no	—
552	C₂²	—	2	2	no	—
553	C₂²	—	2	2	no	—
554	C₂²	—	2	2	no	—
555	C₂²	—	2	2	no	—
556	C₂²	C₃×C₄×C₅×Q₈	1	4	yes	complemented
557	C₂²	C₂³×C₃×C₄×C₅	1	1	yes	characteristic
558	C₂²	C₂²×C₃×C₅×D₄	1	1	yes	characteristic
559	C₂²	C₂²×C₃×C₅×Q₈	1	1	yes	characteristic
560	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
561	C₂²	C₂×C₃×C₅×#41	1	1	yes	characteristic
562	C₂²	C₃×C₅×H(5,𝔽₂)	1	1	yes	characteristic
563	C₂²	C₃×C₅×2₋¹⁺⁴	1	1	yes	characteristic
564	C₄	—	2	2	no	—
565	C₄	—	2	4	no	—
566	C₄	—	2	4	no	—
567	C₄	—	2	4	no	—
568	C₄	—	2	2	no	—
569	C₄	—	2	2	no	—
570	C₄	—	4	2	no	—
571	C₄	—	4	1	no	—
572	C₄	—	4	1	no	—
573	C₄	C₃×C₄×C₅×D₄	1	4	yes	—
574	C₃	C₅×#2360	1	1	yes	characteristic, direct product factor, Sylow
575	C₂	—	2	4	no	—
576	C₂	C₂×C₃×C₄×C₅×D₄	1	1	yes	characteristic
577	C₂	C₂×C₃×C₄×C₅×Q₈	1	1	yes	characteristic
578	C₂	C₃×C₅×#520	1	1	yes	characteristic
579	C₂	C₃×C₅×#546	1	1	yes	characteristic
580	C₂	C₃×C₅×D₄×Q₈	1	1	yes	characteristic
581	C₂	C₃×C₅×#552	1	1	yes	characteristic
582	C₂	C₃×C₅×#554	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₃×C₅	C₂⁴
commutator	C₂²	C₂³×C₃×C₄×C₅
Frattini, cosocle	C₂³	C₂⁴×C₃×C₅
prime radical	C₂⁴×C₃×C₅	C₂³
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×Q₈	C₂	semidirect
4. C₃×C₅×#391	C₂	semidirect
5. C₃×C₅×#389	C₂	semidirect
6. C₃×C₅×#389	C₂	semidirect
7. C₃×C₅×#387	C₂	semidirect
9. C₃×C₄×C₅×C₄⋊C₄	C₂	semidirect
12. C₅×#2360	C₃	direct (N × H)
16. C₃×C₅×C₂²⋊Q₈	C₄	semidirect
39. C₃×#2360	C₅	direct (N × H)
41. C₂×C₄×C₅×Q₈	C₂×C₃	semidirect
43. C₅×#391	C₂×C₃	semidirect
44. C₅×#389	C₂×C₃	semidirect
45. C₅×#389	C₂×C₃	semidirect
46. C₅×#387	C₂×C₃	semidirect
48. C₄×C₅×C₄⋊C₄	C₂×C₃	semidirect
54. C₂×C₃×C₅×Q₈	C₂×C₄	semidirect
75. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
76. C₃×C₅×C₄⋊C₄	C₂×C₄	semidirect
80. C₃×C₅×C₂²⋊C₄	Q₈	semidirect
86. C₂×C₃×C₄×Q₈	C₂×C₅	semidirect
88. C₃×#391	C₂×C₅	semidirect
89. C₃×#389	C₂×C₅	semidirect
90. C₃×#389	C₂×C₅	semidirect
91. C₃×#387	C₂×C₅	semidirect
93. C₃×C₄×C₄⋊C₄	C₂×C₅	semidirect
99. C₅×C₂²⋊Q₈	C₃×C₄	semidirect
122. #2360	C₃×C₅	direct (N × H)
167. C₃×C₂²⋊Q₈	C₄×C₅	semidirect
193. C₂×C₅×Q₈	C₂×C₃×C₄	semidirect
214. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
215. C₅×C₄⋊C₄	C₂×C₃×C₄	semidirect
219. C₅×C₂²⋊C₄	C₃×Q₈	semidirect
225. C₂×C₄×Q₈	C₂×C₃×C₅	semidirect
227. #391	C₂×C₃×C₅	semidirect
228. #389	C₂×C₃×C₅	semidirect
229. #389	C₂×C₃×C₅	semidirect
230. #387	C₂×C₃×C₅	semidirect
232. C₄×C₄⋊C₄	C₂×C₃×C₅	semidirect
241. C₂²×C₃×C₅	C₄×Q₈	semidirect
262. C₂×C₃×Q₈	C₂×C₄×C₅	semidirect
283. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
284. C₃×C₄⋊C₄	C₂×C₄×C₅	semidirect
288. C₃×C₂²⋊C₄	C₅×Q₈	semidirect
337. C₂²⋊Q₈	C₃×C₄×C₅	semidirect
415. C₂²×C₅	C₃×C₄×Q₈	semidirect
436. C₂×Q₈	C₂×C₃×C₄×C₅	semidirect
457. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
458. C₄⋊C₄	C₂×C₃×C₄×C₅	semidirect
462. C₂²⋊C₄	C₃×C₅×Q₈	semidirect
467. C₃×C₅	#2360	direct (N × H)
474. C₂²×C₃	C₄×C₅×Q₈	semidirect
549. C₅	C₃×#2360	direct (N × H)
556. C₂²	C₃×C₄×C₅×Q₈	semidirect
574. C₃	C₅×#2360	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×C₂²⋊Q₈	2
C₂×C₃×C₄×C₅×Q₈	2
C₂²×C₃×C₅×C₄⋊C₄	2
C₃×C₅×#391	2
C₃×C₅×#389	2
C₃×C₅×#387	2
C₃×C₅×#385	2
C₃×C₄×C₅×C₄⋊C₄	2
C₃×C₄×C₅×C₂²⋊C₄	2
C₅×#2360	3
C₃×#2360	5

Subgroups — C3×C5×#2360 #14275394

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₃×C₅×#2360 #14275394